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 #!/usr/bin/env python # coding=utf-8 # The MIT License (MIT) # # Copyright (c) 2015-2016 the fiat-crypto authors (see the AUTHORS file). # # Permission is hereby granted, free of charge, to any person obtaining a copy # of this software and associated documentation files (the "Software"), to deal # in the Software without restriction, including without limitation the rights # to use, copy, modify, merge, publish, distribute, sublicense, and/or sell # copies of the Software, and to permit persons to whom the Software is # furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included in all # copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR # IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE # AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER # LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, # OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE # SOFTWARE. import StringIO import subprocess # Base field Z_p p = 2**255 - 19 def modp_inv(x): return pow(x, p-2, p) # Square root of -1 modp_sqrt_m1 = pow(2, (p-1) // 4, p) # Compute corresponding x-coordinate, with low bit corresponding to # sign, or return None on failure def recover_x(y, sign): if y >= p: return None x2 = (y*y-1) * modp_inv(d*y*y+1) if x2 == 0: if sign: return None else: return 0 # Compute square root of x2 x = pow(x2, (p+3) // 8, p) if (x*x - x2) % p != 0: x = x * modp_sqrt_m1 % p if (x*x - x2) % p != 0: return None if (x & 1) != sign: x = p - x return x # Curve constant d = -121665 * modp_inv(121666) % p # Base point g_y = 4 * modp_inv(5) % p g_x = recover_x(g_y, 0) # Points are represented as affine tuples (x, y). def point_add(P, Q): x1, y1 = P x2, y2 = Q x3 = ((x1*y2 + y1*x2) * modp_inv(1 + d*x1*x2*y1*y2)) % p y3 = ((y1*y2 + x1*x2) * modp_inv(1 - d*x1*x2*y1*y2)) % p return (x3, y3) # Computes Q = s * P def point_mul(s, P): Q = (0, 1) # Neutral element while s > 0: if s & 1: Q = point_add(Q, P) P = point_add(P, P) s >>= 1 return Q def to_bytes(x): ret = bytearray(32) for i in range(len(ret)): ret[i] = x % 256 x >>= 8 assert x == 0 return ret def to_ge_precomp(P): # typedef struct { # fe_loose yplusx; # fe_loose yminusx; # fe_loose xy2d; # } ge_precomp; x, y = P return ((y + x) % p, (y - x) % p, (x * y * 2 * d) % p) def to_base_25_5(x): limbs = (26, 25, 26, 25, 26, 25, 26, 25, 26, 25) ret = [] for l in limbs: ret.append(x & ((1<>= l assert x == 0 return ret def to_base_51(x): ret = [] for _ in range(5): ret.append(x & ((1<<51) - 1)) x >>= 51 assert x == 0 return ret def to_literal(x): ret = "{{\n#if defined(BORINGSSL_CURVE25519_64BIT)\n" ret += ", ".join(map(str, to_base_51(x))) ret += "\n#else\n" ret += ", ".join(map(str, to_base_25_5(x))) ret += "\n#endif\n}}" return ret def main(): d2 = (2 * d) % p small_precomp = bytearray() for i in range(1, 16): s = (i&1) | ((i&2) << (64-1)) | ((i&4) << (128-2)) | ((i&8) << (192-3)) P = point_mul(s, (g_x, g_y)) small_precomp += to_bytes(P[0]) small_precomp += to_bytes(P[1]) large_precomp = [] for i in range(32): large_precomp.append([]) for j in range(8): P = point_mul((j + 1) << (i * 8), (g_x, g_y)) large_precomp[-1].append(to_ge_precomp(P)) bi_precomp = [] for i in range(8): P = point_mul(2*i + 1, (g_x, g_y)) bi_precomp.append(to_ge_precomp(P)) buf = StringIO.StringIO() buf.write("""// The MIT License (MIT) // // Copyright (c) 2015-2016 the fiat-crypto authors (see the AUTHORS file). // // Permission is hereby granted, free of charge, to any person obtaining a copy // of this software and associated documentation files (the "Software"), to deal // in the Software without restriction, including without limitation the rights // to use, copy, modify, merge, publish, distribute, sublicense, and/or sell // copies of the Software, and to permit persons to whom the Software is // furnished to do so, subject to the following conditions: // // The above copyright notice and this permission notice shall be included in // all copies or substantial portions of the Software. // // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE // SOFTWARE. // This file is generated from // ./make_curve25519_tables.py > curve25519_tables.h static const fe d = """) buf.write(to_literal(d)) buf.write("""; static const fe sqrtm1 = """) buf.write(to_literal(modp_sqrt_m1)) buf.write("""; static const fe d2 = """) buf.write(to_literal(d2)) buf.write("""; #if defined(OPENSSL_SMALL) // This block of code replaces the standard base-point table with a much smaller // one. The standard table is 30,720 bytes while this one is just 960. // // This table contains 15 pairs of group elements, (x, y), where each field // element is serialised with |fe_tobytes|. If |i| is the index of the group // element then consider i+1 as a four-bit number: (i₀, i₁, i₂, i₃) (where i₀ // is the most significant bit). The value of the group element is then: // (i₀×2^192 + i₁×2^128 + i₂×2^64 + i₃)G, where G is the generator. static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = {""") for i, b in enumerate(small_precomp): buf.write("0x%02x, " % b) buf.write(""" }; #else // k25519Precomp[i][j] = (j+1)*256^i*B static const ge_precomp k25519Precomp[32][8] = { """) for child in large_precomp: buf.write("{\n") for val in child: buf.write("{\n") for term in val: buf.write(to_literal(term) + ",\n") buf.write("},\n") buf.write("},\n") buf.write("""}; #endif // OPENSSL_SMALL // Bi[i] = (2*i+1)*B static const ge_precomp Bi[8] = { """) for val in bi_precomp: buf.write("{\n") for term in val: buf.write(to_literal(term) + ",\n") buf.write("},\n") buf.write("""}; """) proc = subprocess.Popen(["clang-format"], stdin=subprocess.PIPE) proc.communicate(buf.getvalue()) if __name__ == "__main__": main()