diff options
| -rw-r--r-- | core/crypto/_fiat/field_p256r1/field.odin | 346 | ||||
| -rw-r--r-- | core/crypto/_fiat/field_p256r1/field64.odin | 501 | ||||
| -rw-r--r-- | core/crypto/_fiat/field_scalarp256r1/field.odin | 210 | ||||
| -rw-r--r-- | core/crypto/_fiat/field_scalarp256r1/field64.odin | 569 | ||||
| -rw-r--r-- | core/crypto/_weierstrass/fe.odin | 135 | ||||
| -rw-r--r-- | core/crypto/_weierstrass/point.odin | 548 | ||||
| -rw-r--r-- | core/crypto/_weierstrass/point_s11n_sec.odin | 95 | ||||
| -rw-r--r-- | core/crypto/_weierstrass/sc.odin | 76 | ||||
| -rw-r--r-- | core/crypto/_weierstrass/scalar_mul.odin | 204 | ||||
| -rw-r--r-- | core/crypto/_weierstrass/secp256r1_table.odin | 3985 | ||||
| -rw-r--r-- | core/crypto/_weierstrass/tools/ecc_gen_tables.odin | 99 | ||||
| -rw-r--r-- | core/crypto/crypto.odin | 3 | ||||
| -rw-r--r-- | tests/core/crypto/test_core_crypto_weierstrass.odin | 486 |
13 files changed, 7257 insertions, 0 deletions
diff --git a/core/crypto/_fiat/field_p256r1/field.odin b/core/crypto/_fiat/field_p256r1/field.odin new file mode 100644 index 000000000..b1662fd48 --- /dev/null +++ b/core/crypto/_fiat/field_p256r1/field.odin @@ -0,0 +1,346 @@ +package field_p256r1 + +import subtle "core:crypto/_subtle" +import "core:encoding/endian" +import "core:math/bits" +import "core:mem" + +fe_clear :: proc "contextless" (arg1: ^Montgomery_Domain_Field_Element) { + mem.zero_explicit(arg1, size_of(Montgomery_Domain_Field_Element)) +} + +fe_clear_vec :: proc "contextless" ( + arg1: []^Montgomery_Domain_Field_Element, +) { + for fe in arg1 { + fe_clear(fe) + } +} + +fe_from_bytes :: proc "contextless" ( + out1: ^Montgomery_Domain_Field_Element, + arg1: []byte, + unsafe_assume_canonical := false, +) -> bool { + ensure_contextless(len(arg1) == 32, "p256r1: invalid fe input buffer") + + // Note: We assume the input is in big-endian. + tmp := Non_Montgomery_Domain_Field_Element { + endian.unchecked_get_u64be(arg1[24:]), + endian.unchecked_get_u64be(arg1[16:]), + endian.unchecked_get_u64be(arg1[8:]), + endian.unchecked_get_u64be(arg1[0:]), + } + defer mem.zero_explicit(&tmp, size_of(tmp)) + + // Check that tmp is in the the range [0, ELL). + if !unsafe_assume_canonical { + _, borrow := bits.sub_u64(ELL[0] - 1, tmp[0], 0) + _, borrow = bits.sub_u64(ELL[1], tmp[1], borrow) + _, borrow = bits.sub_u64(ELL[2], tmp[2], borrow) + _, borrow = bits.sub_u64(ELL[3], tmp[3], borrow) + if borrow != 0 { + return false + } + } + + fe_to_montgomery(out1, &tmp) + + return true +} + +fe_to_bytes :: proc "contextless" (out1: []byte, arg1: ^Montgomery_Domain_Field_Element) { + ensure_contextless(len(out1) == 32, "p256r1: invalid fe output buffer") + + tmp: Non_Montgomery_Domain_Field_Element + fe_from_montgomery(&tmp, arg1) + + // Note: Likewise, output in big-endian. + endian.unchecked_put_u64be(out1[24:], tmp[0]) + endian.unchecked_put_u64be(out1[16:], tmp[1]) + endian.unchecked_put_u64be(out1[8:], tmp[2]) + endian.unchecked_put_u64be(out1[0:], tmp[3]) + + mem.zero_explicit(&tmp, size_of(tmp)) +} + +@(require_results) +fe_equal :: proc "contextless" (arg1, arg2: ^Montgomery_Domain_Field_Element) -> int { + tmp: Montgomery_Domain_Field_Element + fe_sub(&tmp, arg1, arg2) + + // This will only underflow iff arg1 == arg2, and we return the borrow, + // which will be 1. + is_eq := subtle.u64_is_zero(fe_non_zero(&tmp)) + + fe_clear(&tmp) + + return int(is_eq) +} + +@(require_results) +fe_is_odd :: proc "contextless" (arg1: ^Montgomery_Domain_Field_Element) -> int { + tmp: Non_Montgomery_Domain_Field_Element + defer mem.zero_explicit(&tmp, size_of(tmp)) + + fe_from_montgomery(&tmp, arg1) + return int(tmp[0] & 1) +} + +fe_pow2k :: proc "contextless" ( + out1: ^Montgomery_Domain_Field_Element, + arg1: ^Montgomery_Domain_Field_Element, + arg2: uint, +) { + // Special case: `arg1^(2 * 0) = 1`, though this should never happen. + if arg2 == 0 { + fe_one(out1) + return + } + + fe_square(out1, arg1) + for _ in 1 ..< arg2 { + fe_square(out1, out1) + } +} + +fe_inv :: proc "contextless" (out1, arg1: ^Montgomery_Domain_Field_Element) { + // Inversion computation is derived from the addition chain: + // + // _10 = 2*1 + // _11 = 1 + _10 + // _110 = 2*_11 + // _111 = 1 + _110 + // _111000 = _111 << 3 + // _111111 = _111 + _111000 + // x12 = _111111 << 6 + _111111 + // x15 = x12 << 3 + _111 + // x16 = 2*x15 + 1 + // x32 = x16 << 16 + x16 + // i53 = x32 << 15 + // x47 = x15 + i53 + // i263 = ((i53 << 17 + 1) << 143 + x47) << 47 + // return (x47 + i263) << 2 + // + // Operations: 255 squares 11 multiplies + // + // Generated by github.com/mmcloughlin/addchain v0.4.0. + + // Note: Need to stash `arg1` (`xx`) in the case that `out1`/`arg1` alias, + // as `arg1` is used after `out1` has been altered. + t0, t1, xx: Montgomery_Domain_Field_Element = ---, ---, arg1^ + + // Step 1: z = x^0x2 + fe_square(out1, arg1) + + // Step 2: z = x^0x3 + fe_mul(out1, &xx, out1) + + // Step 3: z = x^0x6 + fe_square(out1, out1) + + // Step 4: z = x^0x7 + fe_mul(out1, &xx, out1) + + // Step 7: t0 = x^0x38 + fe_pow2k(&t0, out1, 3) + + // Step 8: t0 = x^0x3f + fe_mul(&t0, out1, &t0) + + // Step 14: t1 = x^0xfc0 + fe_pow2k(&t1, &t0, 6) + + // Step 15: t0 = x^0xfff + fe_mul(&t0, &t0, &t1) + + // Step 18: t0 = x^0x7ff8 + fe_pow2k(&t0, &t0, 3) + + // Step 19: z = x^0x7fff + fe_mul(out1, out1, &t0) + + // Step 20: t0 = x^0xfffe + fe_square(&t0, out1) + + // Step 21: t0 = x^0xffff + fe_mul(&t0, &xx, &t0) + + // Step 37: t1 = x^0xffff0000 + fe_pow2k(&t1, &t0, 16) + + // Step 38: t0 = x^0xffffffff + fe_mul(&t0, &t0, &t1) + + // Step 53: t0 = x^0x7fffffff8000 + fe_pow2k(&t0, &t0, 15) + + // Step 54: z = x^0x7fffffffffff + fe_mul(out1, out1, &t0) + + // Step 71: t0 = x^0xffffffff00000000 + fe_pow2k(&t0, &t0, 17) + + // Step 72: t0 = x^0xffffffff00000001 + fe_mul(&t0, &xx, &t0) + + // Step 215: t0 = x^0x7fffffff80000000800000000000000000000000000000000000 + fe_pow2k(&t0, &t0, 143) + + // Step 216: t0 = x^0x7fffffff800000008000000000000000000000007fffffffffff + fe_mul(&t0, out1, &t0) + + // Step 263: t0 = x^0x3fffffffc00000004000000000000000000000003fffffffffff800000000000 + fe_pow2k(&t0, &t0, 47) + + // Step 264: z = x^0x3fffffffc00000004000000000000000000000003fffffffffffffffffffffff + fe_mul(out1, out1, &t0) + + // Step 266: z = x^0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc + fe_pow2k(out1, out1, 2) + + fe_mul(out1, out1, &xx) + + fe_clear_vec([]^Montgomery_Domain_Field_Element{&t0, &t1, &xx}) +} + +@(require_results) +fe_sqrt :: proc "contextless" (out1, arg1: ^Montgomery_Domain_Field_Element) -> int { + // Square root candidate can be derived via exponentiation by `(p + 1) / 4` + // From sage: 28948022302589062190674361737351893382521535853822578548883407827216774463488 + // + // // Inversion computation is derived from the addition chain: + // + // _10 = 2*1 + // _11 = 1 + _10 + // _1100 = _11 << 2 + // _1111 = _11 + _1100 + // _11110000 = _1111 << 4 + // _11111111 = _1111 + _11110000 + // x16 = _11111111 << 8 + _11111111 + // x32 = x16 << 16 + x16 + // return ((x32 << 32 + 1) << 96 + 1) << 94 + // + // Operations: 253 squares 7 multiplies + // + // Generated by github.com/mmcloughlin/addchain v0.4.0. + + // Likewise this tramples over arg1, so stash another copy. + t0, xx: Montgomery_Domain_Field_Element = ---, arg1^ + + // Step 1: z = x^0x2 + fe_square(out1, arg1) + + // Step 2: z = x^0x3 + fe_mul(out1, &xx, out1) + + // Step 4: t0 = x^0xc + fe_pow2k(&t0, &xx, 2) + + // Step 5: z = x^0xf + fe_mul(out1, out1, &t0) + + // Step 9: t0 = x^0xf0 + fe_pow2k(&t0, out1, 4) + + // Step 10: z = x^0xff + fe_mul(out1, out1, &t0) + + // Step 18: t0 = x^0xff00 + fe_pow2k(&t0, out1, 8) + + // Step 19: z = x^0xffff + fe_mul(out1, out1, &t0) + + // Step 35: t0 = x^0xffff0000 + fe_pow2k(&t0, out1, 16) + + // Step 36: z = x^0xffffffff + fe_mul(out1, out1, &t0) + + // Step 68: z = x^0xffffffff00000000 + fe_pow2k(out1, out1, 32) + + // Step 69: z = x^0xffffffff00000001 + fe_mul(out1, &xx, out1) + + // Step 165: z = x^0xffffffff00000001000000000000000000000000 + fe_pow2k(out1, out1, 96) + + // Step 166: z = x^0xffffffff00000001000000000000000000000001 + fe_mul(out1, &xx, out1) + + // Step 260: z = x^0x3fffffffc0000000400000000000000000000000400000000000000000000000 + fe_pow2k(out1, out1, 94) + + // Ensure that our candidate is actually the square root. + check, zero: Montgomery_Domain_Field_Element + fe_square(&check, out1) + + is_valid := fe_equal(&check, &xx) + fe_cond_select(out1, &zero, out1, is_valid) + + fe_clear_vec([]^Montgomery_Domain_Field_Element{&t0, &xx, &check}) + + return is_valid + +} + +fe_zero :: proc "contextless" (out1: ^Montgomery_Domain_Field_Element) { + out1[0] = 0 + out1[1] = 0 + out1[2] = 0 + out1[3] = 0 +} + +fe_set :: proc "contextless" (out1, arg1: ^Montgomery_Domain_Field_Element) { + x1 := arg1[0] + x2 := arg1[1] + x3 := arg1[2] + x4 := arg1[3] + out1[0] = x1 + out1[1] = x2 + out1[2] = x3 + out1[3] = x4 +} + +@(optimization_mode = "none") +fe_cond_swap :: #force_no_inline proc "contextless" (out1, out2: ^Montgomery_Domain_Field_Element, arg1: int) { + mask := (u64(arg1) * 0xffffffffffffffff) + x := (out1[0] ~ out2[0]) & mask + x1, y1 := out1[0] ~ x, out2[0] ~ x + x = (out1[1] ~ out2[1]) & mask + x2, y2 := out1[1] ~ x, out2[1] ~ x + x = (out1[2] ~ out2[2]) & mask + x3, y3 := out1[2] ~ x, out2[2] ~ x + x = (out1[3] ~ out2[3]) & mask + x4, y4 := out1[3] ~ x, out2[3] ~ x + out1[0], out2[0] = x1, y1 + out1[1], out2[1] = x2, y2 + out1[2], out2[2] = x3, y3 + out1[3], out2[3] = x4, y4 +} + +@(optimization_mode = "none") +fe_cond_select :: #force_no_inline proc "contextless" ( + out1, arg1, arg2: ^Montgomery_Domain_Field_Element, + arg3: int, +) { + mask := (u64(arg3) * 0xffffffffffffffff) + x1 := ((mask & arg2[0]) | ((~mask) & arg1[0])) + x2 := ((mask & arg2[1]) | ((~mask) & arg1[1])) + x3 := ((mask & arg2[2]) | ((~mask) & arg1[2])) + x4 := ((mask & arg2[3]) | ((~mask) & arg1[3])) + out1[0] = x1 + out1[1] = x2 + out1[2] = x3 + out1[3] = x4 +} + +fe_cond_negate :: proc "contextless" (out1, arg1: ^Montgomery_Domain_Field_Element, ctrl: int) { + tmp1: Montgomery_Domain_Field_Element = --- + fe_opp(&tmp1, arg1) + fe_cond_select(out1, arg1, &tmp1, ctrl) + + fe_clear(&tmp1) +} diff --git a/core/crypto/_fiat/field_p256r1/field64.odin b/core/crypto/_fiat/field_p256r1/field64.odin new file mode 100644 index 000000000..940f2cd07 --- /dev/null +++ b/core/crypto/_fiat/field_p256r1/field64.odin @@ -0,0 +1,501 @@ +// The BSD 1-Clause License (BSD-1-Clause) +// +// Copyright (c) 2015-2020 the fiat-crypto authors (see the AUTHORS file) +// All rights reserved. +// +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are +// met: +// +// 1. Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// +// THIS SOFTWARE IS PROVIDED BY the fiat-crypto authors "AS IS" +// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, +// THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL Berkeley Software Design, +// Inc. BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF +// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING +// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +package field_p256r1 + +// The file provides arithmetic on the field Z/(2^256 - 2^224 + 2^192 + 2^96 - 1) +// using a 64-bit Montgomery form internal representation. It is derived +// primarily from the machine generated Golang output from the fiat-crypto +// project. +// +// While the base implementation is provably correct, this implementation +// makes no such claims as the port and optimizations were done by hand. +// +// WARNING: While big-endian is the common representation used for this +// curve, the fiat output uses least-significant-limb first. + +import fiat "core:crypto/_fiat" +import "core:math/bits" + +// ELL is the saturated representation of the field order, least-significant +// limb first. +ELL :: [4]u64{0xffffffffffffffff, 0xffffffff, 0x0, 0xffffffff00000001} + +Montgomery_Domain_Field_Element :: distinct [4]u64 +Non_Montgomery_Domain_Field_Element :: distinct [4]u64 + +fe_mul :: proc "contextless" (out1, arg1, arg2: ^Montgomery_Domain_Field_Element) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[0] + x6, x5 := bits.mul_u64(x4, arg2[3]) + x8, x7 := bits.mul_u64(x4, arg2[2]) + x10, x9 := bits.mul_u64(x4, arg2[1]) + x12, x11 := bits.mul_u64(x4, arg2[0]) + x13, x14 := bits.add_u64(x12, x9, u64(0x0)) + x15, x16 := bits.add_u64(x10, x7, u64(fiat.u1(x14))) + x17, x18 := bits.add_u64(x8, x5, u64(fiat.u1(x16))) + x19 := (u64(fiat.u1(x18)) + x6) + x21, x20 := bits.mul_u64(x11, 0xffffffff00000001) + x23, x22 := bits.mul_u64(x11, 0xffffffff) + x25, x24 := bits.mul_u64(x11, 0xffffffffffffffff) + x26, x27 := bits.add_u64(x25, x22, u64(0x0)) + x28 := (u64(fiat.u1(x27)) + x23) + _, x30 := bits.add_u64(x11, x24, u64(0x0)) + x31, x32 := bits.add_u64(x13, x26, u64(fiat.u1(x30))) + x33, x34 := bits.add_u64(x15, x28, u64(fiat.u1(x32))) + x35, x36 := bits.add_u64(x17, x20, u64(fiat.u1(x34))) + x37, x38 := bits.add_u64(x19, x21, u64(fiat.u1(x36))) + x40, x39 := bits.mul_u64(x1, arg2[3]) + x42, x41 := bits.mul_u64(x1, arg2[2]) + x44, x43 := bits.mul_u64(x1, arg2[1]) + x46, x45 := bits.mul_u64(x1, arg2[0]) + x47, x48 := bits.add_u64(x46, x43, u64(0x0)) + x49, x50 := bits.add_u64(x44, x41, u64(fiat.u1(x48))) + x51, x52 := bits.add_u64(x42, x39, u64(fiat.u1(x50))) + x53 := (u64(fiat.u1(x52)) + x40) + x54, x55 := bits.add_u64(x31, x45, u64(0x0)) + x56, x57 := bits.add_u64(x33, x47, u64(fiat.u1(x55))) + x58, x59 := bits.add_u64(x35, x49, u64(fiat.u1(x57))) + x60, x61 := bits.add_u64(x37, x51, u64(fiat.u1(x59))) + x62, x63 := bits.add_u64(u64(fiat.u1(x38)), x53, u64(fiat.u1(x61))) + x65, x64 := bits.mul_u64(x54, 0xffffffff00000001) + x67, x66 := bits.mul_u64(x54, 0xffffffff) + x69, x68 := bits.mul_u64(x54, 0xffffffffffffffff) + x70, x71 := bits.add_u64(x69, x66, u64(0x0)) + x72 := (u64(fiat.u1(x71)) + x67) + _, x74 := bits.add_u64(x54, x68, u64(0x0)) + x75, x76 := bits.add_u64(x56, x70, u64(fiat.u1(x74))) + x77, x78 := bits.add_u64(x58, x72, u64(fiat.u1(x76))) + x79, x80 := bits.add_u64(x60, x64, u64(fiat.u1(x78))) + x81, x82 := bits.add_u64(x62, x65, u64(fiat.u1(x80))) + x83 := (u64(fiat.u1(x82)) + u64(fiat.u1(x63))) + x85, x84 := bits.mul_u64(x2, arg2[3]) + x87, x86 := bits.mul_u64(x2, arg2[2]) + x89, x88 := bits.mul_u64(x2, arg2[1]) + x91, x90 := bits.mul_u64(x2, arg2[0]) + x92, x93 := bits.add_u64(x91, x88, u64(0x0)) + x94, x95 := bits.add_u64(x89, x86, u64(fiat.u1(x93))) + x96, x97 := bits.add_u64(x87, x84, u64(fiat.u1(x95))) + x98 := (u64(fiat.u1(x97)) + x85) + x99, x100 := bits.add_u64(x75, x90, u64(0x0)) + x101, x102 := bits.add_u64(x77, x92, u64(fiat.u1(x100))) + x103, x104 := bits.add_u64(x79, x94, u64(fiat.u1(x102))) + x105, x106 := bits.add_u64(x81, x96, u64(fiat.u1(x104))) + x107, x108 := bits.add_u64(x83, x98, u64(fiat.u1(x106))) + x110, x109 := bits.mul_u64(x99, 0xffffffff00000001) + x112, x111 := bits.mul_u64(x99, 0xffffffff) + x114, x113 := bits.mul_u64(x99, 0xffffffffffffffff) + x115, x116 := bits.add_u64(x114, x111, u64(0x0)) + x117 := (u64(fiat.u1(x116)) + x112) + _, x119 := bits.add_u64(x99, x113, u64(0x0)) + x120, x121 := bits.add_u64(x101, x115, u64(fiat.u1(x119))) + x122, x123 := bits.add_u64(x103, x117, u64(fiat.u1(x121))) + x124, x125 := bits.add_u64(x105, x109, u64(fiat.u1(x123))) + x126, x127 := bits.add_u64(x107, x110, u64(fiat.u1(x125))) + x128 := (u64(fiat.u1(x127)) + u64(fiat.u1(x108))) + x130, x129 := bits.mul_u64(x3, arg2[3]) + x132, x131 := bits.mul_u64(x3, arg2[2]) + x134, x133 := bits.mul_u64(x3, arg2[1]) + x136, x135 := bits.mul_u64(x3, arg2[0]) + x137, x138 := bits.add_u64(x136, x133, u64(0x0)) + x139, x140 := bits.add_u64(x134, x131, u64(fiat.u1(x138))) + x141, x142 := bits.add_u64(x132, x129, u64(fiat.u1(x140))) + x143 := (u64(fiat.u1(x142)) + x130) + x144, x145 := bits.add_u64(x120, x135, u64(0x0)) + x146, x147 := bits.add_u64(x122, x137, u64(fiat.u1(x145))) + x148, x149 := bits.add_u64(x124, x139, u64(fiat.u1(x147))) + x150, x151 := bits.add_u64(x126, x141, u64(fiat.u1(x149))) + x152, x153 := bits.add_u64(x128, x143, u64(fiat.u1(x151))) + x155, x154 := bits.mul_u64(x144, 0xffffffff00000001) + x157, x156 := bits.mul_u64(x144, 0xffffffff) + x159, x158 := bits.mul_u64(x144, 0xffffffffffffffff) + x160, x161 := bits.add_u64(x159, x156, u64(0x0)) + x162 := (u64(fiat.u1(x161)) + x157) + _, x164 := bits.add_u64(x144, x158, u64(0x0)) + x165, x166 := bits.add_u64(x146, x160, u64(fiat.u1(x164))) + x167, x168 := bits.add_u64(x148, x162, u64(fiat.u1(x166))) + x169, x170 := bits.add_u64(x150, x154, u64(fiat.u1(x168))) + x171, x172 := bits.add_u64(x152, x155, u64(fiat.u1(x170))) + x173 := (u64(fiat.u1(x172)) + u64(fiat.u1(x153))) + x174, x175 := bits.sub_u64(x165, 0xffffffffffffffff, u64(0x0)) + x176, x177 := bits.sub_u64(x167, 0xffffffff, u64(fiat.u1(x175))) + x178, x179 := bits.sub_u64(x169, u64(0x0), u64(fiat.u1(x177))) + x180, x181 := bits.sub_u64(x171, 0xffffffff00000001, u64(fiat.u1(x179))) + _, x183 := bits.sub_u64(x173, u64(0x0), u64(fiat.u1(x181))) + x184 := fiat.cmovznz_u64(fiat.u1(x183), x174, x165) + x185 := fiat.cmovznz_u64(fiat.u1(x183), x176, x167) + x186 := fiat.cmovznz_u64(fiat.u1(x183), x178, x169) + x187 := fiat.cmovznz_u64(fiat.u1(x183), x180, x171) + out1[0] = x184 + out1[1] = x185 + out1[2] = x186 + out1[3] = x187 +} + +fe_square :: proc "contextless" (out1, arg1: ^Montgomery_Domain_Field_Element) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[0] + x6, x5 := bits.mul_u64(x4, arg1[3]) + x8, x7 := bits.mul_u64(x4, arg1[2]) + x10, x9 := bits.mul_u64(x4, arg1[1]) + x12, x11 := bits.mul_u64(x4, arg1[0]) + x13, x14 := bits.add_u64(x12, x9, u64(0x0)) + x15, x16 := bits.add_u64(x10, x7, u64(fiat.u1(x14))) + x17, x18 := bits.add_u64(x8, x5, u64(fiat.u1(x16))) + x19 := (u64(fiat.u1(x18)) + x6) + x21, x20 := bits.mul_u64(x11, 0xffffffff00000001) + x23, x22 := bits.mul_u64(x11, 0xffffffff) + x25, x24 := bits.mul_u64(x11, 0xffffffffffffffff) + x26, x27 := bits.add_u64(x25, x22, u64(0x0)) + x28 := (u64(fiat.u1(x27)) + x23) + _, x30 := bits.add_u64(x11, x24, u64(0x0)) + x31, x32 := bits.add_u64(x13, x26, u64(fiat.u1(x30))) + x33, x34 := bits.add_u64(x15, x28, u64(fiat.u1(x32))) + x35, x36 := bits.add_u64(x17, x20, u64(fiat.u1(x34))) + x37, x38 := bits.add_u64(x19, x21, u64(fiat.u1(x36))) + x40, x39 := bits.mul_u64(x1, arg1[3]) + x42, x41 := bits.mul_u64(x1, arg1[2]) + x44, x43 := bits.mul_u64(x1, arg1[1]) + x46, x45 := bits.mul_u64(x1, arg1[0]) + x47, x48 := bits.add_u64(x46, x43, u64(0x0)) + x49, x50 := bits.add_u64(x44, x41, u64(fiat.u1(x48))) + x51, x52 := bits.add_u64(x42, x39, u64(fiat.u1(x50))) + x53 := (u64(fiat.u1(x52)) + x40) + x54, x55 := bits.add_u64(x31, x45, u64(0x0)) + x56, x57 := bits.add_u64(x33, x47, u64(fiat.u1(x55))) + x58, x59 := bits.add_u64(x35, x49, u64(fiat.u1(x57))) + x60, x61 := bits.add_u64(x37, x51, u64(fiat.u1(x59))) + x62, x63 := bits.add_u64(u64(fiat.u1(x38)), x53, u64(fiat.u1(x61))) + x65, x64 := bits.mul_u64(x54, 0xffffffff00000001) + x67, x66 := bits.mul_u64(x54, 0xffffffff) + x69, x68 := bits.mul_u64(x54, 0xffffffffffffffff) + x70, x71 := bits.add_u64(x69, x66, u64(0x0)) + x72 := (u64(fiat.u1(x71)) + x67) + _, x74 := bits.add_u64(x54, x68, u64(0x0)) + x75, x76 := bits.add_u64(x56, x70, u64(fiat.u1(x74))) + x77, x78 := bits.add_u64(x58, x72, u64(fiat.u1(x76))) + x79, x80 := bits.add_u64(x60, x64, u64(fiat.u1(x78))) + x81, x82 := bits.add_u64(x62, x65, u64(fiat.u1(x80))) + x83 := (u64(fiat.u1(x82)) + u64(fiat.u1(x63))) + x85, x84 := bits.mul_u64(x2, arg1[3]) + x87, x86 := bits.mul_u64(x2, arg1[2]) + x89, x88 := bits.mul_u64(x2, arg1[1]) + x91, x90 := bits.mul_u64(x2, arg1[0]) + x92, x93 := bits.add_u64(x91, x88, u64(0x0)) + x94, x95 := bits.add_u64(x89, x86, u64(fiat.u1(x93))) + x96, x97 := bits.add_u64(x87, x84, u64(fiat.u1(x95))) + x98 := (u64(fiat.u1(x97)) + x85) + x99, x100 := bits.add_u64(x75, x90, u64(0x0)) + x101, x102 := bits.add_u64(x77, x92, u64(fiat.u1(x100))) + x103, x104 := bits.add_u64(x79, x94, u64(fiat.u1(x102))) + x105, x106 := bits.add_u64(x81, x96, u64(fiat.u1(x104))) + x107, x108 := bits.add_u64(x83, x98, u64(fiat.u1(x106))) + x110, x109 := bits.mul_u64(x99, 0xffffffff00000001) + x112, x111 := bits.mul_u64(x99, 0xffffffff) + x114, x113 := bits.mul_u64(x99, 0xffffffffffffffff) + x115, x116 := bits.add_u64(x114, x111, u64(0x0)) + x117 := (u64(fiat.u1(x116)) + x112) + _, x119 := bits.add_u64(x99, x113, u64(0x0)) + x120, x121 := bits.add_u64(x101, x115, u64(fiat.u1(x119))) + x122, x123 := bits.add_u64(x103, x117, u64(fiat.u1(x121))) + x124, x125 := bits.add_u64(x105, x109, u64(fiat.u1(x123))) + x126, x127 := bits.add_u64(x107, x110, u64(fiat.u1(x125))) + x128 := (u64(fiat.u1(x127)) + u64(fiat.u1(x108))) + x130, x129 := bits.mul_u64(x3, arg1[3]) + x132, x131 := bits.mul_u64(x3, arg1[2]) + x134, x133 := bits.mul_u64(x3, arg1[1]) + x136, x135 := bits.mul_u64(x3, arg1[0]) + x137, x138 := bits.add_u64(x136, x133, u64(0x0)) + x139, x140 := bits.add_u64(x134, x131, u64(fiat.u1(x138))) + x141, x142 := bits.add_u64(x132, x129, u64(fiat.u1(x140))) + x143 := (u64(fiat.u1(x142)) + x130) + x144, x145 := bits.add_u64(x120, x135, u64(0x0)) + x146, x147 := bits.add_u64(x122, x137, u64(fiat.u1(x145))) + x148, x149 := bits.add_u64(x124, x139, u64(fiat.u1(x147))) + x150, x151 := bits.add_u64(x126, x141, u64(fiat.u1(x149))) + x152, x153 := bits.add_u64(x128, x143, u64(fiat.u1(x151))) + x155, x154 := bits.mul_u64(x144, 0xffffffff00000001) + x157, x156 := bits.mul_u64(x144, 0xffffffff) + x159, x158 := bits.mul_u64(x144, 0xffffffffffffffff) + x160, x161 := bits.add_u64(x159, x156, u64(0x0)) + x162 := (u64(fiat.u1(x161)) + x157) + _, x164 := bits.add_u64(x144, x158, u64(0x0)) + x165, x166 := bits.add_u64(x146, x160, u64(fiat.u1(x164))) + x167, x168 := bits.add_u64(x148, x162, u64(fiat.u1(x166))) + x169, x170 := bits.add_u64(x150, x154, u64(fiat.u1(x168))) + x171, x172 := bits.add_u64(x152, x155, u64(fiat.u1(x170))) + x173 := (u64(fiat.u1(x172)) + u64(fiat.u1(x153))) + x174, x175 := bits.sub_u64(x165, 0xffffffffffffffff, u64(0x0)) + x176, x177 := bits.sub_u64(x167, 0xffffffff, u64(fiat.u1(x175))) + x178, x179 := bits.sub_u64(x169, u64(0x0), u64(fiat.u1(x177))) + x180, x181 := bits.sub_u64(x171, 0xffffffff00000001, u64(fiat.u1(x179))) + _, x183 := bits.sub_u64(x173, u64(0x0), u64(fiat.u1(x181))) + x184 := fiat.cmovznz_u64(fiat.u1(x183), x174, x165) + x185 := fiat.cmovznz_u64(fiat.u1(x183), x176, x167) + x186 := fiat.cmovznz_u64(fiat.u1(x183), x178, x169) + x187 := fiat.cmovznz_u64(fiat.u1(x183), x180, x171) + out1[0] = x184 + out1[1] = x185 + out1[2] = x186 + out1[3] = x187 +} + +fe_add :: proc "contextless" (out1, arg1, arg2: ^Montgomery_Domain_Field_Element) { + x1, x2 := bits.add_u64(arg1[0], arg2[0], u64(0x0)) + x3, x4 := bits.add_u64(arg1[1], arg2[1], u64(fiat.u1(x2))) + x5, x6 := bits.add_u64(arg1[2], arg2[2], u64(fiat.u1(x4))) + x7, x8 := bits.add_u64(arg1[3], arg2[3], u64(fiat.u1(x6))) + x9, x10 := bits.sub_u64(x1, 0xffffffffffffffff, u64(0x0)) + x11, x12 := bits.sub_u64(x3, 0xffffffff, u64(fiat.u1(x10))) + x13, x14 := bits.sub_u64(x5, u64(0x0), u64(fiat.u1(x12))) + x15, x16 := bits.sub_u64(x7, 0xffffffff00000001, u64(fiat.u1(x14))) + _, x18 := bits.sub_u64(u64(fiat.u1(x8)), u64(0x0), u64(fiat.u1(x16))) + x19 := fiat.cmovznz_u64(fiat.u1(x18), x9, x1) + x20 := fiat.cmovznz_u64(fiat.u1(x18), x11, x3) + x21 := fiat.cmovznz_u64(fiat.u1(x18), x13, x5) + x22 := fiat.cmovznz_u64(fiat.u1(x18), x15, x7) + out1[0] = x19 + out1[1] = x20 + out1[2] = x21 + out1[3] = x22 +} + +fe_sub :: proc "contextless" (out1, arg1, arg2: ^Montgomery_Domain_Field_Element) { + x1, x2 := bits.sub_u64(arg1[0], arg2[0], u64(0x0)) + x3, x4 := bits.sub_u64(arg1[1], arg2[1], u64(fiat.u1(x2))) + x5, x6 := bits.sub_u64(arg1[2], arg2[2], u64(fiat.u1(x4))) + x7, x8 := bits.sub_u64(arg1[3], arg2[3], u64(fiat.u1(x6))) + x9 := fiat.cmovznz_u64(fiat.u1(x8), u64(0x0), 0xffffffffffffffff) + x10, x11 := bits.add_u64(x1, x9, u64(0x0)) + x12, x13 := bits.add_u64(x3, (x9 & 0xffffffff), u64(fiat.u1(x11))) + x14, x15 := bits.add_u64(x5, u64(0x0), u64(fiat.u1(x13))) + x16, _ := bits.add_u64(x7, (x9 & 0xffffffff00000001), u64(fiat.u1(x15))) + out1[0] = x10 + out1[1] = x12 + out1[2] = x14 + out1[3] = x16 +} + +fe_opp :: proc "contextless" (out1, arg1: ^Montgomery_Domain_Field_Element) { + x1, x2 := bits.sub_u64(u64(0x0), arg1[0], u64(0x0)) + x3, x4 := bits.sub_u64(u64(0x0), arg1[1], u64(fiat.u1(x2))) + x5, x6 := bits.sub_u64(u64(0x0), arg1[2], u64(fiat.u1(x4))) + x7, x8 := bits.sub_u64(u64(0x0), arg1[3], u64(fiat.u1(x6))) + x9 := fiat.cmovznz_u64(fiat.u1(x8), u64(0x0), 0xffffffffffffffff) + x10, x11 := bits.add_u64(x1, x9, u64(0x0)) + x12, x13 := bits.add_u64(x3, (x9 & 0xffffffff), u64(fiat.u1(x11))) + x14, x15 := bits.add_u64(x5, u64(0x0), u64(fiat.u1(x13))) + x16, _ := bits.add_u64(x7, (x9 & 0xffffffff00000001), u64(fiat.u1(x15))) + out1[0] = x10 + out1[1] = x12 + out1[2] = x14 + out1[3] = x16 +} + +fe_one :: proc "contextless" (out1: ^Montgomery_Domain_Field_Element) { + out1[0] = 0x1 + out1[1] = 0xffffffff00000000 + out1[2] = 0xffffffffffffffff + out1[3] = 0xfffffffe +} + +fe_non_zero :: proc "contextless" (arg1: ^Montgomery_Domain_Field_Element) -> u64 { + return arg1[0] | (arg1[1] | (arg1[2] | arg1[3])) +} + +@(optimization_mode = "none") +fe_cond_assign :: #force_no_inline proc "contextless" ( + out1, arg1: ^Montgomery_Domain_Field_Element, + arg2: int, +) { + x1 := fiat.cmovznz_u64(fiat.u1(arg2), out1[0], arg1[0]) + x2 := fiat.cmovznz_u64(fiat.u1(arg2), out1[1], arg1[1]) + x3 := fiat.cmovznz_u64(fiat.u1(arg2), out1[2], arg1[2]) + x4 := fiat.cmovznz_u64(fiat.u1(arg2), out1[3], arg1[3]) + out1[0] = x1 + out1[1] = x2 + out1[2] = x3 + out1[3] = x4 +} + +fe_from_montgomery :: proc "contextless" ( + out1: ^Non_Montgomery_Domain_Field_Element, + arg1: ^Montgomery_Domain_Field_Element, +) { + x1 := arg1[0] + x3, x2 := bits.mul_u64(x1, 0xffffffff00000001) + x5, x4 := bits.mul_u64(x1, 0xffffffff) + x7, x6 := bits.mul_u64(x1, 0xffffffffffffffff) + x8, x9 := bits.add_u64(x7, x4, u64(0x0)) + _, x11 := bits.add_u64(x1, x6, u64(0x0)) + x12, x13 := bits.add_u64(u64(0x0), x8, u64(fiat.u1(x11))) + x14, x15 := bits.add_u64(x12, arg1[1], u64(0x0)) + x17, x16 := bits.mul_u64(x14, 0xffffffff00000001) + x19, x18 := bits.mul_u64(x14, 0xffffffff) + x21, x20 := bits.mul_u64(x14, 0xffffffffffffffff) + x22, x23 := bits.add_u64(x21, x18, u64(0x0)) + _, x25 := bits.add_u64(x14, x20, u64(0x0)) + x26, x27 := bits.add_u64((u64(fiat.u1(x15)) + (u64(fiat.u1(x13)) + (u64(fiat.u1(x9)) + x5))), x22, u64(fiat.u1(x25))) + x28, x29 := bits.add_u64(x2, (u64(fiat.u1(x23)) + x19), u64(fiat.u1(x27))) + x30, x31 := bits.add_u64(x3, x16, u64(fiat.u1(x29))) + x32, x33 := bits.add_u64(x26, arg1[2], u64(0x0)) + x34, x35 := bits.add_u64(x28, u64(0x0), u64(fiat.u1(x33))) + x36, x37 := bits.add_u64(x30, u64(0x0), u64(fiat.u1(x35))) + x39, x38 := bits.mul_u64(x32, 0xffffffff00000001) + x41, x40 := bits.mul_u64(x32, 0xffffffff) + x43, x42 := bits.mul_u64(x32, 0xffffffffffffffff) + x44, x45 := bits.add_u64(x43, x40, u64(0x0)) + _, x47 := bits.add_u64(x32, x42, u64(0x0)) + x48, x49 := bits.add_u64(x34, x44, u64(fiat.u1(x47))) + x50, x51 := bits.add_u64(x36, (u64(fiat.u1(x45)) + x41), u64(fiat.u1(x49))) + x52, x53 := bits.add_u64((u64(fiat.u1(x37)) + (u64(fiat.u1(x31)) + x17)), x38, u64(fiat.u1(x51))) + x54, x55 := bits.add_u64(x48, arg1[3], u64(0x0)) + x56, x57 := bits.add_u64(x50, u64(0x0), u64(fiat.u1(x55))) + x58, x59 := bits.add_u64(x52, u64(0x0), u64(fiat.u1(x57))) + x61, x60 := bits.mul_u64(x54, 0xffffffff00000001) + x63, x62 := bits.mul_u64(x54, 0xffffffff) + x65, x64 := bits.mul_u64(x54, 0xffffffffffffffff) + x66, x67 := bits.add_u64(x65, x62, u64(0x0)) + _, x69 := bits.add_u64(x54, x64, u64(0x0)) + x70, x71 := bits.add_u64(x56, x66, u64(fiat.u1(x69))) + x72, x73 := bits.add_u64(x58, (u64(fiat.u1(x67)) + x63), u64(fiat.u1(x71))) + x74, x75 := bits.add_u64((u64(fiat.u1(x59)) + (u64(fiat.u1(x53)) + x39)), x60, u64(fiat.u1(x73))) + x76 := (u64(fiat.u1(x75)) + x61) + x77, x78 := bits.sub_u64(x70, 0xffffffffffffffff, u64(0x0)) + x79, x80 := bits.sub_u64(x72, 0xffffffff, u64(fiat.u1(x78))) + x81, x82 := bits.sub_u64(x74, u64(0x0), u64(fiat.u1(x80))) + x83, x84 := bits.sub_u64(x76, 0xffffffff00000001, u64(fiat.u1(x82))) + _, x86 := bits.sub_u64(u64(0x0), u64(0x0), u64(fiat.u1(x84))) + x87 := fiat.cmovznz_u64(fiat.u1(x86), x77, x70) + x88 := fiat.cmovznz_u64(fiat.u1(x86), x79, x72) + x89 := fiat.cmovznz_u64(fiat.u1(x86), x81, x74) + x90 := fiat.cmovznz_u64(fiat.u1(x86), x83, x76) + out1[0] = x87 + out1[1] = x88 + out1[2] = x89 + out1[3] = x90 +} + +fe_to_montgomery :: proc "contextless" ( + out1: ^Montgomery_Domain_Field_Element, + arg1: ^Non_Montgomery_Domain_Field_Element, +) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[0] + x6, x5 := bits.mul_u64(x4, 0x4fffffffd) + x8, x7 := bits.mul_u64(x4, 0xfffffffffffffffe) + x10, x9 := bits.mul_u64(x4, 0xfffffffbffffffff) + x12, x11 := bits.mul_u64(x4, 0x3) + x13, x14 := bits.add_u64(x12, x9, u64(0x0)) + x15, x16 := bits.add_u64(x10, x7, u64(fiat.u1(x14))) + x17, x18 := bits.add_u64(x8, x5, u64(fiat.u1(x16))) + x20, x19 := bits.mul_u64(x11, 0xffffffff00000001) + x22, x21 := bits.mul_u64(x11, 0xffffffff) + x24, x23 := bits.mul_u64(x11, 0xffffffffffffffff) + x25, x26 := bits.add_u64(x24, x21, u64(0x0)) + _, x28 := bits.add_u64(x11, x23, u64(0x0)) + x29, x30 := bits.add_u64(x13, x25, u64(fiat.u1(x28))) + x31, x32 := bits.add_u64(x15, (u64(fiat.u1(x26)) + x22), u64(fiat.u1(x30))) + x33, x34 := bits.add_u64(x17, x19, u64(fiat.u1(x32))) + x35, x36 := bits.add_u64((u64(fiat.u1(x18)) + x6), x20, u64(fiat.u1(x34))) + x38, x37 := bits.mul_u64(x1, 0x4fffffffd) + x40, x39 := bits.mul_u64(x1, 0xfffffffffffffffe) + x42, x41 := bits.mul_u64(x1, 0xfffffffbffffffff) + x44, x43 := bits.mul_u64(x1, 0x3) + x45, x46 := bits.add_u64(x44, x41, u64(0x0)) + x47, x48 := bits.add_u64(x42, x39, u64(fiat.u1(x46))) + x49, x50 := bits.add_u64(x40, x37, u64(fiat.u1(x48))) + x51, x52 := bits.add_u64(x29, x43, u64(0x0)) + x53, x54 := bits.add_u64(x31, x45, u64(fiat.u1(x52))) + x55, x56 := bits.add_u64(x33, x47, u64(fiat.u1(x54))) + x57, x58 := bits.add_u64(x35, x49, u64(fiat.u1(x56))) + x60, x59 := bits.mul_u64(x51, 0xffffffff00000001) + x62, x61 := bits.mul_u64(x51, 0xffffffff) + x64, x63 := bits.mul_u64(x51, 0xffffffffffffffff) + x65, x66 := bits.add_u64(x64, x61, u64(0x0)) + _, x68 := bits.add_u64(x51, x63, u64(0x0)) + x69, x70 := bits.add_u64(x53, x65, u64(fiat.u1(x68))) + x71, x72 := bits.add_u64(x55, (u64(fiat.u1(x66)) + x62), u64(fiat.u1(x70))) + x73, x74 := bits.add_u64(x57, x59, u64(fiat.u1(x72))) + x75, x76 := bits.add_u64(((u64(fiat.u1(x58)) + u64(fiat.u1(x36))) + (u64(fiat.u1(x50)) + x38)), x60, u64(fiat.u1(x74))) + x78, x77 := bits.mul_u64(x2, 0x4fffffffd) + x80, x79 := bits.mul_u64(x2, 0xfffffffffffffffe) + x82, x81 := bits.mul_u64(x2, 0xfffffffbffffffff) + x84, x83 := bits.mul_u64(x2, 0x3) + x85, x86 := bits.add_u64(x84, x81, u64(0x0)) + x87, x88 := bits.add_u64(x82, x79, u64(fiat.u1(x86))) + x89, x90 := bits.add_u64(x80, x77, u64(fiat.u1(x88))) + x91, x92 := bits.add_u64(x69, x83, u64(0x0)) + x93, x94 := bits.add_u64(x71, x85, u64(fiat.u1(x92))) + x95, x96 := bits.add_u64(x73, x87, u64(fiat.u1(x94))) + x97, x98 := bits.add_u64(x75, x89, u64(fiat.u1(x96))) + x100, x99 := bits.mul_u64(x91, 0xffffffff00000001) + x102, x101 := bits.mul_u64(x91, 0xffffffff) + x104, x103 := bits.mul_u64(x91, 0xffffffffffffffff) + x105, x106 := bits.add_u64(x104, x101, u64(0x0)) + _, x108 := bits.add_u64(x91, x103, u64(0x0)) + x109, x110 := bits.add_u64(x93, x105, u64(fiat.u1(x108))) + x111, x112 := bits.add_u64(x95, (u64(fiat.u1(x106)) + x102), u64(fiat.u1(x110))) + x113, x114 := bits.add_u64(x97, x99, u64(fiat.u1(x112))) + x115, x116 := bits.add_u64(((u64(fiat.u1(x98)) + u64(fiat.u1(x76))) + (u64(fiat.u1(x90)) + x78)), x100, u64(fiat.u1(x114))) + x118, x117 := bits.mul_u64(x3, 0x4fffffffd) + x120, x119 := bits.mul_u64(x3, 0xfffffffffffffffe) + x122, x121 := bits.mul_u64(x3, 0xfffffffbffffffff) + x124, x123 := bits.mul_u64(x3, 0x3) + x125, x126 := bits.add_u64(x124, x121, u64(0x0)) + x127, x128 := bits.add_u64(x122, x119, u64(fiat.u1(x126))) + x129, x130 := bits.add_u64(x120, x117, u64(fiat.u1(x128))) + x131, x132 := bits.add_u64(x109, x123, u64(0x0)) + x133, x134 := bits.add_u64(x111, x125, u64(fiat.u1(x132))) + x135, x136 := bits.add_u64(x113, x127, u64(fiat.u1(x134))) + x137, x138 := bits.add_u64(x115, x129, u64(fiat.u1(x136))) + x140, x139 := bits.mul_u64(x131, 0xffffffff00000001) + x142, x141 := bits.mul_u64(x131, 0xffffffff) + x144, x143 := bits.mul_u64(x131, 0xffffffffffffffff) + x145, x146 := bits.add_u64(x144, x141, u64(0x0)) + _, x148 := bits.add_u64(x131, x143, u64(0x0)) + x149, x150 := bits.add_u64(x133, x145, u64(fiat.u1(x148))) + x151, x152 := bits.add_u64(x135, (u64(fiat.u1(x146)) + x142), u64(fiat.u1(x150))) + x153, x154 := bits.add_u64(x137, x139, u64(fiat.u1(x152))) + x155, x156 := bits.add_u64(((u64(fiat.u1(x138)) + u64(fiat.u1(x116))) + (u64(fiat.u1(x130)) + x118)), x140, u64(fiat.u1(x154))) + x157, x158 := bits.sub_u64(x149, 0xffffffffffffffff, u64(0x0)) + x159, x160 := bits.sub_u64(x151, 0xffffffff, u64(fiat.u1(x158))) + x161, x162 := bits.sub_u64(x153, u64(0x0), u64(fiat.u1(x160))) + x163, x164 := bits.sub_u64(x155, 0xffffffff00000001, u64(fiat.u1(x162))) + _, x166 := bits.sub_u64(u64(fiat.u1(x156)), u64(0x0), u64(fiat.u1(x164))) + x167 := fiat.cmovznz_u64(fiat.u1(x166), x157, x149) + x168 := fiat.cmovznz_u64(fiat.u1(x166), x159, x151) + x169 := fiat.cmovznz_u64(fiat.u1(x166), x161, x153) + x170 := fiat.cmovznz_u64(fiat.u1(x166), x163, x155) + out1[0] = x167 + out1[1] = x168 + out1[2] = x169 + out1[3] = x170 +} diff --git a/core/crypto/_fiat/field_scalarp256r1/field.odin b/core/crypto/_fiat/field_scalarp256r1/field.odin new file mode 100644 index 000000000..73c01fb46 --- /dev/null +++ b/core/crypto/_fiat/field_scalarp256r1/field.odin @@ -0,0 +1,210 @@ +package field_scalarp256r1 + +import subtle "core:crypto/_subtle" +import "core:encoding/endian" +import "core:math/bits" +import "core:mem" + +@(private, rodata) +TWO_192 := Montgomery_Domain_Field_Element{ + 2482910415990817935, + 2879494685571067143, + 8732918506673730078, + 85565669603516024, +} +@(private, rodata) +TWO_384 := Montgomery_Domain_Field_Element{ + 2127524300190691059, + 17014302137236182484, + 16604910261202196099, + 3621421107472562910, +} +// 2^384 % p (From sage) +// 0x431905529c0166ce652e96b7ccca0a99679b73e19ad16947f01cf013fc632551 + +fe_clear :: proc "contextless" (arg1: ^Montgomery_Domain_Field_Element) { + mem.zero_explicit(arg1, size_of(Montgomery_Domain_Field_Element)) +} + +fe_clear_vec :: proc "contextless" ( + arg1: []^Montgomery_Domain_Field_Element, +) { + for fe in arg1 { + fe_clear(fe) + } +} + +fe_from_bytes :: proc "contextless" ( + out1: ^Montgomery_Domain_Field_Element, + arg1: []byte, +) -> bool { + ensure_contextless(len(out1) <= 64, "p256r1: invalid scalar input buffer") + + is_canonical := false + s_len := len(arg1) + switch { + case s_len < 32: + // No way this can be greater than the order. + fe_unchecked_set(out1, arg1) + is_canonical = true + case s_len == 32: + // It is quite likely that a reduction mod p is required, + // as the order of the curve is sufficiently smaller than + // 2^256-1, so just check if we actually needed to reduced + // and do the reduction anyway, so that things that require + // canonical scalars can reject non-canonical encodings. + is_canonical = fe_is_canonical(arg1) + fallthrough + case: + // Use Frank Denis' trick, as documented by Filippo Valsorda + // at https://words.filippo.io/dispatches/wide-reduction/ + // + // "I represent the value as a+b*2^192+c*2^384" + // + // Note: Omitting the `c` computation is fine as, reduction + // being length dependent provides no useful timing information. + + // Zero extend to 512-bits. + src_512: [64]byte + copy(src_512[64-s_len:], arg1) + defer mem.zero_explicit(&src_512, size_of(src_512)) + + fe_unchecked_set(out1, src_512[40:]) // a + b: Montgomery_Domain_Field_Element + fe_unchecked_set(&b, src_512[16:40]) // b + + fe_mul(&b, &b, &TWO_192) + fe_add(out1, out1, &b) + if s_len >= 48 { + c: Montgomery_Domain_Field_Element + fe_unchecked_set(&c, src_512[:16]) // c + fe_mul(&c, &c, &TWO_384) + fe_add(out1, out1, &c) + + fe_clear(&c) + } + + fe_clear(&b) + } + + return !is_canonical +} + +@(private) +fe_is_canonical :: proc "contextless" (arg1: []byte) -> bool { + _, borrow := bits.sub_u64(ELL[0] - 1, endian.unchecked_get_u64be(arg1[24:]), 0) + _, borrow = bits.sub_u64(ELL[1], endian.unchecked_get_u64be(arg1[16:]), borrow) + _, borrow = bits.sub_u64(ELL[2], endian.unchecked_get_u64be(arg1[8:]), borrow) + _, borrow = bits.sub_u64(ELL[3], endian.unchecked_get_u64be(arg1[0:]), borrow) + return borrow == 0 +} + +@(private) +fe_unchecked_set :: proc "contextless" (out1: ^Montgomery_Domain_Field_Element, arg1: []byte) { + arg1_256: [32]byte + defer mem.zero_explicit(&arg1_256, size_of(arg1_256)) + copy(arg1_256[32-len(arg1):], arg1) + + tmp := Non_Montgomery_Domain_Field_Element { + endian.unchecked_get_u64be(arg1_256[24:]), + endian.unchecked_get_u64be(arg1_256[16:]), + endian.unchecked_get_u64be(arg1_256[8:]), + endian.unchecked_get_u64be(arg1_256[0:]), + } + defer mem.zero_explicit(&tmp, size_of(tmp)) + + fe_to_montgomery(out1, &tmp) +} + +fe_to_bytes :: proc "contextless" (out1: []byte, arg1: ^Montgomery_Domain_Field_Element) { + ensure_contextless(len(out1) == 32, "p256r1: invalid scalar output buffer") + + tmp: Non_Montgomery_Domain_Field_Element + fe_from_montgomery(&tmp, arg1) + + // Note: Likewise, output in big-endian. + endian.unchecked_put_u64be(out1[24:], tmp[0]) + endian.unchecked_put_u64be(out1[16:], tmp[1]) + endian.unchecked_put_u64be(out1[8:], tmp[2]) + endian.unchecked_put_u64be(out1[0:], tmp[3]) + + mem.zero_explicit(&tmp, size_of(tmp)) +} + +fe_equal :: proc "contextless" (arg1, arg2: ^Montgomery_Domain_Field_Element) -> int { + tmp: Montgomery_Domain_Field_Element + fe_sub(&tmp, arg1, arg2) + + is_eq := subtle.u64_is_zero(fe_non_zero(&tmp)) + + fe_clear(&tmp) + + return int(is_eq) +} + +fe_is_odd :: proc "contextless" (arg1: ^Montgomery_Domain_Field_Element) -> int { + tmp: Non_Montgomery_Domain_Field_Element + defer mem.zero_explicit(&tmp, size_of(tmp)) + + fe_from_montgomery(&tmp, arg1) + return int(tmp[0] & 1) +} + +fe_zero :: proc "contextless" (out1: ^Montgomery_Domain_Field_Element) { + out1[0] = 0 + out1[1] = 0 + out1[2] = 0 + out1[3] = 0 +} + +fe_set :: proc "contextless" (out1, arg1: ^Montgomery_Domain_Field_Element) { + x1 := arg1[0] + x2 := arg1[1] + x3 := arg1[2] + x4 := arg1[3] + out1[0] = x1 + out1[1] = x2 + out1[2] = x3 + out1[3] = x4 +} + +@(optimization_mode = "none") +fe_cond_swap :: #force_no_inline proc "contextless" (out1, out2: ^Montgomery_Domain_Field_Element, arg1: int) { + mask := (u64(arg1) * 0xffffffffffffffff) + x := (out1[0] ~ out2[0]) & mask + x1, y1 := out1[0] ~ x, out2[0] ~ x + x = (out1[1] ~ out2[1]) & mask + x2, y2 := out1[1] ~ x, out2[1] ~ x + x = (out1[2] ~ out2[2]) & mask + x3, y3 := out1[2] ~ x, out2[2] ~ x + x = (out1[3] ~ out2[3]) & mask + x4, y4 := out1[3] ~ x, out2[3] ~ x + out1[0], out2[0] = x1, y1 + out1[1], out2[1] = x2, y2 + out1[2], out2[2] = x3, y3 + out1[3], out2[3] = x4, y4 +} + +@(optimization_mode = "none") +fe_cond_select :: #force_no_inline proc "contextless" ( + out1, arg1, arg2: ^Montgomery_Domain_Field_Element, + arg3: int, +) { + mask := (u64(arg3) * 0xffffffffffffffff) + x1 := ((mask & arg2[0]) | ((~mask) & arg1[0])) + x2 := ((mask & arg2[1]) | ((~mask) & arg1[1])) + x3 := ((mask & arg2[2]) | ((~mask) & arg1[2])) + x4 := ((mask & arg2[3]) | ((~mask) & arg1[3])) + out1[0] = x1 + out1[1] = x2 + out1[2] = x3 + out1[3] = x4 +} + +fe_cond_negate :: proc "contextless" (out1, arg1: ^Montgomery_Domain_Field_Element, ctrl: int) { + tmp1: Montgomery_Domain_Field_Element = --- + fe_opp(&tmp1, arg1) + fe_cond_select(out1, arg1, &tmp1, ctrl) + + fe_clear(&tmp1) +} diff --git a/core/crypto/_fiat/field_scalarp256r1/field64.odin b/core/crypto/_fiat/field_scalarp256r1/field64.odin new file mode 100644 index 000000000..4217374a7 --- /dev/null +++ b/core/crypto/_fiat/field_scalarp256r1/field64.odin @@ -0,0 +1,569 @@ +// The BSD 1-Clause License (BSD-1-Clause) +// +// Copyright (c) 2015-2020 the fiat-crypto authors (see the AUTHORS file) +// All rights reserved. +// +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are +// met: +// +// 1. Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// +// THIS SOFTWARE IS PROVIDED BY the fiat-crypto authors "AS IS" +// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, +// THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL Berkeley Software Design, +// Inc. BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF +// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING +// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +package field_scalarp256r1 + +// The file provides arithmetic on the field Z/(2^256 - 2^224 + 2^192 - +// 89188191075325690597107910205041859247) using a 64-bit Montgomery form +// internal representation. It is derived primarily from the machine +// generated Golang output from the fiat-crypto project. +// +// While the base implementation is provably correct, this implementation +// makes no such claims as the port and optimizations were done by hand. +// +// WARNING: While big-endian is the common representation used for this +// curve, the fiat output uses least-significant-limb first. + +import fiat "core:crypto/_fiat" +import "core:math/bits" + +// ELL is the saturated representation of the field order, least-significant +// limb first. +ELL :: [4]u64{0xf3b9cac2fc632551, 0xbce6faada7179e84, 0xffffffffffffffff, 0xffffffff00000000} + +Montgomery_Domain_Field_Element :: distinct [4]u64 +Non_Montgomery_Domain_Field_Element :: distinct [4]u64 + +fe_mul :: proc "contextless" (out1, arg1, arg2: ^Montgomery_Domain_Field_Element) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[0] + x6, x5 := bits.mul_u64(x4, arg2[3]) + x8, x7 := bits.mul_u64(x4, arg2[2]) + x10, x9 := bits.mul_u64(x4, arg2[1]) + x12, x11 := bits.mul_u64(x4, arg2[0]) + x13, x14 := bits.add_u64(x12, x9, u64(0x0)) + x15, x16 := bits.add_u64(x10, x7, u64(fiat.u1(x14))) + x17, x18 := bits.add_u64(x8, x5, u64(fiat.u1(x16))) + x19 := (u64(fiat.u1(x18)) + x6) + _, x20 := bits.mul_u64(x11, 0xccd1c8aaee00bc4f) + x23, x22 := bits.mul_u64(x20, 0xffffffff00000000) + x25, x24 := bits.mul_u64(x20, 0xffffffffffffffff) + x27, x26 := bits.mul_u64(x20, 0xbce6faada7179e84) + x29, x28 := bits.mul_u64(x20, 0xf3b9cac2fc632551) + x30, x31 := bits.add_u64(x29, x26, u64(0x0)) + x32, x33 := bits.add_u64(x27, x24, u64(fiat.u1(x31))) + x34, x35 := bits.add_u64(x25, x22, u64(fiat.u1(x33))) + x36 := (u64(fiat.u1(x35)) + x23) + _, x38 := bits.add_u64(x11, x28, u64(0x0)) + x39, x40 := bits.add_u64(x13, x30, u64(fiat.u1(x38))) + x41, x42 := bits.add_u64(x15, x32, u64(fiat.u1(x40))) + x43, x44 := bits.add_u64(x17, x34, u64(fiat.u1(x42))) + x45, x46 := bits.add_u64(x19, x36, u64(fiat.u1(x44))) + x48, x47 := bits.mul_u64(x1, arg2[3]) + x50, x49 := bits.mul_u64(x1, arg2[2]) + x52, x51 := bits.mul_u64(x1, arg2[1]) + x54, x53 := bits.mul_u64(x1, arg2[0]) + x55, x56 := bits.add_u64(x54, x51, u64(0x0)) + x57, x58 := bits.add_u64(x52, x49, u64(fiat.u1(x56))) + x59, x60 := bits.add_u64(x50, x47, u64(fiat.u1(x58))) + x61 := (u64(fiat.u1(x60)) + x48) + x62, x63 := bits.add_u64(x39, x53, u64(0x0)) + x64, x65 := bits.add_u64(x41, x55, u64(fiat.u1(x63))) + x66, x67 := bits.add_u64(x43, x57, u64(fiat.u1(x65))) + x68, x69 := bits.add_u64(x45, x59, u64(fiat.u1(x67))) + x70, x71 := bits.add_u64(u64(fiat.u1(x46)), x61, u64(fiat.u1(x69))) + _, x72 := bits.mul_u64(x62, 0xccd1c8aaee00bc4f) + x75, x74 := bits.mul_u64(x72, 0xffffffff00000000) + x77, x76 := bits.mul_u64(x72, 0xffffffffffffffff) + x79, x78 := bits.mul_u64(x72, 0xbce6faada7179e84) + x81, x80 := bits.mul_u64(x72, 0xf3b9cac2fc632551) + x82, x83 := bits.add_u64(x81, x78, u64(0x0)) + x84, x85 := bits.add_u64(x79, x76, u64(fiat.u1(x83))) + x86, x87 := bits.add_u64(x77, x74, u64(fiat.u1(x85))) + x88 := (u64(fiat.u1(x87)) + x75) + _, x90 := bits.add_u64(x62, x80, u64(0x0)) + x91, x92 := bits.add_u64(x64, x82, u64(fiat.u1(x90))) + x93, x94 := bits.add_u64(x66, x84, u64(fiat.u1(x92))) + x95, x96 := bits.add_u64(x68, x86, u64(fiat.u1(x94))) + x97, x98 := bits.add_u64(x70, x88, u64(fiat.u1(x96))) + x99 := (u64(fiat.u1(x98)) + u64(fiat.u1(x71))) + x101, x100 := bits.mul_u64(x2, arg2[3]) + x103, x102 := bits.mul_u64(x2, arg2[2]) + x105, x104 := bits.mul_u64(x2, arg2[1]) + x107, x106 := bits.mul_u64(x2, arg2[0]) + x108, x109 := bits.add_u64(x107, x104, u64(0x0)) + x110, x111 := bits.add_u64(x105, x102, u64(fiat.u1(x109))) + x112, x113 := bits.add_u64(x103, x100, u64(fiat.u1(x111))) + x114 := (u64(fiat.u1(x113)) + x101) + x115, x116 := bits.add_u64(x91, x106, u64(0x0)) + x117, x118 := bits.add_u64(x93, x108, u64(fiat.u1(x116))) + x119, x120 := bits.add_u64(x95, x110, u64(fiat.u1(x118))) + x121, x122 := bits.add_u64(x97, x112, u64(fiat.u1(x120))) + x123, x124 := bits.add_u64(x99, x114, u64(fiat.u1(x122))) + _, x125 := bits.mul_u64(x115, 0xccd1c8aaee00bc4f) + x128, x127 := bits.mul_u64(x125, 0xffffffff00000000) + x130, x129 := bits.mul_u64(x125, 0xffffffffffffffff) + x132, x131 := bits.mul_u64(x125, 0xbce6faada7179e84) + x134, x133 := bits.mul_u64(x125, 0xf3b9cac2fc632551) + x135, x136 := bits.add_u64(x134, x131, u64(0x0)) + x137, x138 := bits.add_u64(x132, x129, u64(fiat.u1(x136))) + x139, x140 := bits.add_u64(x130, x127, u64(fiat.u1(x138))) + x141 := (u64(fiat.u1(x140)) + x128) + _, x143 := bits.add_u64(x115, x133, u64(0x0)) + x144, x145 := bits.add_u64(x117, x135, u64(fiat.u1(x143))) + x146, x147 := bits.add_u64(x119, x137, u64(fiat.u1(x145))) + x148, x149 := bits.add_u64(x121, x139, u64(fiat.u1(x147))) + x150, x151 := bits.add_u64(x123, x141, u64(fiat.u1(x149))) + x152 := (u64(fiat.u1(x151)) + u64(fiat.u1(x124))) + x154, x153 := bits.mul_u64(x3, arg2[3]) + x156, x155 := bits.mul_u64(x3, arg2[2]) + x158, x157 := bits.mul_u64(x3, arg2[1]) + x160, x159 := bits.mul_u64(x3, arg2[0]) + x161, x162 := bits.add_u64(x160, x157, u64(0x0)) + x163, x164 := bits.add_u64(x158, x155, u64(fiat.u1(x162))) + x165, x166 := bits.add_u64(x156, x153, u64(fiat.u1(x164))) + x167 := (u64(fiat.u1(x166)) + x154) + x168, x169 := bits.add_u64(x144, x159, u64(0x0)) + x170, x171 := bits.add_u64(x146, x161, u64(fiat.u1(x169))) + x172, x173 := bits.add_u64(x148, x163, u64(fiat.u1(x171))) + x174, x175 := bits.add_u64(x150, x165, u64(fiat.u1(x173))) + x176, x177 := bits.add_u64(x152, x167, u64(fiat.u1(x175))) + _, x178 := bits.mul_u64(x168, 0xccd1c8aaee00bc4f) + x181, x180 := bits.mul_u64(x178, 0xffffffff00000000) + x183, x182 := bits.mul_u64(x178, 0xffffffffffffffff) + x185, x184 := bits.mul_u64(x178, 0xbce6faada7179e84) + x187, x186 := bits.mul_u64(x178, 0xf3b9cac2fc632551) + x188, x189 := bits.add_u64(x187, x184, u64(0x0)) + x190, x191 := bits.add_u64(x185, x182, u64(fiat.u1(x189))) + x192, x193 := bits.add_u64(x183, x180, u64(fiat.u1(x191))) + x194 := (u64(fiat.u1(x193)) + x181) + _, x196 := bits.add_u64(x168, x186, u64(0x0)) + x197, x198 := bits.add_u64(x170, x188, u64(fiat.u1(x196))) + x199, x200 := bits.add_u64(x172, x190, u64(fiat.u1(x198))) + x201, x202 := bits.add_u64(x174, x192, u64(fiat.u1(x200))) + x203, x204 := bits.add_u64(x176, x194, u64(fiat.u1(x202))) + x205 := (u64(fiat.u1(x204)) + u64(fiat.u1(x177))) + x206, x207 := bits.sub_u64(x197, 0xf3b9cac2fc632551, u64(0x0)) + x208, x209 := bits.sub_u64(x199, 0xbce6faada7179e84, u64(fiat.u1(x207))) + x210, x211 := bits.sub_u64(x201, 0xffffffffffffffff, u64(fiat.u1(x209))) + x212, x213 := bits.sub_u64(x203, 0xffffffff00000000, u64(fiat.u1(x211))) + _, x215 := bits.sub_u64(x205, u64(0x0), u64(fiat.u1(x213))) + x216 := fiat.cmovznz_u64(fiat.u1(x215), x206, x197) + x217 := fiat.cmovznz_u64(fiat.u1(x215), x208, x199) + x218 := fiat.cmovznz_u64(fiat.u1(x215), x210, x201) + x219 := fiat.cmovznz_u64(fiat.u1(x215), x212, x203) + out1[0] = x216 + out1[1] = x217 + out1[2] = x218 + out1[3] = x219 +} + +fe_square :: proc "contextless" (out1, arg1: ^Montgomery_Domain_Field_Element) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[0] + x6, x5 := bits.mul_u64(x4, arg1[3]) + x8, x7 := bits.mul_u64(x4, arg1[2]) + x10, x9 := bits.mul_u64(x4, arg1[1]) + x12, x11 := bits.mul_u64(x4, arg1[0]) + x13, x14 := bits.add_u64(x12, x9, u64(0x0)) + x15, x16 := bits.add_u64(x10, x7, u64(fiat.u1(x14))) + x17, x18 := bits.add_u64(x8, x5, u64(fiat.u1(x16))) + x19 := (u64(fiat.u1(x18)) + x6) + _, x20 := bits.mul_u64(x11, 0xccd1c8aaee00bc4f) + x23, x22 := bits.mul_u64(x20, 0xffffffff00000000) + x25, x24 := bits.mul_u64(x20, 0xffffffffffffffff) + x27, x26 := bits.mul_u64(x20, 0xbce6faada7179e84) + x29, x28 := bits.mul_u64(x20, 0xf3b9cac2fc632551) + x30, x31 := bits.add_u64(x29, x26, u64(0x0)) + x32, x33 := bits.add_u64(x27, x24, u64(fiat.u1(x31))) + x34, x35 := bits.add_u64(x25, x22, u64(fiat.u1(x33))) + x36 := (u64(fiat.u1(x35)) + x23) + _, x38 := bits.add_u64(x11, x28, u64(0x0)) + x39, x40 := bits.add_u64(x13, x30, u64(fiat.u1(x38))) + x41, x42 := bits.add_u64(x15, x32, u64(fiat.u1(x40))) + x43, x44 := bits.add_u64(x17, x34, u64(fiat.u1(x42))) + x45, x46 := bits.add_u64(x19, x36, u64(fiat.u1(x44))) + x48, x47 := bits.mul_u64(x1, arg1[3]) + x50, x49 := bits.mul_u64(x1, arg1[2]) + x52, x51 := bits.mul_u64(x1, arg1[1]) + x54, x53 := bits.mul_u64(x1, arg1[0]) + x55, x56 := bits.add_u64(x54, x51, u64(0x0)) + x57, x58 := bits.add_u64(x52, x49, u64(fiat.u1(x56))) + x59, x60 := bits.add_u64(x50, x47, u64(fiat.u1(x58))) + x61 := (u64(fiat.u1(x60)) + x48) + x62, x63 := bits.add_u64(x39, x53, u64(0x0)) + x64, x65 := bits.add_u64(x41, x55, u64(fiat.u1(x63))) + x66, x67 := bits.add_u64(x43, x57, u64(fiat.u1(x65))) + x68, x69 := bits.add_u64(x45, x59, u64(fiat.u1(x67))) + x70, x71 := bits.add_u64(u64(fiat.u1(x46)), x61, u64(fiat.u1(x69))) + _, x72 := bits.mul_u64(x62, 0xccd1c8aaee00bc4f) + x75, x74 := bits.mul_u64(x72, 0xffffffff00000000) + x77, x76 := bits.mul_u64(x72, 0xffffffffffffffff) + x79, x78 := bits.mul_u64(x72, 0xbce6faada7179e84) + x81, x80 := bits.mul_u64(x72, 0xf3b9cac2fc632551) + x82, x83 := bits.add_u64(x81, x78, u64(0x0)) + x84, x85 := bits.add_u64(x79, x76, u64(fiat.u1(x83))) + x86, x87 := bits.add_u64(x77, x74, u64(fiat.u1(x85))) + x88 := (u64(fiat.u1(x87)) + x75) + _, x90 := bits.add_u64(x62, x80, u64(0x0)) + x91, x92 := bits.add_u64(x64, x82, u64(fiat.u1(x90))) + x93, x94 := bits.add_u64(x66, x84, u64(fiat.u1(x92))) + x95, x96 := bits.add_u64(x68, x86, u64(fiat.u1(x94))) + x97, x98 := bits.add_u64(x70, x88, u64(fiat.u1(x96))) + x99 := (u64(fiat.u1(x98)) + u64(fiat.u1(x71))) + x101, x100 := bits.mul_u64(x2, arg1[3]) + x103, x102 := bits.mul_u64(x2, arg1[2]) + x105, x104 := bits.mul_u64(x2, arg1[1]) + x107, x106 := bits.mul_u64(x2, arg1[0]) + x108, x109 := bits.add_u64(x107, x104, u64(0x0)) + x110, x111 := bits.add_u64(x105, x102, u64(fiat.u1(x109))) + x112, x113 := bits.add_u64(x103, x100, u64(fiat.u1(x111))) + x114 := (u64(fiat.u1(x113)) + x101) + x115, x116 := bits.add_u64(x91, x106, u64(0x0)) + x117, x118 := bits.add_u64(x93, x108, u64(fiat.u1(x116))) + x119, x120 := bits.add_u64(x95, x110, u64(fiat.u1(x118))) + x121, x122 := bits.add_u64(x97, x112, u64(fiat.u1(x120))) + x123, x124 := bits.add_u64(x99, x114, u64(fiat.u1(x122))) + _, x125 := bits.mul_u64(x115, 0xccd1c8aaee00bc4f) + x128, x127 := bits.mul_u64(x125, 0xffffffff00000000) + x130, x129 := bits.mul_u64(x125, 0xffffffffffffffff) + x132, x131 := bits.mul_u64(x125, 0xbce6faada7179e84) + x134, x133 := bits.mul_u64(x125, 0xf3b9cac2fc632551) + x135, x136 := bits.add_u64(x134, x131, u64(0x0)) + x137, x138 := bits.add_u64(x132, x129, u64(fiat.u1(x136))) + x139, x140 := bits.add_u64(x130, x127, u64(fiat.u1(x138))) + x141 := (u64(fiat.u1(x140)) + x128) + _, x143 := bits.add_u64(x115, x133, u64(0x0)) + x144, x145 := bits.add_u64(x117, x135, u64(fiat.u1(x143))) + x146, x147 := bits.add_u64(x119, x137, u64(fiat.u1(x145))) + x148, x149 := bits.add_u64(x121, x139, u64(fiat.u1(x147))) + x150, x151 := bits.add_u64(x123, x141, u64(fiat.u1(x149))) + x152 := (u64(fiat.u1(x151)) + u64(fiat.u1(x124))) + x154, x153 := bits.mul_u64(x3, arg1[3]) + x156, x155 := bits.mul_u64(x3, arg1[2]) + x158, x157 := bits.mul_u64(x3, arg1[1]) + x160, x159 := bits.mul_u64(x3, arg1[0]) + x161, x162 := bits.add_u64(x160, x157, u64(0x0)) + x163, x164 := bits.add_u64(x158, x155, u64(fiat.u1(x162))) + x165, x166 := bits.add_u64(x156, x153, u64(fiat.u1(x164))) + x167 := (u64(fiat.u1(x166)) + x154) + x168, x169 := bits.add_u64(x144, x159, u64(0x0)) + x170, x171 := bits.add_u64(x146, x161, u64(fiat.u1(x169))) + x172, x173 := bits.add_u64(x148, x163, u64(fiat.u1(x171))) + x174, x175 := bits.add_u64(x150, x165, u64(fiat.u1(x173))) + x176, x177 := bits.add_u64(x152, x167, u64(fiat.u1(x175))) + _, x178 := bits.mul_u64(x168, 0xccd1c8aaee00bc4f) + x181, x180 := bits.mul_u64(x178, 0xffffffff00000000) + x183, x182 := bits.mul_u64(x178, 0xffffffffffffffff) + x185, x184 := bits.mul_u64(x178, 0xbce6faada7179e84) + x187, x186 := bits.mul_u64(x178, 0xf3b9cac2fc632551) + x188, x189 := bits.add_u64(x187, x184, u64(0x0)) + x190, x191 := bits.add_u64(x185, x182, u64(fiat.u1(x189))) + x192, x193 := bits.add_u64(x183, x180, u64(fiat.u1(x191))) + x194 := (u64(fiat.u1(x193)) + x181) + _, x196 := bits.add_u64(x168, x186, u64(0x0)) + x197, x198 := bits.add_u64(x170, x188, u64(fiat.u1(x196))) + x199, x200 := bits.add_u64(x172, x190, u64(fiat.u1(x198))) + x201, x202 := bits.add_u64(x174, x192, u64(fiat.u1(x200))) + x203, x204 := bits.add_u64(x176, x194, u64(fiat.u1(x202))) + x205 := (u64(fiat.u1(x204)) + u64(fiat.u1(x177))) + x206, x207 := bits.sub_u64(x197, 0xf3b9cac2fc632551, u64(0x0)) + x208, x209 := bits.sub_u64(x199, 0xbce6faada7179e84, u64(fiat.u1(x207))) + x210, x211 := bits.sub_u64(x201, 0xffffffffffffffff, u64(fiat.u1(x209))) + x212, x213 := bits.sub_u64(x203, 0xffffffff00000000, u64(fiat.u1(x211))) + _, x215 := bits.sub_u64(x205, u64(0x0), u64(fiat.u1(x213))) + x216 := fiat.cmovznz_u64(fiat.u1(x215), x206, x197) + x217 := fiat.cmovznz_u64(fiat.u1(x215), x208, x199) + x218 := fiat.cmovznz_u64(fiat.u1(x215), x210, x201) + x219 := fiat.cmovznz_u64(fiat.u1(x215), x212, x203) + out1[0] = x216 + out1[1] = x217 + out1[2] = x218 + out1[3] = x219 +} + +fe_add :: proc "contextless" (out1, arg1, arg2: ^Montgomery_Domain_Field_Element) { + x1, x2 := bits.add_u64(arg1[0], arg2[0], u64(0x0)) + x3, x4 := bits.add_u64(arg1[1], arg2[1], u64(fiat.u1(x2))) + x5, x6 := bits.add_u64(arg1[2], arg2[2], u64(fiat.u1(x4))) + x7, x8 := bits.add_u64(arg1[3], arg2[3], u64(fiat.u1(x6))) + x9, x10 := bits.sub_u64(x1, 0xf3b9cac2fc632551, u64(0x0)) + x11, x12 := bits.sub_u64(x3, 0xbce6faada7179e84, u64(fiat.u1(x10))) + x13, x14 := bits.sub_u64(x5, 0xffffffffffffffff, u64(fiat.u1(x12))) + x15, x16 := bits.sub_u64(x7, 0xffffffff00000000, u64(fiat.u1(x14))) + _, x18 := bits.sub_u64(u64(fiat.u1(x8)), u64(0x0), u64(fiat.u1(x16))) + x19 := fiat.cmovznz_u64(fiat.u1(x18), x9, x1) + x20 := fiat.cmovznz_u64(fiat.u1(x18), x11, x3) + x21 := fiat.cmovznz_u64(fiat.u1(x18), x13, x5) + x22 := fiat.cmovznz_u64(fiat.u1(x18), x15, x7) + out1[0] = x19 + out1[1] = x20 + out1[2] = x21 + out1[3] = x22 +} + +fe_sub :: proc "contextless" (out1, arg1, arg2: ^Montgomery_Domain_Field_Element) { + x1, x2 := bits.sub_u64(arg1[0], arg2[0], u64(0x0)) + x3, x4 := bits.sub_u64(arg1[1], arg2[1], u64(fiat.u1(x2))) + x5, x6 := bits.sub_u64(arg1[2], arg2[2], u64(fiat.u1(x4))) + x7, x8 := bits.sub_u64(arg1[3], arg2[3], u64(fiat.u1(x6))) + x9 := fiat.cmovznz_u64(fiat.u1(x8), u64(0x0), 0xffffffffffffffff) + x10, x11 := bits.add_u64(x1, (x9 & 0xf3b9cac2fc632551), u64(0x0)) + x12, x13 := bits.add_u64(x3, (x9 & 0xbce6faada7179e84), u64(fiat.u1(x11))) + x14, x15 := bits.add_u64(x5, x9, u64(fiat.u1(x13))) + x16, _ := bits.add_u64(x7, (x9 & 0xffffffff00000000), u64(fiat.u1(x15))) + out1[0] = x10 + out1[1] = x12 + out1[2] = x14 + out1[3] = x16 +} + +fe_opp :: proc "contextless" (out1, arg1: ^Montgomery_Domain_Field_Element) { + x1, x2 := bits.sub_u64(u64(0x0), arg1[0], u64(0x0)) + x3, x4 := bits.sub_u64(u64(0x0), arg1[1], u64(fiat.u1(x2))) + x5, x6 := bits.sub_u64(u64(0x0), arg1[2], u64(fiat.u1(x4))) + x7, x8 := bits.sub_u64(u64(0x0), arg1[3], u64(fiat.u1(x6))) + x9 := fiat.cmovznz_u64(fiat.u1(x8), u64(0x0), 0xffffffffffffffff) + x10, x11 := bits.add_u64(x1, (x9 & 0xf3b9cac2fc632551), u64(0x0)) + x12, x13 := bits.add_u64(x3, (x9 & 0xbce6faada7179e84), u64(fiat.u1(x11))) + x14, x15 := bits.add_u64(x5, x9, u64(fiat.u1(x13))) + x16, _ := bits.add_u64(x7, (x9 & 0xffffffff00000000), u64(fiat.u1(x15))) + out1[0] = x10 + out1[1] = x12 + out1[2] = x14 + out1[3] = x16 +} + +fe_one :: proc "contextless" (out1: ^Montgomery_Domain_Field_Element) { + out1[0] = 0xc46353d039cdaaf + out1[1] = 0x4319055258e8617b + out1[2] = u64(0x0) + out1[3] = 0xffffffff +} + +fe_non_zero :: proc "contextless" (arg1: ^Montgomery_Domain_Field_Element) -> u64 { + return arg1[0] | (arg1[1] | (arg1[2] | arg1[3])) +} + +@(optimization_mode = "none") +fe_cond_assign :: #force_no_inline proc "contextless" ( + out1, arg1: ^Montgomery_Domain_Field_Element, + arg2: int, +) { + x1 := fiat.cmovznz_u64(fiat.u1(arg2), out1[0], arg1[0]) + x2 := fiat.cmovznz_u64(fiat.u1(arg2), out1[1], arg1[1]) + x3 := fiat.cmovznz_u64(fiat.u1(arg2), out1[2], arg1[2]) + x4 := fiat.cmovznz_u64(fiat.u1(arg2), out1[3], arg1[3]) + out1[0] = x1 + out1[1] = x2 + out1[2] = x3 + out1[3] = x4 +} + +fe_from_montgomery :: proc "contextless" ( + out1: ^Non_Montgomery_Domain_Field_Element, + arg1: ^Montgomery_Domain_Field_Element, +) { + x1 := arg1[0] + _, x2 := bits.mul_u64(x1, 0xccd1c8aaee00bc4f) + x5, x4 := bits.mul_u64(x2, 0xffffffff00000000) + x7, x6 := bits.mul_u64(x2, 0xffffffffffffffff) + x9, x8 := bits.mul_u64(x2, 0xbce6faada7179e84) + x11, x10 := bits.mul_u64(x2, 0xf3b9cac2fc632551) + x12, x13 := bits.add_u64(x11, x8, u64(0x0)) + x14, x15 := bits.add_u64(x9, x6, u64(fiat.u1(x13))) + x16, x17 := bits.add_u64(x7, x4, u64(fiat.u1(x15))) + _, x19 := bits.add_u64(x1, x10, u64(0x0)) + x20, x21 := bits.add_u64(u64(0x0), x12, u64(fiat.u1(x19))) + x22, x23 := bits.add_u64(u64(0x0), x14, u64(fiat.u1(x21))) + x24, x25 := bits.add_u64(u64(0x0), x16, u64(fiat.u1(x23))) + x26, x27 := bits.add_u64(x20, arg1[1], u64(0x0)) + x28, x29 := bits.add_u64(x22, u64(0x0), u64(fiat.u1(x27))) + x30, x31 := bits.add_u64(x24, u64(0x0), u64(fiat.u1(x29))) + _, x32 := bits.mul_u64(x26, 0xccd1c8aaee00bc4f) + x35, x34 := bits.mul_u64(x32, 0xffffffff00000000) + x37, x36 := bits.mul_u64(x32, 0xffffffffffffffff) + x39, x38 := bits.mul_u64(x32, 0xbce6faada7179e84) + x41, x40 := bits.mul_u64(x32, 0xf3b9cac2fc632551) + x42, x43 := bits.add_u64(x41, x38, u64(0x0)) + x44, x45 := bits.add_u64(x39, x36, u64(fiat.u1(x43))) + x46, x47 := bits.add_u64(x37, x34, u64(fiat.u1(x45))) + _, x49 := bits.add_u64(x26, x40, u64(0x0)) + x50, x51 := bits.add_u64(x28, x42, u64(fiat.u1(x49))) + x52, x53 := bits.add_u64(x30, x44, u64(fiat.u1(x51))) + x54, x55 := bits.add_u64((u64(fiat.u1(x31)) + (u64(fiat.u1(x25)) + (u64(fiat.u1(x17)) + x5))), x46, u64(fiat.u1(x53))) + x56, x57 := bits.add_u64(x50, arg1[2], u64(0x0)) + x58, x59 := bits.add_u64(x52, u64(0x0), u64(fiat.u1(x57))) + x60, x61 := bits.add_u64(x54, u64(0x0), u64(fiat.u1(x59))) + _, x62 := bits.mul_u64(x56, 0xccd1c8aaee00bc4f) + x65, x64 := bits.mul_u64(x62, 0xffffffff00000000) + x67, x66 := bits.mul_u64(x62, 0xffffffffffffffff) + x69, x68 := bits.mul_u64(x62, 0xbce6faada7179e84) + x71, x70 := bits.mul_u64(x62, 0xf3b9cac2fc632551) + x72, x73 := bits.add_u64(x71, x68, u64(0x0)) + x74, x75 := bits.add_u64(x69, x66, u64(fiat.u1(x73))) + x76, x77 := bits.add_u64(x67, x64, u64(fiat.u1(x75))) + _, x79 := bits.add_u64(x56, x70, u64(0x0)) + x80, x81 := bits.add_u64(x58, x72, u64(fiat.u1(x79))) + x82, x83 := bits.add_u64(x60, x74, u64(fiat.u1(x81))) + x84, x85 := bits.add_u64((u64(fiat.u1(x61)) + (u64(fiat.u1(x55)) + (u64(fiat.u1(x47)) + x35))), x76, u64(fiat.u1(x83))) + x86, x87 := bits.add_u64(x80, arg1[3], u64(0x0)) + x88, x89 := bits.add_u64(x82, u64(0x0), u64(fiat.u1(x87))) + x90, x91 := bits.add_u64(x84, u64(0x0), u64(fiat.u1(x89))) + _, x92 := bits.mul_u64(x86, 0xccd1c8aaee00bc4f) + x95, x94 := bits.mul_u64(x92, 0xffffffff00000000) + x97, x96 := bits.mul_u64(x92, 0xffffffffffffffff) + x99, x98 := bits.mul_u64(x92, 0xbce6faada7179e84) + x101, x100 := bits.mul_u64(x92, 0xf3b9cac2fc632551) + x102, x103 := bits.add_u64(x101, x98, u64(0x0)) + x104, x105 := bits.add_u64(x99, x96, u64(fiat.u1(x103))) + x106, x107 := bits.add_u64(x97, x94, u64(fiat.u1(x105))) + _, x109 := bits.add_u64(x86, x100, u64(0x0)) + x110, x111 := bits.add_u64(x88, x102, u64(fiat.u1(x109))) + x112, x113 := bits.add_u64(x90, x104, u64(fiat.u1(x111))) + x114, x115 := bits.add_u64((u64(fiat.u1(x91)) + (u64(fiat.u1(x85)) + (u64(fiat.u1(x77)) + x65))), x106, u64(fiat.u1(x113))) + x116 := (u64(fiat.u1(x115)) + (u64(fiat.u1(x107)) + x95)) + x117, x118 := bits.sub_u64(x110, 0xf3b9cac2fc632551, u64(0x0)) + x119, x120 := bits.sub_u64(x112, 0xbce6faada7179e84, u64(fiat.u1(x118))) + x121, x122 := bits.sub_u64(x114, 0xffffffffffffffff, u64(fiat.u1(x120))) + x123, x124 := bits.sub_u64(x116, 0xffffffff00000000, u64(fiat.u1(x122))) + _, x126 := bits.sub_u64(u64(0x0), u64(0x0), u64(fiat.u1(x124))) + x127 := fiat.cmovznz_u64(fiat.u1(x126), x117, x110) + x128 := fiat.cmovznz_u64(fiat.u1(x126), x119, x112) + x129 := fiat.cmovznz_u64(fiat.u1(x126), x121, x114) + x130 := fiat.cmovznz_u64(fiat.u1(x126), x123, x116) + out1[0] = x127 + out1[1] = x128 + out1[2] = x129 + out1[3] = x130 +} + +fe_to_montgomery :: proc "contextless" ( + out1: ^Montgomery_Domain_Field_Element, + arg1: ^Non_Montgomery_Domain_Field_Element, +) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[0] + x6, x5 := bits.mul_u64(x4, 0x66e12d94f3d95620) + x8, x7 := bits.mul_u64(x4, 0x2845b2392b6bec59) + x10, x9 := bits.mul_u64(x4, 0x4699799c49bd6fa6) + x12, x11 := bits.mul_u64(x4, 0x83244c95be79eea2) + x13, x14 := bits.add_u64(x12, x9, u64(0x0)) + x15, x16 := bits.add_u64(x10, x7, u64(fiat.u1(x14))) + x17, x18 := bits.add_u64(x8, x5, u64(fiat.u1(x16))) + _, x19 := bits.mul_u64(x11, 0xccd1c8aaee00bc4f) + x22, x21 := bits.mul_u64(x19, 0xffffffff00000000) + x24, x23 := bits.mul_u64(x19, 0xffffffffffffffff) + x26, x25 := bits.mul_u64(x19, 0xbce6faada7179e84) + x28, x27 := bits.mul_u64(x19, 0xf3b9cac2fc632551) + x29, x30 := bits.add_u64(x28, x25, u64(0x0)) + x31, x32 := bits.add_u64(x26, x23, u64(fiat.u1(x30))) + x33, x34 := bits.add_u64(x24, x21, u64(fiat.u1(x32))) + _, x36 := bits.add_u64(x11, x27, u64(0x0)) + x37, x38 := bits.add_u64(x13, x29, u64(fiat.u1(x36))) + x39, x40 := bits.add_u64(x15, x31, u64(fiat.u1(x38))) + x41, x42 := bits.add_u64(x17, x33, u64(fiat.u1(x40))) + x43, x44 := bits.add_u64((u64(fiat.u1(x18)) + x6), (u64(fiat.u1(x34)) + x22), u64(fiat.u1(x42))) + x46, x45 := bits.mul_u64(x1, 0x66e12d94f3d95620) + x48, x47 := bits.mul_u64(x1, 0x2845b2392b6bec59) + x50, x49 := bits.mul_u64(x1, 0x4699799c49bd6fa6) + x52, x51 := bits.mul_u64(x1, 0x83244c95be79eea2) + x53, x54 := bits.add_u64(x52, x49, u64(0x0)) + x55, x56 := bits.add_u64(x50, x47, u64(fiat.u1(x54))) + x57, x58 := bits.add_u64(x48, x45, u64(fiat.u1(x56))) + x59, x60 := bits.add_u64(x37, x51, u64(0x0)) + x61, x62 := bits.add_u64(x39, x53, u64(fiat.u1(x60))) + x63, x64 := bits.add_u64(x41, x55, u64(fiat.u1(x62))) + x65, x66 := bits.add_u64(x43, x57, u64(fiat.u1(x64))) + _, x67 := bits.mul_u64(x59, 0xccd1c8aaee00bc4f) + x70, x69 := bits.mul_u64(x67, 0xffffffff00000000) + x72, x71 := bits.mul_u64(x67, 0xffffffffffffffff) + x74, x73 := bits.mul_u64(x67, 0xbce6faada7179e84) + x76, x75 := bits.mul_u64(x67, 0xf3b9cac2fc632551) + x77, x78 := bits.add_u64(x76, x73, u64(0x0)) + x79, x80 := bits.add_u64(x74, x71, u64(fiat.u1(x78))) + x81, x82 := bits.add_u64(x72, x69, u64(fiat.u1(x80))) + _, x84 := bits.add_u64(x59, x75, u64(0x0)) + x85, x86 := bits.add_u64(x61, x77, u64(fiat.u1(x84))) + x87, x88 := bits.add_u64(x63, x79, u64(fiat.u1(x86))) + x89, x90 := bits.add_u64(x65, x81, u64(fiat.u1(x88))) + x91, x92 := bits.add_u64(((u64(fiat.u1(x66)) + u64(fiat.u1(x44))) + (u64(fiat.u1(x58)) + x46)), (u64(fiat.u1(x82)) + x70), u64(fiat.u1(x90))) + x94, x93 := bits.mul_u64(x2, 0x66e12d94f3d95620) + x96, x95 := bits.mul_u64(x2, 0x2845b2392b6bec59) + x98, x97 := bits.mul_u64(x2, 0x4699799c49bd6fa6) + x100, x99 := bits.mul_u64(x2, 0x83244c95be79eea2) + x101, x102 := bits.add_u64(x100, x97, u64(0x0)) + x103, x104 := bits.add_u64(x98, x95, u64(fiat.u1(x102))) + x105, x106 := bits.add_u64(x96, x93, u64(fiat.u1(x104))) + x107, x108 := bits.add_u64(x85, x99, u64(0x0)) + x109, x110 := bits.add_u64(x87, x101, u64(fiat.u1(x108))) + x111, x112 := bits.add_u64(x89, x103, u64(fiat.u1(x110))) + x113, x114 := bits.add_u64(x91, x105, u64(fiat.u1(x112))) + _, x115 := bits.mul_u64(x107, 0xccd1c8aaee00bc4f) + x118, x117 := bits.mul_u64(x115, 0xffffffff00000000) + x120, x119 := bits.mul_u64(x115, 0xffffffffffffffff) + x122, x121 := bits.mul_u64(x115, 0xbce6faada7179e84) + x124, x123 := bits.mul_u64(x115, 0xf3b9cac2fc632551) + x125, x126 := bits.add_u64(x124, x121, u64(0x0)) + x127, x128 := bits.add_u64(x122, x119, u64(fiat.u1(x126))) + x129, x130 := bits.add_u64(x120, x117, u64(fiat.u1(x128))) + _, x132 := bits.add_u64(x107, x123, u64(0x0)) + x133, x134 := bits.add_u64(x109, x125, u64(fiat.u1(x132))) + x135, x136 := bits.add_u64(x111, x127, u64(fiat.u1(x134))) + x137, x138 := bits.add_u64(x113, x129, u64(fiat.u1(x136))) + x139, x140 := bits.add_u64(((u64(fiat.u1(x114)) + u64(fiat.u1(x92))) + (u64(fiat.u1(x106)) + x94)), (u64(fiat.u1(x130)) + x118), u64(fiat.u1(x138))) + x142, x141 := bits.mul_u64(x3, 0x66e12d94f3d95620) + x144, x143 := bits.mul_u64(x3, 0x2845b2392b6bec59) + x146, x145 := bits.mul_u64(x3, 0x4699799c49bd6fa6) + x148, x147 := bits.mul_u64(x3, 0x83244c95be79eea2) + x149, x150 := bits.add_u64(x148, x145, u64(0x0)) + x151, x152 := bits.add_u64(x146, x143, u64(fiat.u1(x150))) + x153, x154 := bits.add_u64(x144, x141, u64(fiat.u1(x152))) + x155, x156 := bits.add_u64(x133, x147, u64(0x0)) + x157, x158 := bits.add_u64(x135, x149, u64(fiat.u1(x156))) + x159, x160 := bits.add_u64(x137, x151, u64(fiat.u1(x158))) + x161, x162 := bits.add_u64(x139, x153, u64(fiat.u1(x160))) + _, x163 := bits.mul_u64(x155, 0xccd1c8aaee00bc4f) + x166, x165 := bits.mul_u64(x163, 0xffffffff00000000) + x168, x167 := bits.mul_u64(x163, 0xffffffffffffffff) + x170, x169 := bits.mul_u64(x163, 0xbce6faada7179e84) + x172, x171 := bits.mul_u64(x163, 0xf3b9cac2fc632551) + x173, x174 := bits.add_u64(x172, x169, u64(0x0)) + x175, x176 := bits.add_u64(x170, x167, u64(fiat.u1(x174))) + x177, x178 := bits.add_u64(x168, x165, u64(fiat.u1(x176))) + _, x180 := bits.add_u64(x155, x171, u64(0x0)) + x181, x182 := bits.add_u64(x157, x173, u64(fiat.u1(x180))) + x183, x184 := bits.add_u64(x159, x175, u64(fiat.u1(x182))) + x185, x186 := bits.add_u64(x161, x177, u64(fiat.u1(x184))) + x187, x188 := bits.add_u64(((u64(fiat.u1(x162)) + u64(fiat.u1(x140))) + (u64(fiat.u1(x154)) + x142)), (u64(fiat.u1(x178)) + x166), u64(fiat.u1(x186))) + x189, x190 := bits.sub_u64(x181, 0xf3b9cac2fc632551, u64(0x0)) + x191, x192 := bits.sub_u64(x183, 0xbce6faada7179e84, u64(fiat.u1(x190))) + x193, x194 := bits.sub_u64(x185, 0xffffffffffffffff, u64(fiat.u1(x192))) + x195, x196 := bits.sub_u64(x187, 0xffffffff00000000, u64(fiat.u1(x194))) + _, x198 := bits.sub_u64(u64(fiat.u1(x188)), u64(0x0), u64(fiat.u1(x196))) + x199 := fiat.cmovznz_u64(fiat.u1(x198), x189, x181) + x200 := fiat.cmovznz_u64(fiat.u1(x198), x191, x183) + x201 := fiat.cmovznz_u64(fiat.u1(x198), x193, x185) + x202 := fiat.cmovznz_u64(fiat.u1(x198), x195, x187) + out1[0] = x199 + out1[1] = x200 + out1[2] = x201 + out1[3] = x202 +} diff --git a/core/crypto/_weierstrass/fe.odin b/core/crypto/_weierstrass/fe.odin new file mode 100644 index 000000000..1a160a03c --- /dev/null +++ b/core/crypto/_weierstrass/fe.odin @@ -0,0 +1,135 @@ +package _weierstrass + +import p256r1 "core:crypto/_fiat/field_p256r1" +import "core:math/bits" + +Field_Element_p256r1 :: p256r1.Montgomery_Domain_Field_Element + +FE_SIZE_P256R1 :: 32 + +fe_clear :: proc { + p256r1.fe_clear, +} + +fe_clear_vec :: proc { + p256r1.fe_clear_vec, +} + +fe_set_bytes :: proc { + p256r1.fe_from_bytes, +} +fe_bytes :: proc { + p256r1.fe_to_bytes, +} + +fe_set :: proc { + p256r1.fe_set, +} + +fe_zero :: proc { + p256r1.fe_zero, +} + +fe_a :: proc { + fe_a_p256r1, +} + +fe_b :: proc { + fe_b_p256r1, +} + +fe_gen_x :: proc { + fe_gen_x_p256r1, +} + +fe_gen_y :: proc { + fe_gen_y_p256r1, +} + +fe_one :: proc { + p256r1.fe_one, +} + +fe_add :: proc { + p256r1.fe_add, +} + +fe_sub :: proc { + p256r1.fe_sub, +} + +fe_negate :: proc { + p256r1.fe_opp, +} + +fe_mul :: proc { + p256r1.fe_mul, +} + +fe_square :: proc { + p256r1.fe_square, +} + +fe_inv :: proc { + p256r1.fe_inv, +} + +fe_sqrt :: proc { + p256r1.fe_sqrt, +} + +fe_equal :: proc { + p256r1.fe_equal, +} + +fe_is_odd :: proc { + p256r1.fe_is_odd, +} + +fe_is_zero :: proc { + fe_is_zero_p256r1, +} + +fe_cond_select :: proc { + p256r1.fe_cond_select, +} + +fe_a_p256r1 :: proc "contextless" (fe: ^Field_Element_p256r1) { + // a = 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc + // = -3 mod p + fe[0] = 18446744073709551612 + fe[1] = 17179869183 + fe[2] = 0 + fe[3] = 18446744056529682436 +} + +fe_b_p256r1 :: proc "contextless" (fe: ^Field_Element_p256r1) { + // b = 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b + fe[0] = 15608596021259845087 + fe[1] = 12461466548982526096 + fe[2] = 16546823903870267094 + fe[3] = 15866188208926050356 +} + +fe_gen_x_p256r1 :: proc "contextless" (fe: ^Field_Element_p256r1) { + // G_x = 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296 + fe[0] = 8784043285714375740 + fe[1] = 8483257759279461889 + fe[2] = 8789745728267363600 + fe[3] = 1770019616739251654 +} + +fe_gen_y_p256r1 :: proc "contextless" (fe: ^Field_Element_p256r1) { + // G_y = 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5 + fe[0] = 15992936863339206154 + fe[1] = 10037038012062884956 + fe[2] = 15197544864945402661 + fe[3] = 9615747158586711429 +} + +@(require_results) +fe_is_zero_p256r1 :: proc "contextless" (fe: ^Field_Element_p256r1) -> int { + ctrl := p256r1.fe_non_zero(fe) + _, borrow := bits.sub_u64(ctrl, 1, 0) + return int(borrow) +} diff --git a/core/crypto/_weierstrass/point.odin b/core/crypto/_weierstrass/point.odin new file mode 100644 index 000000000..cde82ebb2 --- /dev/null +++ b/core/crypto/_weierstrass/point.odin @@ -0,0 +1,548 @@ +package _weierstrass + +/* +This implements prime order short Weierstrass curves defined over a field +k with char(k) != 2, 3 (`y^2 = x^3 + ax + b`). for the purpose of +implementing ECDH and ECDSA. Use of this package for other purposes is +NOT RECOMMENDED. + +As an explicit simplicity/performance tradeoff, projective representation +was chosen so that it is possible to use the complete addition +formulas. + +See: +- https://eprint.iacr.org/2015/1060.pdf +- https://hyperelliptic.org/EFD/g1p/auto-shortw-projective.html + +WARNING: The point addition and doubling formulas are specialized for +`a = -3`, which covers secp256r1, secp384r1, secp521r1, FRP256v1, SM2, +and GOST 34.10. The brainpool curves and secp256k1 are NOT SUPPORTED +and would require slightly different formulas. +*/ + +Point_p256r1 :: struct { + x: Field_Element_p256r1, + y: Field_Element_p256r1, + z: Field_Element_p256r1, +} + +@(require_results) +pt_set_xy_bytes :: proc "contextless" (p: ^$T, x_raw, y_raw: []byte) -> bool { + when T == Point_p256r1 { + FE_SZ :: FE_SIZE_P256R1 + x, y: Field_Element_p256r1 + defer fe_clear_vec([]^Field_Element_p256r1{&x, &y}) + } else { + #panic("weierstrass: invalid curve") + } + + if len(x_raw) != FE_SZ || len(y_raw) != FE_SZ { + return false + } + + if !fe_set_bytes(&x, x_raw) { + return false + } + if !fe_set_bytes(&y, y_raw) { + return false + } + if !is_on_curve(&x, &y) { + return false + } + + fe_set(&p.x, &x) + fe_set(&p.y, &y) + fe_one(&p.z) + + return true +} + +@(require_results) +pt_set_x_bytes :: proc "contextless" (p: ^$T, x_raw: []byte, y_is_odd: int) -> bool { + when T == Point_p256r1 { + FE_SZ :: FE_SIZE_P256R1 + x, y, yy, y_neg: Field_Element_p256r1 + defer fe_clear_vec([]^Field_Element_p256r1{&x, &y, &yy, &y_neg}) + } else { + #panic("weierstrass: invalid curve") + } + + if len(x_raw) != FE_SZ { + return false + } + + if !fe_set_bytes(&x, x_raw) { + return false + } + set_yy_candidate(&yy, &x) + if fe_sqrt(&y, &yy) != 1 { + return false + } + + // Pick the correct y-coordinate. + fe_negate(&y_neg, &y) + parity_neq := (y_is_odd ~ fe_is_odd(&y)) & 1 + + fe_set(&p.x, &x) + fe_cond_select(&p.y, &y, &y_neg, parity_neq) + fe_one(&p.z) + + return true +} + +@(require_results) +pt_bytes :: proc "contextless" (x, y: []byte, p: ^$T) -> bool { + when T == Point_p256r1 { + FE_SZ :: FE_SIZE_P256R1 + } else { + #panic("weierstrass: invalid curve") + } + + if pt_is_identity(p) == 1 { + return false + } + + // Convert to affine coordinates. + pt_rescale(p, p) + + switch len(x) { + case 0: + case FE_SZ: + fe_bytes(x, &p.x) + case: + panic_contextless("weierstrass: invalid x buffer") + } + switch len(y) { + case 0: + case FE_SZ: + fe_bytes(y, &p.y) + case: + panic_contextless("weierstrass: invalid y buffer") + } + + return true +} + +pt_set :: proc "contextless" (p, q: ^$T) { + fe_set(&p.x, &q.x) + fe_set(&p.y, &q.y) + fe_set(&p.z, &q.z) +} + +pt_identity :: proc "contextless" (p: ^$T) { + fe_zero(&p.x) + fe_one(&p.y) + fe_zero(&p.z) +} + +pt_generator :: proc "contextless" (p: ^$T) { + fe_gen_x(&p.x) + fe_gen_y(&p.y) + fe_one(&p.z) +} + +pt_clear :: proc "contextless" (p: ^$T) { + fe_clear(&p.x) + fe_clear(&p.y) + fe_clear(&p.z) +} + +pt_clear_vec :: proc "contextless" (arg: []^$T) { + for p in arg { + pt_clear(p) + } +} + +pt_add :: proc "contextless" (p, a, b: ^$T) { + // Algorithm 4 from "Complete addition formulas for prime + // order elliptic curves" by Renes, Costello, and Batina. + // + // The formula is complete in that it is valid for all a and b, + // without exceptions or extra assumptions about the inputs. + // + // The operation costs are `12M + 2mb + 29a`. + + when T == Point_p256r1 { + t0, t1, t2, t3, t4, b_fe: Field_Element_p256r1 + x3, y3, z3: Field_Element_p256r1 + defer fe_clear_vec([]^Field_Element_p256r1{&t0, &t1, &t2, &t3, &t4, &x3, &y3, &z3}) + } else { + #panic("weierstrass: invalid curve") + } + + x1, y1, z1 := &a.x, &a.y, &a.z + x2, y2, z2 := &b.x, &b.y, &b.z + + fe_b(&b_fe) + + // t0 := X1 * X2 ; t1 := Y1 * Y2 ; t2 := Z1 * Z2 ; + fe_mul(&t0, x1, x2) + fe_mul(&t1, y1, y2) + fe_mul(&t2, z1, z2) + + // t3 := X1 + Y1 ; t4 := X2 + Y2 ; t3 := t3 * t4 ; + fe_add(&t3, x1, y1) + fe_add(&t4, x2, y2) + fe_mul(&t3, &t3, &t4) + + // t4 := t0 + t1 ; t3 := t3 - t4 ; t4 := Y1 + Z1 ; + fe_add(&t4, &t0, &t1) + fe_sub(&t3, &t3, &t4) + fe_add(&t4, y1, z1) + + // X3 := Y2 + Z2 ; t4 := t4 * X3 ; X3 := t1 + t2 ; + fe_add(&x3, y2, z2) + fe_mul(&t4, &t4, &x3) + fe_add(&x3, &t1, &t2) + + // t4 := t4 - X3 ; X3 := X1 + Z1 ; Y3 := X2 + Z2 ; + fe_sub(&t4, &t4, &x3) + fe_add(&x3, x1, z1) + fe_add(&y3, x2, z2) + + // X3 := X3 * Y3 ; Y3 := t0 + t2 ; Y3 := X3 - Y3 ; + fe_mul(&x3, &x3, &y3) + fe_add(&y3, &t0, &t2) + fe_sub(&y3, &x3, &y3) + + // Z3 := b * t2 ; X3 := Y3 - Z3 ; Z3 := X3 + X3 ; + fe_mul(&z3, &b_fe, &t2) + fe_sub(&x3, &y3, &z3) + fe_add(&z3, &x3, &x3) + + // X3 := X3 + Z3 ; Z3 := t1 - X3 ; X3 := t1 + X3 ; + fe_add(&x3, &x3, &z3) + fe_sub(&z3, &t1, &x3) + fe_add(&x3, &t1, &x3) + + // Y3 := b * Y3 ; t1 := t2 + t2 ; t2 := t1 + t2 ; + fe_mul(&y3, &b_fe, &y3) + fe_add(&t1, &t2, &t2) + fe_add(&t2, &t1, &t2) + + // Y3 := Y3 - t2 ; Y3 := Y3 - t0 ; t1 := Y3 + Y3 ; + fe_sub(&y3, &y3, &t2) + fe_sub(&y3, &y3, &t0) + fe_add(&t1, &y3, &y3) + + // Y3 := t1 + Y3 ; t1 := t0 + t0 ; t0 := t1 + t0 ; + fe_add(&y3, &t1, &y3) + fe_add(&t1, &t0, &t0) + fe_add(&t0, &t1, &t0) + + // t0 := t0 - t2 ; t1 := t4 * Y3 ; t2 := t0 * Y3 ; + fe_sub(&t0, &t0, &t2) + fe_mul(&t1, &t4, &y3) + fe_mul(&t2, &t0, &y3) + + // Y3 := X3 * Z3 ; Y3 := Y3 + t2 ; X3 := t3 * X3 ; + fe_mul(&y3, &x3, &z3) + fe_add(&y3, &y3, &t2) + fe_mul(&x3, &t3, &x3) + + // X3 := X3 - t1 ; Z3 := t4 * Z3 ; t1 := t3 * t0 ; + fe_sub(&x3, &x3, &t1) + fe_mul(&z3, &t4, &z3) + fe_mul(&t1, &t3, &t0) + + // Z3 := Z3 + t1 ; + fe_add(&z3, &z3, &t1) + + // return X3 , Y3 , Z3 ; + fe_set(&p.x, &x3) + fe_set(&p.y, &y3) + fe_set(&p.z, &z3) +} + +@(private) +pt_add_mixed :: proc "contextless" (p, a: ^$T, x2, y2: ^$U) { + // Algorithm 5 from "Complete addition formulas for prime + // order elliptic curves" by Renes, Costello, and Batina. + // + // The formula is mixed in that it assumes the z-coordinate + // of the addend (`Z2`) is `1`, meaning that it CAN NOT + // handle the addend being the point at infinity. + // + // The operation costs are `11M + 2mb + 23a` saving + // `1M + 6a` over `pt_add`. + + when T == Point_p256r1 && U == Field_Element_p256r1 { + t0, t1, t2, t3, t4, b_fe: Field_Element_p256r1 + x3, y3, z3: Field_Element_p256r1 + defer fe_clear_vec([]^Field_Element_p256r1{&t0, &t1, &t2, &t3, &t4, &x3, &y3, &z3}) + } else { + #panic("weierstrass: invalid curve") + } + + x1, y1, z1 := &a.x, &a.y, &a.z + + fe_b(&b_fe) + + // t0 := X1 * X2 ; t1 := Y1 * Y2 ; t3 := X2 + Y2 ; + fe_mul(&t0, x1, x2) + fe_mul(&t1, y1, y2) + fe_add(&t3, x2, y2) + + // t4 := X1 + Y1 ; t3 := t3 * t4 ; t4 := t0 + t1 ; + fe_add(&t4, x1, y1) + fe_mul(&t3, &t3, &t4) + fe_add(&t4, &t0, &t1) + + // t3 := t3 − t4 ; t4 := Y2 * Z1 ; t4 := t4 + Y1 ; + fe_sub(&t3, &t3, &t4) + fe_mul(&t4, y2, z1) + fe_add(&t4, &t4, y1) + + // Y3 := X2 * Z1 ; Y3 := Y3 + X1 ; Z3 := b * Z1 ; + fe_mul(&y3, x2, z1) + fe_add(&y3, &y3, x1) + fe_mul(&z3, &b_fe, z1) + + // X3 := Y3 − Z3 ; Z3 := X3 + X3 ; X3 := X3 + Z3 ; + fe_sub(&x3, &y3, &z3) + fe_add(&z3, &x3, &x3) + fe_add(&x3, &x3, &z3) + + // Z3 := t1 − X3 ; X3 := t1 + X3 ;. Y3 := b * Y3 ; + fe_sub(&z3, &t1, &x3) + fe_add(&x3, &t1, &x3) + fe_mul(&y3, &b_fe, &y3) + + // t1 := Z1 + Z1 ; t2 := t1 + Z1 ; Y3 := Y3 − t2 ; + fe_add(&t1, z1, z1) + fe_add(&t2, &t1, z1) + fe_sub(&y3, &y3, &t2) + + // Y3 := Y3 − t0 ; t1 := Y3 + Y3 ; Y3 := t1 + Y3 ; + fe_sub(&y3, &y3, &t0) + fe_add(&t1, &y3, &y3) + fe_add(&y3, &t1, &y3) + + // t1 := t0 + t0 ; t0 := t1 + t0 ; t0 := t0 − t2 ; + fe_add(&t1, &t0, &t0) + fe_add(&t0, &t1, &t0) + fe_sub(&t0, &t0, &t2) + + // t1 := t4 * Y3 ; t2 := t0 * Y3 ; Y3 := X3 * Z3 ; + fe_mul(&t1, &t4, &y3) + fe_mul(&t2, &t0, &y3) + fe_mul(&y3, &x3, &z3) + + // Y3 := Y3 + t2 ; X3 := t3 * X3 ; X3 := X3 − t1 ; + fe_add(&y3, &y3, &t2) + fe_mul(&x3, &t3, &x3) + fe_sub(&x3, &x3, &t1) + + // Z3 := t4 * Z3 ; t1 := t3 * t0 ; Z3 := Z3 + t1 ; + fe_mul(&z3, &t4, &z3) + fe_mul(&t1, &t3, &t0) + fe_add(&z3, &z3, &t1) + + // return X3 , Y3 , Z3 ; + fe_set(&p.x, &x3) + fe_set(&p.y, &y3) + fe_set(&p.z, &z3) +} + +pt_double :: proc "contextless" (p, a: ^$T) { + // Algorithm 6 from "Complete addition formulas for prime + // order elliptic curves" by Renes, Costello, and Batina. + // + // The formula is complete in that it is valid for all a, + // without exceptions or extra assumptions about the inputs. + // + // The operation costs are `8M + 3S + 2mb + 21a`. + + when T == Point_p256r1 { + t0, t1, t2, t3, b_fe: Field_Element_p256r1 + x3, y3, z3: Field_Element_p256r1 + defer fe_clear_vec([]^Field_Element_p256r1{&t0, &t1, &t2, &t3, &x3, &y3, &z3}) + } else { + #panic("weierstrass: invalid curve") + } + + x, y, z := &a.x, &a.y, &a.z + + fe_b(&b_fe) + + // t0 := X ^2; t1 := Y ^2; t2 := Z ^2; + fe_square(&t0, x) + fe_square(&t1, y) + fe_square(&t2, z) + + // t3 := X * Y ; t3 := t3 + t3 ; Z3 := X * Z ; + fe_mul(&t3, x, y) + fe_add(&t3, &t3, &t3) + fe_mul(&z3, x, z) + + // Z3 := Z3 + Z3 ; Y3 := b * t2 ; Y3 := Y3 - Z3 ; + fe_add(&z3, &z3, &z3) + fe_mul(&y3, &b_fe, &t2) + fe_sub(&y3, &y3, &z3) + + // X3 := Y3 + Y3 ; Y3 := X3 + Y3 ; X3 := t1 - Y3 ; + fe_add(&x3, &y3, &y3) + fe_add(&y3, &x3, &y3) + fe_sub(&x3, &t1, &y3) + + // Y3 := t1 + Y3 ; Y3 := X3 * Y3 ; X3 := X3 * t3 ; + fe_add(&y3, &t1, &y3) + fe_mul(&y3, &x3, &y3) + fe_mul(&x3, &x3, &t3) + + // t3 := t2 + t2 ; t2 := t2 + t3 ; Z3 := b * Z3 ; + fe_add(&t3, &t2, &t2) + fe_add(&t2, &t2, &t3) + fe_mul(&z3, &b_fe, &z3) + + // Z3 := Z3 - t2 ; Z3 := Z3 - t0 ; t3 := Z3 + Z3 ; + fe_sub(&z3, &z3, &t2) + fe_sub(&z3, &z3, &t0) + fe_add(&t3, &z3, &z3) + + // Z3 := Z3 + t3 ; t3 := t0 + t0 ; t0 := t3 + t0 ; + fe_add(&z3, &z3, &t3) + fe_add(&t3, &t0, &t0) + fe_add(&t0, &t3, &t0) + + // t0 := t0 - t2 ; t0 := t0 * Z3 ; Y3 := Y3 + t0 ; + fe_sub(&t0, &t0, &t2) + fe_mul(&t0, &t0, &z3) + fe_add(&y3, &y3, &t0) + + // t0 := Y * Z ; t0 := t0 + t0 ; Z3 := t0 * Z3 ; + fe_mul(&t0, y, z) + fe_add(&t0, &t0, &t0) + fe_mul(&z3, &t0, &z3) + + // X3 := X3 - Z3 ; Z3 := t0 * t1 ; Z3 := Z3 + Z3 ; + fe_sub(&x3, &x3, &z3) + fe_mul(&z3, &t0, &t1) + fe_add(&z3, &z3, &z3) + + // Z3 := Z3 + Z3 ; + fe_add(&z3, &z3, &z3) + + // return X3 , Y3 , Z3 ; + fe_set(&p.x, &x3) + fe_set(&p.y, &y3) + fe_set(&p.z, &z3) +} + +pt_sub :: proc "contextless" (p, a, b: ^$T) { + b_neg: T + pt_negate(&b_neg, b) + pt_add(p, a, &b_neg) + + fe_clear(&b_neg) +} + +pt_negate :: proc "contextless" (p, a: ^$T) { + fe_set(&p.x, &a.x) + fe_negate(&p.y, &a.y) + fe_set(&p.z, &a.z) +} + +pt_rescale :: proc "contextless" (p, a: ^$T) { + // A = 1/Z1 + // X3 = A*X1 + // Y3 = A*Y1 + // Z3 = 1 + // + // As per "From A to Z: Projective coordinates leakage in the wild" + // leaking the Z-coordinate is bad. The modular inversion algorithm + // used in this library is based on Fermat's Little Theorem. + // + // See: https://eprint.iacr.org/2020/432.pdf + + was_identity := pt_is_identity(a) + + when T == Point_p256r1 { + z_inv: Field_Element_p256r1 + } else { + #panic("weierstrass: invalid curve") + } + + ident: T + fe_inv(&z_inv, &a.z) + fe_mul(&p.x, &a.x, &z_inv) + fe_mul(&p.y, &a.y, &z_inv) + fe_one(&p.z) + + pt_identity(&ident) + pt_cond_select(p, p, &ident, was_identity) + + fe_clear(&z_inv) +} + +pt_cond_select :: proc "contextless" (p, a, b: ^$T, ctrl: int) { + fe_cond_select(&p.x, &a.x, &b.x, ctrl) + fe_cond_select(&p.y, &a.y, &b.y, ctrl) + fe_cond_select(&p.z, &a.z, &b.z, ctrl) +} + +@(require_results) +pt_equal :: proc "contextless" (a, b: ^$T) -> int { + when T == Point_p256r1 { + x1z2, x2z1, y1z2, y2z1: Field_Element_p256r1 + } else { + #panic("weierstrass: invalid curve") + } + + // Check X1Z2 == X2Z1 && Y1Z2 == Y2Z1 + fe_mul(&x1z2, &a.x, &b.z) + fe_mul(&x2z1, &b.x, &a.z) + + fe_mul(&y1z2, &a.y, &b.z) + fe_mul(&y2z1, &b.y, &a.z) + + return fe_equal(&x1z2, &x2z1) & fe_equal(&y1z2, &y2z1) +} + +@(require_results) +pt_is_identity :: proc "contextless" (p: ^$T) -> int { + return fe_is_zero(&p.z) +} + +@(require_results) +pt_is_y_odd :: proc "contextless" (p: ^$T) -> int { + tmp: T + defer pt_clear(&tmp) + + fe_set(&tmp, p) + pt_rescale(&tmp) + + return fe_is_odd(&tmp.y) +} + +@(private) +is_on_curve :: proc "contextless" (x, y: ^$T) -> bool { + maybe_yy, yy: T + defer fe_clear_vec([]^T{&maybe_yy, &yy}) + + // RHS: x^3 + ax + b + set_yy_candidate(&maybe_yy, x) + + // LHS: y^2 + fe_square(&yy, y) + + return fe_equal(&maybe_yy, &yy) == 1 +} + +@(private) +set_yy_candidate :: proc "contextless" (maybe_yy, x: ^$T) { + // RHS: x^3 + ax + b + rhs, tmp: T + + fe_square(&tmp, x) + fe_mul(&rhs, &tmp, x) + + fe_a(&tmp) + fe_mul(&tmp, &tmp, x) + fe_add(&rhs, &rhs, &tmp) + + fe_b(&tmp) + fe_add(maybe_yy, &rhs, &tmp) + + fe_clear(&rhs) +} diff --git a/core/crypto/_weierstrass/point_s11n_sec.odin b/core/crypto/_weierstrass/point_s11n_sec.odin new file mode 100644 index 000000000..ae009edb0 --- /dev/null +++ b/core/crypto/_weierstrass/point_s11n_sec.odin @@ -0,0 +1,95 @@ +package _weierstrass + +@(require) import "core:mem" + +@(private) +SEC_PREFIX_IDENTITY :: 0x00 +@(private) +SEC_PREFIX_COMPRESSED_EVEN :: 0x02 +@(private) +SEC_PREFIX_COMPRESSED_ODD :: 0x03 +SEC_PREFIX_UNCOMPRESSED :: 0x04 + +@(require_results) +pt_set_sec_bytes :: proc "contextless" (p: ^$T, b: []byte) -> bool { + when T == Point_p256r1 { + FE_SZ :: FE_SIZE_P256R1 + } else { + #panic("weierstrass: invalid curve") + } + + b_len := len(b) + if b_len < 1 { + return false + } + + switch b[0] { + case SEC_PREFIX_IDENTITY: + if b_len != 1 { + return false + } + pt_identity(p) + return true + case SEC_PREFIX_COMPRESSED_EVEN, SEC_PREFIX_COMPRESSED_ODD: + if b_len != 1 + FE_SZ { + return false + } + y_is_odd := b[0] - SEC_PREFIX_COMPRESSED_EVEN + return pt_set_x_bytes(p, b[1:], int(y_is_odd)) + case SEC_PREFIX_UNCOMPRESSED: + if b_len != 1 + 2 * FE_SZ { + return false + } + x, y := b[1:1+FE_SZ], b[1+FE_SZ:] + return pt_set_xy_bytes(p, x, y) + case: + return false + } +} + +@(require_results) +pt_sec_bytes :: proc "contextless" (b: []byte, p: ^$T, compressed: bool) -> bool { + when T == Point_p256r1 { + FE_SZ :: FE_SIZE_P256R1 + } else { + #panic("weierstrass: invalid curve") + } + + b_len := len(b) + if pt_is_identity(p) == 1 { + if b_len != 1 { + return false + } + b[0] = SEC_PREFIX_IDENTITY + return true + } + + x, y: []byte + y_: [FE_SZ]byte + switch compressed { + case true: + if b_len != 1 + FE_SZ { + return false + } + x, y = b[1:], y_[:] + case false: + if b_len != 1 + 2 * FE_SZ { + return false + } + b[0]= SEC_PREFIX_UNCOMPRESSED + x, y = b[1:1+FE_SZ], b[1+FE_SZ:] + } + if !pt_bytes(x, y, p) { + return false + } + if compressed { + // Instead of calling pt_is_y_odd, just serializing + // y into a temp buffer and checking the parity saves + // 1 redundant rescale call. + y_is_odd := byte(y[FE_SZ-1] & 1) + b[0] = SEC_PREFIX_COMPRESSED_EVEN + y_is_odd + mem.zero_explicit(&y_, size_of(y_)) + } + + return true +} diff --git a/core/crypto/_weierstrass/sc.odin b/core/crypto/_weierstrass/sc.odin new file mode 100644 index 000000000..2ed9459bc --- /dev/null +++ b/core/crypto/_weierstrass/sc.odin @@ -0,0 +1,76 @@ +package _weierstrass + +import p256r1 "core:crypto/_fiat/field_scalarp256r1" +import subtle "core:crypto/_subtle" + +Scalar_p256r1 :: p256r1.Montgomery_Domain_Field_Element + +SC_SIZE_P256R1 :: 32 + +sc_clear :: proc { + p256r1.fe_clear, +} + +sc_clear_vec :: proc { + p256r1.fe_clear_vec, +} + +sc_set_bytes :: proc { + p256r1.fe_from_bytes, +} +sc_bytes :: proc { + p256r1.fe_to_bytes, +} + +sc_set :: proc { + p256r1.fe_set, +} + +sc_zero :: proc { + p256r1.fe_zero, +} + +sc_one_p256r1 :: proc { + p256r1.fe_one, +} + +sc_add :: proc { + p256r1.fe_add, +} + +sc_sub :: proc { + p256r1.fe_sub, +} + +sc_negate :: proc { + p256r1.fe_opp, +} + +sc_mul :: proc { + p256r1.fe_mul, +} + +sc_square :: proc { + p256r1.fe_square, +} + +sc_cond_assign :: proc { + p256r1.fe_cond_assign, +} + +sc_equal :: proc { + p256r1.fe_equal, +} + +sc_is_odd :: proc { + p256r1.fe_is_odd, +} + +sc_is_zero :: proc { + sc_is_zero_p256r1, +} + +@(require_results) +sc_is_zero_p256r1 :: proc "contextless" (fe: ^Scalar_p256r1) -> int { + return int(subtle.u64_is_zero(p256r1.fe_non_zero(fe))) +} diff --git a/core/crypto/_weierstrass/scalar_mul.odin b/core/crypto/_weierstrass/scalar_mul.odin new file mode 100644 index 000000000..1781ac3b6 --- /dev/null +++ b/core/crypto/_weierstrass/scalar_mul.odin @@ -0,0 +1,204 @@ +package _weierstrass + +import "core:crypto" +import subtle "core:crypto/_subtle" +import "core:mem" + +pt_scalar_mul :: proc "contextless" ( + p, a: ^$T, + sc: ^$S, + unsafe_is_vartime: bool = false, +) { + when T == Point_p256r1 && S == Scalar_p256r1 { + SC_SZ :: SC_SIZE_P256R1 + } else { + #panic("weierstrass: invalid curve") + } + + b: [SC_SZ]byte = --- + sc_bytes(b[:], sc) + + pt_scalar_mul_bytes(p, a, b[:], unsafe_is_vartime) + + if !unsafe_is_vartime { + mem.zero_explicit(&b, size_of(b)) + } +} + +pt_scalar_mul_bytes :: proc "contextless" ( + p, a: ^$T, + sc: []byte, + unsafe_is_vartime: bool = false, +) { + when T == Point_p256r1 { + p_tbl: Multiply_Table_p256r1 = --- + q, tmp: Point_p256r1 = ---, --- + SC_SZ :: SC_SIZE_P256R1 + } else { + #panic("weierstrass: invalid curve") + } + + assert_contextless(len(sc) == SC_SZ, "weierstrass: invalid scalar size") + mul_tbl_set(&p_tbl, a, unsafe_is_vartime) + + pt_identity(&q) + for limb_byte, i in sc { + hi, lo := (limb_byte >> 4) & 0x0f, limb_byte & 0x0f + + if i != 0 { + pt_double(&q, &q) + pt_double(&q, &q) + pt_double(&q, &q) + pt_double(&q, &q) + } + mul_tbl_lookup_add(&q, &tmp, &p_tbl, u64(hi), unsafe_is_vartime) + + pt_double(&q, &q) + pt_double(&q, &q) + pt_double(&q, &q) + pt_double(&q, &q) + mul_tbl_lookup_add(&q, &tmp, &p_tbl, u64(lo), unsafe_is_vartime) + } + + pt_set(p, &q) + + if !unsafe_is_vartime { + mem.zero_explicit(&p_tbl, size_of(p_tbl)) + pt_clear_vec([]^T{&q, &tmp}) + } +} + +when crypto.COMPACT_IMPLS == true { + pt_scalar_mul_generator :: proc "contextless" ( + p: ^$T, + sc: ^$S, + unsafe_is_vartime: bool = false, + ) { + g: T + pt_generator(&g) + + pt_scalar_mul(p, &g, sc, unsafe_is_vartime) + } +} else { + pt_scalar_mul_generator :: proc "contextless" ( + p: ^$T, + sc: ^$S, + unsafe_is_vartime: bool = false, + ) { + when T == Point_p256r1 && S == Scalar_p256r1 { + p_tbl_hi := &Gen_Multiply_Table_p256r1_hi + p_tbl_lo := &Gen_Multiply_Table_p256r1_lo + tmp: Point_p256r1 = --- + SC_SZ :: SC_SIZE_P256R1 + } else { + #panic("weierstrass: invalid curve") + } + + b: [SC_SZ]byte + sc_bytes(b[:], sc) + + pt_identity(p) + for limb_byte, i in b { + hi, lo := (limb_byte >> 4) & 0x0f, limb_byte & 0x0f + mul_affine_tbl_lookup_add(p, &tmp, &p_tbl_hi[i], u64(hi), unsafe_is_vartime) + mul_affine_tbl_lookup_add(p, &tmp, &p_tbl_lo[i], u64(lo), unsafe_is_vartime) + } + + if !unsafe_is_vartime { + mem.zero_explicit(&b, size_of(b)) + pt_clear(&tmp) + } + } +} + +@(private="file") +Multiply_Table_p256r1 :: [15]Point_p256r1 + +@(private="file") +mul_tbl_set :: proc "contextless"( + tbl: ^$T, + point: ^$U, + unsafe_is_vartime: bool, +) { + when T == Multiply_Table_p256r1 && U == Point_p256r1{ + tmp: Point_p256r1 + pt_set(&tmp, point) + } else { + #panic("weierstrass: invalid curve") + } + + pt_set(&tbl[0], &tmp) + for i in 1 ..<15 { + pt_add(&tmp, &tmp, point) + pt_set(&tbl[i], &tmp) + } + + if !unsafe_is_vartime { + pt_clear(&tmp) + } +} + +@(private="file") +mul_tbl_lookup_add :: proc "contextless" ( + point, tmp: ^$T, + tbl: ^$U, + idx: u64, + unsafe_is_vartime: bool, + ) { + if unsafe_is_vartime { + switch idx { + case 0: + case: + pt_add(point, point, &tbl[idx - 1]) + } + return + } + + pt_identity(tmp) + for i in u64(1)..<16 { + ctrl := subtle.eq(i, idx) + pt_cond_select(tmp, tmp, &tbl[i - 1], int(ctrl)) + } + + pt_add(point, point, tmp) +} + +when crypto.COMPACT_IMPLS == false { + @(private) + Affine_Point_p256r1 :: struct { + x: Field_Element_p256r1, + y: Field_Element_p256r1, + } + + @(private="file") + mul_affine_tbl_lookup_add :: proc "contextless" ( + point, tmp: ^$T, + tbl: ^$U, + idx: u64, + unsafe_is_vartime: bool, + ) { + if unsafe_is_vartime { + switch idx { + case 0: + case: + pt_add_mixed(point, point, &tbl[idx - 1].x, &tbl[idx - 1].y) + } + return + } + + pt_identity(tmp) + for i in u64(1)..<16 { + ctrl := int(subtle.eq(i, idx)) + fe_cond_select(&tmp.x, &tmp.x, &tbl[i - 1].x, ctrl) + fe_cond_select(&tmp.y, &tmp.y, &tbl[i - 1].y, ctrl) + } + + // The mixed addition formula assumes that the addend is not + // the neutral element. Do the addition regardless, and then + // conditionally select the right result. + pt_add_mixed(tmp, point, &tmp.x, &tmp.y) + + ctrl := subtle.u64_is_non_zero(idx) + pt_cond_select(point, point, tmp, int(ctrl)) + } +} diff --git a/core/crypto/_weierstrass/secp256r1_table.odin b/core/crypto/_weierstrass/secp256r1_table.odin new file mode 100644 index 000000000..1a6bc3ef6 --- /dev/null +++ b/core/crypto/_weierstrass/secp256r1_table.odin @@ -0,0 +1,3985 @@ +package _weierstrass + +/* + ------ GENERATED ------ DO NOT EDIT ------ GENERATED ------ DO NOT EDIT ------ GENERATED ------ +*/ + +import "core:crypto" + +when crypto.COMPACT_IMPLS == false { + @(private,rodata) + Gen_Multiply_Table_p256r1_hi := [32][15]Affine_Point_p256r1 { + { + { + {9259451175701532574, 15597985540941612547, 4541553034987877619, 8927802479718285609}, + {14672230714928802576, 14284617950605306700, 13339970812390782046, 787078889494395850}, + }, + { + {18165439414433063919, 14693282888419586094, 14992616289789993230, 13232208150801553912}, + {16850347485914337693, 223364064845089224, 7302899015436300563, 4391216311540396088}, + }, + { + {12558388403188680537, 10687978569513354810, 9373570856564649772, 4079327722512691465}, + {5372437374337150740, 3297421622932790851, 9326853593823854687, 8305371884938201251}, + }, + { + {13121472331750731303, 323745485980480220, 15110308702528119977, 4696302365805118372}, + {9859094500834571602, 5315656270700787939, 4187063204400651801, 1695695129564818327}, + }, + { + {12817586844019849804, 15425488216915741929, 15293562913126043054, 11770898970765978555}, + {6806103820345670787, 17789094149138630459, 3807781571713999192, 5823254011289457198}, + }, + { + {10112524230916015604, 13571143908656270599, 6031089010487808103, 5774558171390644848}, + {1808959243244841573, 14071312530426692155, 9241399242704553402, 9836150050655369231}, + }, + { + {14083007972403535491, 16009534514129505275, 12481249112231139039, 10309390659262581143}, + {5782517315325366794, 16717384553294759530, 4578392002424884134, 239005024949492645}, + }, + { + {1836857790164349346, 11263074778654917115, 4786985732596838094, 10525445084936097674}, + {1484357665966453236, 3110871407036679558, 1668700683093601768, 2736269131339849752}, + }, + { + {9249362594190920246, 8088172462140746331, 4080107866285682736, 16205599538438551353}, + {18312943145606312277, 9100632964181080418, 3969991115337154345, 5340098959750368315}, + }, + { + {12122448407048035645, 2891250339380982359, 12794212052932523400, 7166035112141500392}, + {15777441312724841162, 4552528682229856831, 2210391301762911476, 16410254680957321386}, + }, + { + {6910044784455706429, 11951245774670922855, 207795885948948810, 3884359690300962405}, + {4578772752480772344, 2948797025787714138, 16774444535658202808, 1388183483009000463}, + }, + { + {16561979129019905420, 1881862411760441386, 15441950514711322010, 12933020223458438856}, + {5570341451312029630, 18172638959728259059, 9074261777549091198, 6171200053222754816}, + }, + { + {10126435102176037237, 1545112930055760251, 11563139991870561593, 10766754172364938834}, + {5116781688621052838, 14471715119500781375, 4724882615229687192, 10031687030722046325}, + }, + { + {15016829467434780812, 6777508689306592732, 3811682306063049290, 11475361222871876387}, + {6080948654298953274, 11612742274762615033, 5268311600240325047, 9147351973710519861}, + }, + { + {12130203770930472759, 3880998309361490881, 8807462332494735511, 9291388074337055133}, + {18165312304248982432, 12733144434841535979, 18090195697688236271, 5825342884125782172}, + }, + }, + { + { + {194633990068625151, 1028128699653523895, 7436102537486268753, 1855520454959348468}, + {5098690958966904466, 3342676718901330604, 6942212660412942406, 16510188838209674083}, + }, + { + {7963995066277321795, 14986230345162551366, 10616366460602472778, 16186943329215681149}, + {9522855644164647723, 9858336437877021178, 16344942402271072884, 18027353494090590022}, + }, + { + {13392726161043192788, 7606793939450765773, 9543984695709321129, 6135912406103198328}, + {10903991926178685177, 529801710637680784, 8207012095420105234, 4590962949922268360}, + }, + { + {13175608910844763921, 11168387468381338510, 5555873864224342205, 17780559602571640345}, + {1582669533588472814, 8145133762789622706, 1625372887980692455, 4576809104068554285}, + }, + { + {17616803153811079355, 17809794753465712025, 10788493879428408032, 1263026253532745742}, + {331896291298606534, 13299145463579793142, 8951131463540898010, 11121758705853021600}, + }, + { + {17015522374255846157, 7155392284047197223, 1248775493117789546, 9199472299655737207}, + {13126885324657282947, 12092989376083683289, 2035698983314262432, 835441512024005104}, + }, + { + {12481871371020004325, 15786477648044981224, 2586272424816191689, 4208704695692543659}, + {16940467964964992440, 11207566805119564978, 2858987625603639630, 9561510646236248154}, + }, + { + {2900978533555060931, 1749946807863203576, 11705734511931072459, 4446980691693419424}, + {14437524160594907241, 12795912566640000773, 10400036254697939154, 8356113088668925361}, + }, + { + {3770654812111500682, 7723332701546321657, 12057007323752084660, 11871339027463593983}, + {8927366002257844381, 331175455338905356, 6085376066711046662, 195998713859126244}, + }, + { + {15888580251537997623, 14253909833728698978, 14445538492667230716, 4028538972354525849}, + {7720263170150940477, 1190890222876864097, 8657188516818851005, 1987613286973742753}, + }, + { + {1556082539082087499, 9191446579576007527, 16923484407567577707, 4662661048159090855}, + {12760778972220173745, 3942937056545553996, 12952479961991875179, 8914103212381870290}, + }, + { + {8900726473285671992, 890209742292473781, 16059468388719373167, 16577940938542233221}, + {17381766864962227733, 231915274132518769, 16477817024012878700, 15646021286310268545}, + }, + { + {10104554368814337641, 170400126349943750, 16051269335758964391, 7842493858299913771}, + {9246756702190574744, 110682656515867335, 11402798562961521905, 17325237240525801251}, + }, + { + {15837018286366797690, 18114413810565810328, 9441874034567150801, 14075941137889189393}, + {12786763055047269260, 9121030808281463204, 1713778999270814105, 17015261864438490667}, + }, + { + {12997570542605430113, 5500897611058123544, 4160129407772614089, 13768264346635084004}, + {6638654171187871203, 6080635069726153281, 2255431148803290413, 3789670411999607189}, + }, + }, + { + { + {1830819081327272165, 11951292080860646547, 18002500803418629938, 13317986695217403840}, + {5005574200470766330, 10138179785738652504, 1610518863105278224, 13309443265578956954}, + }, + { + {14192194428653714479, 11578618567931657764, 6032668189933768881, 15981535562386193924}, + {8925792218631314923, 9408714146004183681, 8859017894477140398, 1675606340537058506}, + }, + { + {3265119697568866078, 13753322853248061974, 15435163376825672274, 13646180516491714938}, + {15620545622955090250, 18241486585498394565, 459566729126467878, 9728217493753855944}, + }, + { + {9883406233903270985, 17184231210468300584, 5498903678702785900, 6903833261382863389}, + {11489138095102981636, 9021901931786177471, 3227433089132150317, 16639455550797627042}, + }, + { + {839045372102318861, 2032615141683118500, 1921816835840256924, 504869150737570005}, + {15932184001422473505, 7849475855313305697, 1189994394722618598, 9874798350548229684}, + }, + { + {4636201671610663345, 16662311204732135584, 12398897461787695675, 1355753199357412657}, + {14695655628527768564, 1692838776852698754, 7346906782826540912, 14869028424564984700}, + }, + { + {14240080119980315297, 4751983902385717684, 7941412103662252178, 4796803816695225123}, + {9327986654018000413, 15111345676387005726, 3582558555283734415, 11913156735178831102}, + }, + { + {12915868875134296756, 3071143582305760275, 10848717856747030010, 10973183887638314967}, + {5983269487036236823, 9885184706933333413, 14509493669845681951, 9669608065801379977}, + }, + { + {7848634325810890057, 4356492357483949442, 8777700982672429871, 447737364627887590}, + {2892466086138453900, 12013259293340538023, 3423275627272380730, 11171074631447548946}, + }, + { + {14593553227914306527, 7393098159726367793, 959457858782426605, 12924066827318848802}, + {14790800265003508462, 13805969419986022239, 4408523909823076864, 16722715416825698787}, + }, + { + {8554182115079118694, 17233907570567075631, 12336560627384786590, 5123566378696582545}, + {96401035522143140, 10138155491929979850, 17651328686428132420, 3453390145222258032}, + }, + { + {16197242500758474188, 3349369240724295499, 9422940308750670637, 16888844525585804807}, + {14045424784406071799, 13180603138700207746, 2683581192503868543, 3842875784859878}, + }, + { + {17498073686183419231, 6922314891526280784, 16083733402282932920, 15425477806093217459}, + {12425976625898608391, 16458101989314253841, 10013521940061058050, 10858868879196007236}, + }, + { + {123600201037598181, 6690762836954208162, 17157040810691942664, 15263405971805161132}, + {8685477170453562173, 10331174323986544033, 5789045082422148337, 3007978469441468974}, + }, + { + {2402095889286816125, 18054120920831753009, 11753130221915918396, 10341553510464463050}, + {280903370426929900, 14994955837151914025, 13551362401871479612, 14711789630561753093}, + }, + }, + { + { + {14086745261650819748, 17953107869776717888, 1777725846494438428, 2765314406831814212}, + {2603997194371852991, 2223517025105045134, 15579901335531749634, 6571733615332171148}, + }, + { + {5478465698516556930, 287443454357750768, 12201204663663129285, 782849770204658255}, + {11270045035009204251, 18152683972363144337, 10463300037926642739, 14363641589598863851}, + }, + { + {3790592075869665284, 5120320091554329756, 15361581282394028709, 14360464660911164915}, + {15249656958991931940, 2563751872827049233, 13745792006936646733, 14572943674933168173}, + }, + { + {3167679014977537749, 3417445004776702290, 1709246158507866266, 5861367897285174360}, + 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"core:path/filepath" +import "core:os" +import "core:strings" + +// Yes this leaks memory, fite me IRL. + +GENERATED :: `/* + ------ GENERATED ------ DO NOT EDIT ------ GENERATED ------ DO NOT EDIT ------ GENERATED ------ +*/` + +main :: proc() { + gen_p256r1_tables() +} + +gen_p256r1_tables :: proc() { + Affine_Point_p256r1 :: struct { + x: secec.Field_Element_p256r1, + y: secec.Field_Element_p256r1, + } + Multiply_Table_p256r1_hi: [32][15]Affine_Point_p256r1 + Multiply_Table_p256r1_lo: [32][15]Affine_Point_p256r1 + + g, p: secec.Point_p256r1 + secec.pt_generator(&g) + + // Precompute ([1,15] << n) * G multiples of G, MSB->LSB + for i in 0..<32 { + b: [32]byte + for j in 1..<16 { + b[i] = u8(j) << 4 + secec.pt_scalar_mul_bytes(&p, &g, b[:], true) + secec.pt_rescale(&p, &p) + secec.fe_set(&Multiply_Table_p256r1_hi[i][j-1].x, &p.x) + secec.fe_set(&Multiply_Table_p256r1_hi[i][j-1].y, &p.y) + + b[i] = u8(j) + secec.pt_scalar_mul_bytes(&p, &g, b[:], true) + secec.pt_rescale(&p, &p) + secec.fe_set(&Multiply_Table_p256r1_lo[i][j-1].x, &p.x) + secec.fe_set(&Multiply_Table_p256r1_lo[i][j-1].y, &p.y) + + b[i] = 0 + } + } + + fn := path.join({ODIN_ROOT, "core", "crypto", "_weierstrass", "secp256r1_table.odin"}) + bld: strings.Builder + w := strings.to_writer(&bld) + + fmt.wprintln(w, "package _weierstrass") + fmt.wprintln(w, "") + fmt.wprintln(w, GENERATED) + fmt.wprintln(w, "") + fmt.wprintln(w, "import \"core:crypto\"") + fmt.wprintln(w, "") + fmt.wprintln(w, "when crypto.COMPACT_IMPLS == false {") + + fmt.wprintln(w, "\t@(private,rodata)") + fmt.wprintln(w, "\tGen_Multiply_Table_p256r1_hi := [32][15]Affine_Point_p256r1 {") + for &v, i in Multiply_Table_p256r1_hi { + fmt.wprintln(w, "\t\t{") + for &ap, j in v { + fmt.wprintln(w, "\t\t\t{") + + x, y := &ap.x, &ap.y + fmt.wprintf(w, "\t\t\t\t{{%d, %d, %d, %d},\n", x[0], x[1], x[2], x[3]) + fmt.wprintf(w, "\t\t\t\t{{%d, %d, %d, %d},\n", y[0], y[1], y[2], y[3]) + + fmt.wprintln(w, "\t\t\t},") + } + fmt.wprintln(w, "\t\t},") + } + fmt.wprintln(w, "\t}\n") + + fmt.wprintln(w, "\t@(private,rodata)") + fmt.wprintln(w, "\tGen_Multiply_Table_p256r1_lo := [32][15]Affine_Point_p256r1 {") + for &v, i in Multiply_Table_p256r1_lo { + fmt.wprintln(w, "\t\t{") + for &ap, j in v { + fmt.wprintln(w, "\t\t\t{") + + x, y := &ap.x, &ap.y + fmt.wprintf(w, "\t\t\t\t{{%d, %d, %d, %d},\n", x[0], x[1], x[2], x[3]) + fmt.wprintf(w, "\t\t\t\t{{%d, %d, %d, %d},\n", y[0], y[1], y[2], y[3]) + + fmt.wprintln(w, "\t\t\t},") + } + fmt.wprintln(w, "\t\t},") + } + fmt.wprintln(w, "\t}") + + fmt.wprintln(w, "}") + + _ = os.write_entire_file(fn, transmute([]byte)(strings.to_string(bld))) +} diff --git a/core/crypto/crypto.odin b/core/crypto/crypto.odin index 435c5daaf..3fb369a54 100644 --- a/core/crypto/crypto.odin +++ b/core/crypto/crypto.odin @@ -5,6 +5,9 @@ import "base:runtime" import subtle "core:crypto/_subtle" import "core:mem" +// Omit large precomputed tables, trading off performance for size. +COMPACT_IMPLS: bool : #config(ODIN_CRYPTO_COMPACT, false) + // HAS_RAND_BYTES is true iff the runtime provides a cryptographic // entropy source. HAS_RAND_BYTES :: runtime.HAS_RAND_BYTES diff --git a/tests/core/crypto/test_core_crypto_weierstrass.odin b/tests/core/crypto/test_core_crypto_weierstrass.odin new file mode 100644 index 000000000..206e98bd7 --- /dev/null +++ b/tests/core/crypto/test_core_crypto_weierstrass.odin @@ -0,0 +1,486 @@ +package test_core_crypto + +import ec "core:crypto/_weierstrass" +import "core:encoding/hex" +import "core:math/big" +import "core:testing" + +@(private="file") +P256_G_X :: "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296" +@(private="file") +P256_G_Y :: "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5" + +@(private="file") +P256_G_UNCOMPRESSED :: "04" + P256_G_X + P256_G_Y + +@(test) +test_p256_a :: proc(t: ^testing.T) { + a_str := "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc" + + fe, a_fe: ec.Field_Element_p256r1 + ec.fe_a(&fe) + ec.fe_a(&a_fe) + + b: [32]byte + ec.fe_bytes(b[:], &fe) + + s := (string)(hex.encode(b[:], context.temp_allocator)) + + testing.expect(t, s == a_str) + + ec.fe_zero(&fe) + ec.fe_set_bytes(&fe, b[:]) + + testing.expect(t, ec.fe_equal(&fe, &a_fe) == 1) +} + +@(test) +test_p256_b :: proc(t: ^testing.T) { + b_str := "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b" + + fe, b_fe: ec.Field_Element_p256r1 + ec.fe_b(&fe) + ec.fe_b(&b_fe) + + b: [32]byte + ec.fe_bytes(b[:], &fe) + + s := (string)(hex.encode(b[:], context.temp_allocator)) + + testing.expect(t, s == b_str) + + ec.fe_zero(&fe) + ec.fe_set_bytes(&fe, b[:]) + + testing.expect(t, ec.fe_equal(&fe, &b_fe) == 1) +} + +@(test) +test_p256_g_x :: proc(t: ^testing.T) { + fe, x_fe: ec.Field_Element_p256r1 + ec.fe_gen_x(&fe) + ec.fe_gen_x(&x_fe) + + b: [32]byte + ec.fe_bytes(b[:], &fe) + + s := (string)(hex.encode(b[:], context.temp_allocator)) + testing.expect(t, s == P256_G_X) + + ec.fe_zero(&fe) + ec.fe_set_bytes(&fe, b[:]) + + testing.expect(t, ec.fe_equal(&fe, &x_fe) == 1) +} + +@(test) +test_p256_g_y :: proc(t: ^testing.T) { + fe, y_fe: ec.Field_Element_p256r1 + ec.fe_gen_y(&fe) + ec.fe_gen_y(&y_fe) + + b: [32]byte + ec.fe_bytes(b[:], &fe) + + s := (string)(hex.encode(b[:], context.temp_allocator)) + testing.expect(t, s == P256_G_Y) + + ec.fe_zero(&fe) + ec.fe_set_bytes(&fe, b[:]) + + testing.expect(t, ec.fe_equal(&fe, &y_fe) == 1) +} + +@(test) +test_p256_scalar_reduce :: proc(t: ^testing.T) { + test_vectors := []struct { + raw: string, + reduced: string, + } { + // n + { + "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", + "0000000000000000000000000000000000000000000000000000000000000000", + }, + // n + 1 + { + "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632552", + "0000000000000000000000000000000000000000000000000000000000000001", + }, + // 2^384 (Sage) + { + "01000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "431905529c0166ce652e96b7ccca0a99679b73e19ad16947f01cf013fc632551", + }, + // SHA384 odin-linux-amd64-dev-2026-01.tar.gz (Sage) + { + "87622f79b4b0e76001f9c99b0337b61a0bcd2b5a8e9a3937176825ad75ef0fe8742a348a251dd2682d711f76b33df3e6", + "f66db86e28d903033d1e17d818c0eb13fe3d1ae095b4d2ecbcd1a1eccf9f2f8c", + }, + // SHA512 odin-linux-amd64-dev-2026-01.tar.gz (Sage) + { + "6f85507cec3a35fdb3d4f40d23583681144561e77bc4ea88ab0ea219d5c17b7c9178f5f5a6296a2d18eddd4bdf19e61830fc85d7de23fd4fbde31c4cf6694719", + "3217ecbee32c8b0dfcca0f10a884fe43658fbe91458f25d0f1bf2075759c5ebe", + }, + } + + for v, _ in test_vectors { + raw_bytes, _ := hex.decode(transmute([]byte)(v.raw), context.temp_allocator) + + sc: ec.Scalar_p256r1 + _ = ec.sc_set_bytes(&sc, raw_bytes) + + b: [ec.SC_SIZE_P256R1]byte + ec.sc_bytes(b[:], &sc) + s := (string)(hex.encode(b[:], context.temp_allocator)) + + testing.expectf(t, v.reduced == s, "sc: raw %s reduced: %s, expected: %s", v.raw, s, v.reduced) + } +} + +@(test) +test_p256_scalar_mul :: proc(t: ^testing.T) { + test_vectors := []struct { + scalar: string, // NOTE: Base 10 + x, y: string, + } { + // Test vectors from http://point-at-infinity.org/ecc/nisttv + { + "1", + "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296", + "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5", + + }, + { + "2", + "7CF27B188D034F7E8A52380304B51AC3C08969E277F21B35A60B48FC47669978", + "07775510DB8ED040293D9AC69F7430DBBA7DADE63CE982299E04B79D227873D1", + }, + { + "3", + "5ECBE4D1A6330A44C8F7EF951D4BF165E6C6B721EFADA985FB41661BC6E7FD6C", + "8734640C4998FF7E374B06CE1A64A2ECD82AB036384FB83D9A79B127A27D5032", + }, + { + "4", + "E2534A3532D08FBBA02DDE659EE62BD0031FE2DB785596EF509302446B030852", + "E0F1575A4C633CC719DFEE5FDA862D764EFC96C3F30EE0055C42C23F184ED8C6", + }, + { + "5", + "51590B7A515140D2D784C85608668FDFEF8C82FD1F5BE52421554A0DC3D033ED", + "E0C17DA8904A727D8AE1BF36BF8A79260D012F00D4D80888D1D0BB44FDA16DA4", + }, + { + "6", + "B01A172A76A4602C92D3242CB897DDE3024C740DEBB215B4C6B0AAE93C2291A9", + "E85C10743237DAD56FEC0E2DFBA703791C00F7701C7E16BDFD7C48538FC77FE2", + }, + { + "7", + "8E533B6FA0BF7B4625BB30667C01FB607EF9F8B8A80FEF5B300628703187B2A3", + "73EB1DBDE03318366D069F83A6F5900053C73633CB041B21C55E1A86C1F400B4", + }, + { + "8", + "62D9779DBEE9B0534042742D3AB54CADC1D238980FCE97DBB4DD9DC1DB6FB393", + "AD5ACCBD91E9D8244FF15D771167CEE0A2ED51F6BBE76A78DA540A6A0F09957E", + }, + { + "9", + "EA68D7B6FEDF0B71878938D51D71F8729E0ACB8C2C6DF8B3D79E8A4B90949EE0", + "2A2744C972C9FCE787014A964A8EA0C84D714FEAA4DE823FE85A224A4DD048FA", + }, + { + "10", + "CEF66D6B2A3A993E591214D1EA223FB545CA6C471C48306E4C36069404C5723F", + "878662A229AAAE906E123CDD9D3B4C10590DED29FE751EEECA34BBAA44AF0773", + }, + { + "11", + "3ED113B7883B4C590638379DB0C21CDA16742ED0255048BF433391D374BC21D1", + "9099209ACCC4C8A224C843AFA4F4C68A090D04DA5E9889DAE2F8EEFCE82A3740", + }, + { + "12", + "741DD5BDA817D95E4626537320E5D55179983028B2F82C99D500C5EE8624E3C4", + "0770B46A9C385FDC567383554887B1548EEB912C35BA5CA71995FF22CD4481D3", + }, + { + "13", + "177C837AE0AC495A61805DF2D85EE2FC792E284B65EAD58A98E15D9D46072C01", + "63BB58CD4EBEA558A24091ADB40F4E7226EE14C3A1FB4DF39C43BBE2EFC7BFD8", + }, + { + "14", + "54E77A001C3862B97A76647F4336DF3CF126ACBE7A069C5E5709277324D2920B", + "F599F1BB29F4317542121F8C05A2E7C37171EA77735090081BA7C82F60D0B375", + }, + { + "15", + "F0454DC6971ABAE7ADFB378999888265AE03AF92DE3A0EF163668C63E59B9D5F", + "B5B93EE3592E2D1F4E6594E51F9643E62A3B21CE75B5FA3F47E59CDE0D034F36", + }, + { + "16", + "76A94D138A6B41858B821C629836315FCD28392EFF6CA038A5EB4787E1277C6E", + "A985FE61341F260E6CB0A1B5E11E87208599A0040FC78BAA0E9DDD724B8C5110", + }, + { + "17", + "47776904C0F1CC3A9C0984B66F75301A5FA68678F0D64AF8BA1ABCE34738A73E", + "AA005EE6B5B957286231856577648E8381B2804428D5733F32F787FF71F1FCDC", + }, + { + "18", + "1057E0AB5780F470DEFC9378D1C7C87437BB4C6F9EA55C63D936266DBD781FDA", + "F6F1645A15CBE5DC9FA9B7DFD96EE5A7DCC11B5C5EF4F1F78D83B3393C6A45A2", + }, + { + "19", + "CB6D2861102C0C25CE39B7C17108C507782C452257884895C1FC7B74AB03ED83", + "58D7614B24D9EF515C35E7100D6D6CE4A496716E30FA3E03E39150752BCECDAA", + }, + { + "20", + "83A01A9378395BAB9BCD6A0AD03CC56D56E6B19250465A94A234DC4C6B28DA9A", + "76E49B6DE2F73234AE6A5EB9D612B75C9F2202BB6923F54FF8240AAA86F640B8", + }, + { + "112233445566778899", + "339150844EC15234807FE862A86BE77977DBFB3AE3D96F4C22795513AEAAB82F", + "B1C14DDFDC8EC1B2583F51E85A5EB3A155840F2034730E9B5ADA38B674336A21", + }, + { + "112233445566778899112233445566778899", + "1B7E046A076CC25E6D7FA5003F6729F665CC3241B5ADAB12B498CD32F2803264", + "BFEA79BE2B666B073DB69A2A241ADAB0738FE9D2DD28B5604EB8C8CF097C457B", + }, + { + "029852220098221261079183923314599206100666902414330245206392788703677545185283", + "9EACE8F4B071E677C5350B02F2BB2B384AAE89D58AA72CA97A170572E0FB222F", + "1BBDAEC2430B09B93F7CB08678636CE12EAAFD58390699B5FD2F6E1188FC2A78", + }, + { + "057896042899961394862005778464643882389978449576758748073725983489954366354431", + "878F22CC6DB6048D2B767268F22FFAD8E56AB8E2DC615F7BD89F1E350500DD8D", + "714A5D7BB901C9C5853400D12341A892EF45D87FC553786756C4F0C9391D763E", + }, + { + "57896042899961394862005778464643882389978449576758748073725983489954366354431", + "878F22CC6DB6048D2B767268F22FFAD8E56AB8E2DC615F7BD89F1E350500DD8D", + "714A5D7BB901C9C5853400D12341A892EF45D87FC553786756C4F0C9391D763E", + }, + { + "1766845392945710151501889105729049882997660004824848915955419660366636031", + "659A379625AB122F2512B8DADA02C6348D53B54452DFF67AC7ACE4E8856295CA", + "49D81AB97B648464D0B4A288BD7818FAB41A16426E943527C4FED8736C53D0F6", + }, + { + "28948025760307534517734791687894775804466072615242963443097661355606862201087", + "CBCEAAA8A4DD44BBCE58E8DB7740A5510EC2CB7EA8DA8D8F036B3FB04CDA4DE4", + "4BD7AA301A80D7F59FD983FEDBE59BB7B2863FE46494935E3745B360E32332FA", + }, + { + "113078210460870548944811695960290644973229224625838436424477095834645696384", + "F0C4A0576154FF3A33A3460D42EAED806E854DFA37125221D37935124BA462A4", + "5B392FA964434D29EEC6C9DBC261CF116796864AA2FAADB984A2DF38D1AEF7A3", + }, + { + "12078056106883488161242983286051341125085761470677906721917479268909056", + "5E6C8524B6369530B12C62D31EC53E0288173BD662BDF680B53A41ECBCAD00CC", + "447FE742C2BFEF4D0DB14B5B83A2682309B5618E0064A94804E9282179FE089F", + }, + { + "57782969857385448082319957860328652998540760998293976083718804450708503920639", + "03792E541BC209076A3D7920A915021ECD396A6EB5C3960024BE5575F3223484", + "FC774AE092403101563B712F68170312304F20C80B40C06282063DB25F268DE4", + }, + { + "57896017119460046759583662757090100341435943767777707906455551163257755533312", + "2379FF85AB693CDF901D6CE6F2473F39C04A2FE3DCD842CE7AAB0E002095BCF8", + "F8B476530A634589D5129E46F322B02FBC610A703D80875EE70D7CE1877436A1", + }, + { + "452312848374287284681282171017647412726433684238464212999305864837160993279", + "C1E4072C529BF2F44DA769EFC934472848003B3AF2C0F5AA8F8DDBD53E12ED7C", + "39A6EE77812BB37E8079CD01ED649D3830FCA46F718C1D3993E4A591824ABCDB", + }, + { + "904571339174065134293634407946054000774746055866917729876676367558469746684", + "34DFBC09404C21E250A9B40FA8772897AC63A094877DB65862B61BD1507B34F3", + "CF6F8A876C6F99CEAEC87148F18C7E1E0DA6E165FFC8ED82ABB65955215F77D3", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044349", + "83A01A9378395BAB9BCD6A0AD03CC56D56E6B19250465A94A234DC4C6B28DA9A", + "891B64911D08CDCC5195A14629ED48A360DDFD4596DC0AB007DBF5557909BF47", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044350", + "CB6D2861102C0C25CE39B7C17108C507782C452257884895C1FC7B74AB03ED83", + "A7289EB3DB2610AFA3CA18EFF292931B5B698E92CF05C1FC1C6EAF8AD4313255", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044351", + "1057E0AB5780F470DEFC9378D1C7C87437BB4C6F9EA55C63D936266DBD781FDA", + "090E9BA4EA341A246056482026911A58233EE4A4A10B0E08727C4CC6C395BA5D", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044352", + "47776904C0F1CC3A9C0984B66F75301A5FA68678F0D64AF8BA1ABCE34738A73E", + "55FFA1184A46A8D89DCE7A9A889B717C7E4D7FBCD72A8CC0CD0878008E0E0323", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044353", + "76A94D138A6B41858B821C629836315FCD28392EFF6CA038A5EB4787E1277C6E", + "567A019DCBE0D9F2934F5E4A1EE178DF7A665FFCF0387455F162228DB473AEEF", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044354", + "F0454DC6971ABAE7ADFB378999888265AE03AF92DE3A0EF163668C63E59B9D5F", + "4A46C11BA6D1D2E1B19A6B1AE069BC19D5C4DE328A4A05C0B81A6321F2FCB0C9", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044355", + "54E77A001C3862B97A76647F4336DF3CF126ACBE7A069C5E5709277324D2920B", + "0A660E43D60BCE8BBDEDE073FA5D183C8E8E15898CAF6FF7E45837D09F2F4C8A", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044356", + "177C837AE0AC495A61805DF2D85EE2FC792E284B65EAD58A98E15D9D46072C01", + "9C44A731B1415AA85DBF6E524BF0B18DD911EB3D5E04B20C63BC441D10384027", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044357", + "741DD5BDA817D95E4626537320E5D55179983028B2F82C99D500C5EE8624E3C4", + "F88F4B9463C7A024A98C7CAAB7784EAB71146ED4CA45A358E66A00DD32BB7E2C", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044358", + "3ED113B7883B4C590638379DB0C21CDA16742ED0255048BF433391D374BC21D1", + "6F66DF64333B375EDB37BC505B0B3975F6F2FB26A16776251D07110317D5C8BF", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044359", + "CEF66D6B2A3A993E591214D1EA223FB545CA6C471C48306E4C36069404C5723F", + "78799D5CD655517091EDC32262C4B3EFA6F212D7018AE11135CB4455BB50F88C", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044360", + "EA68D7B6FEDF0B71878938D51D71F8729E0ACB8C2C6DF8B3D79E8A4B90949EE0", + "D5D8BB358D36031978FEB569B5715F37B28EB0165B217DC017A5DDB5B22FB705", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044361", + "62D9779DBEE9B0534042742D3AB54CADC1D238980FCE97DBB4DD9DC1DB6FB393", + "52A533416E1627DCB00EA288EE98311F5D12AE0A4418958725ABF595F0F66A81", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044362", + "8E533B6FA0BF7B4625BB30667C01FB607EF9F8B8A80FEF5B300628703187B2A3", + "8C14E2411FCCE7CA92F9607C590A6FFFAC38C9CD34FBE4DE3AA1E5793E0BFF4B", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044363", + "B01A172A76A4602C92D3242CB897DDE3024C740DEBB215B4C6B0AAE93C2291A9", + "17A3EF8ACDC8252B9013F1D20458FC86E3FF0890E381E9420283B7AC7038801D", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044364", + "51590B7A515140D2D784C85608668FDFEF8C82FD1F5BE52421554A0DC3D033ED", + "1F3E82566FB58D83751E40C9407586D9F2FED1002B27F7772E2F44BB025E925B", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044365", + "E2534A3532D08FBBA02DDE659EE62BD0031FE2DB785596EF509302446B030852", + "1F0EA8A4B39CC339E62011A02579D289B103693D0CF11FFAA3BD3DC0E7B12739", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044366", + "5ECBE4D1A6330A44C8F7EF951D4BF165E6C6B721EFADA985FB41661BC6E7FD6C", + "78CB9BF2B6670082C8B4F931E59B5D1327D54FCAC7B047C265864ED85D82AFCD", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044367", + "7CF27B188D034F7E8A52380304B51AC3C08969E277F21B35A60B48FC47669978", + "F888AAEE24712FC0D6C26539608BCF244582521AC3167DD661FB4862DD878C2E", + }, + { + "115792089210356248762697446949407573529996955224135760342422259061068512044368", + "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296", + "B01CBD1C01E58065711814B583F061E9D431CCA994CEA1313449BF97C840AE0A", + }, + } + + for v, _ in test_vectors { + x_bytes, _ := hex.decode(transmute([]byte)(v.x), context.temp_allocator) + y_bytes, _ := hex.decode(transmute([]byte)(v.y), context.temp_allocator) + + k_big: big.Int + err := big.set(&k_big, v.scalar, 10, context.temp_allocator) + testing.expectf(t, err == nil, "failed to parse k", err) + + k_sz: int + k_sz, err = big.int_to_bytes_size(&k_big, allocator = context.temp_allocator) + testing.expect(t, err == nil) + + k_bytes := make([]byte, k_sz, context.temp_allocator) + err = big.int_to_bytes_big(&k_big, k_bytes, allocator = context.temp_allocator) + + p, q, expected, g: ec.Point_p256r1 + sc: ec.Scalar_p256r1 + + _ = ec.sc_set_bytes(&sc, k_bytes) + + ec.pt_generator(&g) + ok := ec.pt_set_xy_bytes(&expected, x_bytes, y_bytes) + testing.expectf(t, ok, "failed to set point; %s, %s", v.x, v.y) + + ec.pt_scalar_mul(&p, &g, &sc) + ec.pt_scalar_mul_generator(&q, &sc) + ec.pt_rescale(&p, &p) + ec.pt_rescale(&q, &q) + + testing.expect(t, ec.pt_equal(&p, &q) == 1) + testing.expectf(t, ec.pt_equal(&p, &expected) == 1, "sc: %s actual: %v expected: %v", v.scalar, &p, &expected) + } +} + +@(test) +test_p256_s11n_sec_identity ::proc(t: ^testing.T) { + p: ec.Point_p256r1 + + ec.pt_generator(&p) + ok := ec.pt_set_sec_bytes(&p, []byte{0x00}) + testing.expect(t, ok) + testing.expectf(t, ec.pt_is_identity(&p) == 1, "%v", p) + + b := []byte{0xff} + ok = ec.pt_sec_bytes(b, &p, true) + testing.expect(t, ok) + testing.expect(t, b[0] == 0x00) + + b = []byte{0xff} + ok = ec.pt_sec_bytes(b, &p, false) + testing.expect(t, ok) + testing.expect(t, b[0] == 0x00) +} + +@(test) +test_p256_s11n_sec_generator ::proc(t: ^testing.T) { + p, g: ec.Point_p256r1 + + ec.pt_generator(&g) + ec.pt_identity(&p) + + b: [65]byte + ok := ec.pt_sec_bytes(b[:], &g, false) + testing.expect(t, ok) + s := (string)(hex.encode(b[:], context.temp_allocator)) + testing.expectf(t, s == P256_G_UNCOMPRESSED, "g: %v bytes: %v, %v", g, P256_G_UNCOMPRESSED, s) + + ok = ec.pt_set_sec_bytes(&p, b[:]) + testing.expectf(t, ok, "%s", s) + testing.expect(t, ec.pt_equal(&g, &p) == 1) +} |