/* Matthew Dempsky Public domain. Derived from public domain code by D. J. Bernstein. */ // Modified very slightly for ZeroTier One by Adam Ierymenko // This code remains in the public domain. #include #include #include #include "Constants.hpp" #include "C25519.hpp" #include "SHA512.hpp" #include "Buffer.hpp" #include "Hashtable.hpp" #include "Mutex.hpp" #ifdef __WINDOWS__ #pragma warning(disable: 4146) #endif #ifdef __GNUC__ #pragma GCC diagnostic ignored "-Wunused-function" #endif namespace { #define crypto_int32 int32_t #define crypto_uint32 uint32_t #define crypto_int64 int64_t #define crypto_uint64 uint64_t #define crypto_hash_sha512_BYTES 64 ////////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////////// typedef uint8_t u8; typedef int32_t s32; typedef int64_t limb; static inline void fsum(limb *output, const limb *in) { unsigned i; for (i = 0; i < 10; i += 2) { output[0+i] = output[0+i] + in[0+i]; output[1+i] = output[1+i] + in[1+i]; } } static inline void fdifference(limb *output, const limb *in) { unsigned i; for (i = 0; i < 10; ++i) { output[i] = in[i] - output[i]; } } static inline void fscalar_product(limb *output, const limb *in, const limb scalar) { unsigned i; for (i = 0; i < 10; ++i) { output[i] = in[i] * scalar; } } static inline void fproduct(limb *output, const limb *in2, const limb *in) { output[0] = ((limb) ((s32) in2[0])) * ((s32) in[0]); output[1] = ((limb) ((s32) in2[0])) * ((s32) in[1]) + ((limb) ((s32) in2[1])) * ((s32) in[0]); output[2] = 2 * ((limb) ((s32) in2[1])) * ((s32) in[1]) + ((limb) ((s32) in2[0])) * ((s32) in[2]) + ((limb) ((s32) in2[2])) * ((s32) in[0]); output[3] = ((limb) ((s32) in2[1])) * ((s32) in[2]) + ((limb) ((s32) in2[2])) * ((s32) in[1]) + ((limb) ((s32) in2[0])) * ((s32) in[3]) + ((limb) ((s32) in2[3])) * ((s32) in[0]); output[4] = ((limb) ((s32) in2[2])) * ((s32) in[2]) + 2 * (((limb) ((s32) in2[1])) * ((s32) in[3]) + ((limb) ((s32) in2[3])) * ((s32) in[1])) + ((limb) ((s32) in2[0])) * ((s32) in[4]) + ((limb) ((s32) in2[4])) * ((s32) in[0]); output[5] = ((limb) ((s32) in2[2])) * ((s32) in[3]) + ((limb) ((s32) in2[3])) * ((s32) in[2]) + ((limb) ((s32) in2[1])) * ((s32) in[4]) + ((limb) ((s32) in2[4])) * ((s32) in[1]) + ((limb) ((s32) in2[0])) * ((s32) in[5]) + ((limb) ((s32) in2[5])) * ((s32) in[0]); output[6] = 2 * (((limb) ((s32) in2[3])) * ((s32) in[3]) + ((limb) ((s32) in2[1])) * ((s32) in[5]) + ((limb) ((s32) in2[5])) * ((s32) in[1])) + ((limb) ((s32) in2[2])) * ((s32) in[4]) + ((limb) ((s32) in2[4])) * ((s32) in[2]) + ((limb) ((s32) in2[0])) * ((s32) in[6]) + ((limb) ((s32) in2[6])) * ((s32) in[0]); output[7] = ((limb) ((s32) in2[3])) * ((s32) in[4]) + ((limb) ((s32) in2[4])) * ((s32) in[3]) + ((limb) ((s32) in2[2])) * ((s32) in[5]) + ((limb) ((s32) in2[5])) * ((s32) in[2]) + ((limb) ((s32) in2[1])) * ((s32) in[6]) + ((limb) ((s32) in2[6])) * ((s32) in[1]) + ((limb) ((s32) in2[0])) * ((s32) in[7]) + ((limb) ((s32) in2[7])) * ((s32) in[0]); output[8] = ((limb) ((s32) in2[4])) * ((s32) in[4]) + 2 * (((limb) ((s32) in2[3])) * ((s32) in[5]) + ((limb) ((s32) in2[5])) * ((s32) in[3]) + ((limb) ((s32) in2[1])) * ((s32) in[7]) + ((limb) ((s32) in2[7])) * ((s32) in[1])) + ((limb) ((s32) in2[2])) * ((s32) in[6]) + ((limb) ((s32) in2[6])) * ((s32) in[2]) + ((limb) ((s32) in2[0])) * ((s32) in[8]) + ((limb) ((s32) in2[8])) * ((s32) in[0]); output[9] = ((limb) ((s32) in2[4])) * ((s32) in[5]) + ((limb) ((s32) in2[5])) * ((s32) in[4]) + ((limb) ((s32) in2[3])) * ((s32) in[6]) + ((limb) ((s32) in2[6])) * ((s32) in[3]) + ((limb) ((s32) in2[2])) * ((s32) in[7]) + ((limb) ((s32) in2[7])) * ((s32) in[2]) + ((limb) ((s32) in2[1])) * ((s32) in[8]) + ((limb) ((s32) in2[8])) * ((s32) in[1]) + ((limb) ((s32) in2[0])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[0]); output[10] = 2 * (((limb) ((s32) in2[5])) * ((s32) in[5]) + ((limb) ((s32) in2[3])) * ((s32) in[7]) + ((limb) ((s32) in2[7])) * ((s32) in[3]) + ((limb) ((s32) in2[1])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[1])) + ((limb) ((s32) in2[4])) * ((s32) in[6]) + ((limb) ((s32) in2[6])) * ((s32) in[4]) + ((limb) ((s32) in2[2])) * ((s32) in[8]) + ((limb) ((s32) in2[8])) * ((s32) in[2]); output[11] = ((limb) ((s32) in2[5])) * ((s32) in[6]) + ((limb) ((s32) in2[6])) * ((s32) in[5]) + ((limb) ((s32) in2[4])) * ((s32) in[7]) + ((limb) ((s32) in2[7])) * ((s32) in[4]) + ((limb) ((s32) in2[3])) * ((s32) in[8]) + ((limb) ((s32) in2[8])) * ((s32) in[3]) + ((limb) ((s32) in2[2])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[2]); output[12] = ((limb) ((s32) in2[6])) * ((s32) in[6]) + 2 * (((limb) ((s32) in2[5])) * ((s32) in[7]) + ((limb) ((s32) in2[7])) * ((s32) in[5]) + ((limb) ((s32) in2[3])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[3])) + ((limb) ((s32) in2[4])) * ((s32) in[8]) + ((limb) ((s32) in2[8])) * ((s32) in[4]); output[13] = ((limb) ((s32) in2[6])) * ((s32) in[7]) + ((limb) ((s32) in2[7])) * ((s32) in[6]) + ((limb) ((s32) in2[5])) * ((s32) in[8]) + ((limb) ((s32) in2[8])) * ((s32) in[5]) + ((limb) ((s32) in2[4])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[4]); output[14] = 2 * (((limb) ((s32) in2[7])) * ((s32) in[7]) + ((limb) ((s32) in2[5])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[5])) + ((limb) ((s32) in2[6])) * ((s32) in[8]) + ((limb) ((s32) in2[8])) * ((s32) in[6]); output[15] = ((limb) ((s32) in2[7])) * ((s32) in[8]) + ((limb) ((s32) in2[8])) * ((s32) in[7]) + ((limb) ((s32) in2[6])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[6]); output[16] = ((limb) ((s32) in2[8])) * ((s32) in[8]) + 2 * (((limb) ((s32) in2[7])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[7])); output[17] = ((limb) ((s32) in2[8])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[8]); output[18] = 2 * ((limb) ((s32) in2[9])) * ((s32) in[9]); } static inline void freduce_degree(limb *output) { output[8] += output[18] << 4; output[8] += output[18] << 1; output[8] += output[18]; output[7] += output[17] << 4; output[7] += output[17] << 1; output[7] += output[17]; output[6] += output[16] << 4; output[6] += output[16] << 1; output[6] += output[16]; output[5] += output[15] << 4; output[5] += output[15] << 1; output[5] += output[15]; output[4] += output[14] << 4; output[4] += output[14] << 1; output[4] += output[14]; output[3] += output[13] << 4; output[3] += output[13] << 1; output[3] += output[13]; output[2] += output[12] << 4; output[2] += output[12] << 1; output[2] += output[12]; output[1] += output[11] << 4; output[1] += output[11] << 1; output[1] += output[11]; output[0] += output[10] << 4; output[0] += output[10] << 1; output[0] += output[10]; } #if (-1 & 3) != 3 #error "This code only works on a two's complement system" #endif static inline limb div_by_2_26(const limb v) { /* High word of v; no shift needed. */ const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32); /* Set to all 1s if v was negative; else set to 0s. */ const int32_t sign = ((int32_t) highword) >> 31; /* Set to 0x3ffffff if v was negative; else set to 0. */ const int32_t roundoff = ((uint32_t) sign) >> 6; /* Should return v / (1<<26) */ return (v + roundoff) >> 26; } static inline limb div_by_2_25(const limb v) { /* High word of v; no shift needed*/ const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32); /* Set to all 1s if v was negative; else set to 0s. */ const int32_t sign = ((int32_t) highword) >> 31; /* Set to 0x1ffffff if v was negative; else set to 0. */ const int32_t roundoff = ((uint32_t) sign) >> 7; /* Should return v / (1<<25) */ return (v + roundoff) >> 25; } static inline void freduce_coefficients(limb *output) { unsigned i; output[10] = 0; for (i = 0; i < 10; i += 2) { limb over = div_by_2_26(output[i]); /* The entry condition (that |output[i]| < 280*2^54) means that over is, at * most, 280*2^28 in the first iteration of this loop. This is added to the * next limb and we can approximate the resulting bound of that limb by * 281*2^54. */ output[i] -= over << 26; output[i+1] += over; /* For the first iteration, |output[i+1]| < 281*2^54, thus |over| < * 281*2^29. When this is added to the next limb, the resulting bound can * be approximated as 281*2^54. * * For subsequent iterations of the loop, 281*2^54 remains a conservative * bound and no overflow occurs. */ over = div_by_2_25(output[i+1]); output[i+1] -= over << 25; output[i+2] += over; } /* Now |output[10]| < 281*2^29 and all other coefficients are reduced. */ output[0] += output[10] << 4; output[0] += output[10] << 1; output[0] += output[10]; output[10] = 0; /* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19*281*2^29 * So |over| will be no more than 2^16. */ { limb over = div_by_2_26(output[0]); output[0] -= over << 26; output[1] += over; } /* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 2^16 < 2^26. The * bound on |output[1]| is sufficient to meet our needs. */ } static inline void fmul(limb *output, const limb *in, const limb *in2) { limb t[19]; fproduct(t, in, in2); /* |t[i]| < 14*2^54 */ freduce_degree(t); freduce_coefficients(t); /* |t[i]| < 2^26 */ memcpy(output, t, sizeof(limb) * 10); } static inline void fsquare_inner(limb *output, const limb *in) { output[0] = ((limb) ((s32) in[0])) * ((s32) in[0]); output[1] = 2 * ((limb) ((s32) in[0])) * ((s32) in[1]); output[2] = 2 * (((limb) ((s32) in[1])) * ((s32) in[1]) + ((limb) ((s32) in[0])) * ((s32) in[2])); output[3] = 2 * (((limb) ((s32) in[1])) * ((s32) in[2]) + ((limb) ((s32) in[0])) * ((s32) in[3])); output[4] = ((limb) ((s32) in[2])) * ((s32) in[2]) + 4 * ((limb) ((s32) in[1])) * ((s32) in[3]) + 2 * ((limb) ((s32) in[0])) * ((s32) in[4]); output[5] = 2 * (((limb) ((s32) in[2])) * ((s32) in[3]) + ((limb) ((s32) in[1])) * ((s32) in[4]) + ((limb) ((s32) in[0])) * ((s32) in[5])); output[6] = 2 * (((limb) ((s32) in[3])) * ((s32) in[3]) + ((limb) ((s32) in[2])) * ((s32) in[4]) + ((limb) ((s32) in[0])) * ((s32) in[6]) + 2 * ((limb) ((s32) in[1])) * ((s32) in[5])); output[7] = 2 * (((limb) ((s32) in[3])) * ((s32) in[4]) + ((limb) ((s32) in[2])) * ((s32) in[5]) + ((limb) ((s32) in[1])) * ((s32) in[6]) + ((limb) ((s32) in[0])) * ((s32) in[7])); output[8] = ((limb) ((s32) in[4])) * ((s32) in[4]) + 2 * (((limb) ((s32) in[2])) * ((s32) in[6]) + ((limb) ((s32) in[0])) * ((s32) in[8]) + 2 * (((limb) ((s32) in[1])) * ((s32) in[7]) + ((limb) ((s32) in[3])) * ((s32) in[5]))); output[9] = 2 * (((limb) ((s32) in[4])) * ((s32) in[5]) + ((limb) ((s32) in[3])) * ((s32) in[6]) + ((limb) ((s32) in[2])) * ((s32) in[7]) + ((limb) ((s32) in[1])) * ((s32) in[8]) + ((limb) ((s32) in[0])) * ((s32) in[9])); output[10] = 2 * (((limb) ((s32) in[5])) * ((s32) in[5]) + ((limb) ((s32) in[4])) * ((s32) in[6]) + ((limb) ((s32) in[2])) * ((s32) in[8]) + 2 * (((limb) ((s32) in[3])) * ((s32) in[7]) + ((limb) ((s32) in[1])) * ((s32) in[9]))); output[11] = 2 * (((limb) ((s32) in[5])) * ((s32) in[6]) + ((limb) ((s32) in[4])) * ((s32) in[7]) + ((limb) ((s32) in[3])) * ((s32) in[8]) + ((limb) ((s32) in[2])) * ((s32) in[9])); output[12] = ((limb) ((s32) in[6])) * ((s32) in[6]) + 2 * (((limb) ((s32) in[4])) * ((s32) in[8]) + 2 * (((limb) ((s32) in[5])) * ((s32) in[7]) + ((limb) ((s32) in[3])) * ((s32) in[9]))); output[13] = 2 * (((limb) ((s32) in[6])) * ((s32) in[7]) + ((limb) ((s32) in[5])) * ((s32) in[8]) + ((limb) ((s32) in[4])) * ((s32) in[9])); output[14] = 2 * (((limb) ((s32) in[7])) * ((s32) in[7]) + ((limb) ((s32) in[6])) * ((s32) in[8]) + 2 * ((limb) ((s32) in[5])) * ((s32) in[9])); output[15] = 2 * (((limb) ((s32) in[7])) * ((s32) in[8]) + ((limb) ((s32) in[6])) * ((s32) in[9])); output[16] = ((limb) ((s32) in[8])) * ((s32) in[8]) + 4 * ((limb) ((s32) in[7])) * ((s32) in[9]); output[17] = 2 * ((limb) ((s32) in[8])) * ((s32) in[9]); output[18] = 2 * ((limb) ((s32) in[9])) * ((s32) in[9]); } static void fsquare(limb *output, const limb *in) { limb t[19]; fsquare_inner(t, in); /* |t[i]| < 14*2^54 because the largest product of two limbs will be < * 2^(27+27) and fsquare_inner adds together, at most, 14 of those * products. */ freduce_degree(t); freduce_coefficients(t); /* |t[i]| < 2^26 */ memcpy(output, t, sizeof(limb) * 10); } static inline void fexpand(limb *output, const u8 *input) { #define F(n,start,shift,mask) \ output[n] = ((((limb) input[start + 0]) | \ ((limb) input[start + 1]) << 8 | \ ((limb) input[start + 2]) << 16 | \ ((limb) input[start + 3]) << 24) >> shift) & mask; F(0, 0, 0, 0x3ffffff); F(1, 3, 2, 0x1ffffff); F(2, 6, 3, 0x3ffffff); F(3, 9, 5, 0x1ffffff); F(4, 12, 6, 0x3ffffff); F(5, 16, 0, 0x1ffffff); F(6, 19, 1, 0x3ffffff); F(7, 22, 3, 0x1ffffff); F(8, 25, 4, 0x3ffffff); F(9, 28, 6, 0x1ffffff); #undef F } #if (-32 >> 1) != -16 #error "This code only works when >> does sign-extension on negative numbers" #endif static inline s32 s32_eq(s32 a, s32 b) { a = ~(a ^ b); a &= a << 16; a &= a << 8; a &= a << 4; a &= a << 2; a &= a << 1; return a >> 31; } static inline s32 s32_gte(s32 a, s32 b) { a -= b; /* a >= 0 iff a >= b. */ return ~(a >> 31); } static inline void fcontract(u8 *output, limb *input_limbs) { int i; int j; s32 input[10]; s32 mask; for (i = 0; i < 10; i++) { input[i] = input_limbs[i]; } for (j = 0; j < 2; ++j) { for (i = 0; i < 9; ++i) { if ((i & 1) == 1) { const s32 mm = input[i] >> 31; const s32 carry = -((input[i] & mm) >> 25); input[i] = input[i] + (carry << 25); input[i+1] = input[i+1] - carry; } else { const s32 mm = input[i] >> 31; const s32 carry = -((input[i] & mm) >> 26); input[i] = input[i] + (carry << 26); input[i+1] = input[i+1] - carry; } } { const s32 mm = input[9] >> 31; const s32 carry = -((input[9] & mm) >> 25); input[9] = input[9] + (carry << 25); input[0] = input[0] - (carry * 19); } } { const s32 mm = input[0] >> 31; const s32 carry = -((input[0] & mm) >> 26); input[0] = input[0] + (carry << 26); input[1] = input[1] - carry; } for (j = 0; j < 2; j++) { for (i = 0; i < 9; i++) { if ((i & 1) == 1) { const s32 carry = input[i] >> 25; input[i] &= 0x1ffffff; input[i+1] += carry; } else { const s32 carry = input[i] >> 26; input[i] &= 0x3ffffff; input[i+1] += carry; } } { const s32 carry = input[9] >> 25; input[9] &= 0x1ffffff; input[0] += 19*carry; } } mask = s32_gte(input[0], 0x3ffffed); for (i = 1; i < 10; i++) { if ((i & 1) == 1) { mask &= s32_eq(input[i], 0x1ffffff); } else { mask &= s32_eq(input[i], 0x3ffffff); } } input[0] -= mask & 0x3ffffed; for (i = 1; i < 10; i++) { if ((i & 1) == 1) { input[i] -= mask & 0x1ffffff; } else { input[i] -= mask & 0x3ffffff; } } input[1] <<= 2; input[2] <<= 3; input[3] <<= 5; input[4] <<= 6; input[6] <<= 1; input[7] <<= 3; input[8] <<= 4; input[9] <<= 6; #define F(i, s) \ output[s+0] |= input[i] & 0xff; \ output[s+1] = (input[i] >> 8) & 0xff; \ output[s+2] = (input[i] >> 16) & 0xff; \ output[s+3] = (input[i] >> 24) & 0xff; output[0] = 0; output[16] = 0; F(0,0); F(1,3); F(2,6); F(3,9); F(4,12); F(5,16); F(6,19); F(7,22); F(8,25); F(9,28); #undef F } static inline void fmonty(limb *x2, limb *z2, /* output 2Q */ limb *x3, limb *z3, /* output Q + Q' */ limb *x, limb *z, /* input Q */ limb *xprime, limb *zprime, /* input Q' */ const limb *qmqp /* input Q - Q' */) { limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19], zzprime[19], zzzprime[19], xxxprime[19]; memcpy(origx, x, 10 * sizeof(limb)); fsum(x, z); /* |x[i]| < 2^27 */ fdifference(z, origx); /* does x - z */ /* |z[i]| < 2^27 */ memcpy(origxprime, xprime, sizeof(limb) * 10); fsum(xprime, zprime); /* |xprime[i]| < 2^27 */ fdifference(zprime, origxprime); /* |zprime[i]| < 2^27 */ fproduct(xxprime, xprime, z); /* |xxprime[i]| < 14*2^54: the largest product of two limbs will be < * 2^(27+27) and fproduct adds together, at most, 14 of those products. * (Approximating that to 2^58 doesn't work out.) */ fproduct(zzprime, x, zprime); /* |zzprime[i]| < 14*2^54 */ freduce_degree(xxprime); freduce_coefficients(xxprime); /* |xxprime[i]| < 2^26 */ freduce_degree(zzprime); freduce_coefficients(zzprime); /* |zzprime[i]| < 2^26 */ memcpy(origxprime, xxprime, sizeof(limb) * 10); fsum(xxprime, zzprime); /* |xxprime[i]| < 2^27 */ fdifference(zzprime, origxprime); /* |zzprime[i]| < 2^27 */ fsquare(xxxprime, xxprime); /* |xxxprime[i]| < 2^26 */ fsquare(zzzprime, zzprime); /* |zzzprime[i]| < 2^26 */ fproduct(zzprime, zzzprime, qmqp); /* |zzprime[i]| < 14*2^52 */ freduce_degree(zzprime); freduce_coefficients(zzprime); /* |zzprime[i]| < 2^26 */ memcpy(x3, xxxprime, sizeof(limb) * 10); memcpy(z3, zzprime, sizeof(limb) * 10); fsquare(xx, x); /* |xx[i]| < 2^26 */ fsquare(zz, z); /* |zz[i]| < 2^26 */ fproduct(x2, xx, zz); /* |x2[i]| < 14*2^52 */ freduce_degree(x2); freduce_coefficients(x2); /* |x2[i]| < 2^26 */ fdifference(zz, xx); // does zz = xx - zz /* |zz[i]| < 2^27 */ memset(zzz + 10, 0, sizeof(limb) * 9); fscalar_product(zzz, zz, 121665); /* |zzz[i]| < 2^(27+17) */ /* No need to call freduce_degree here: fscalar_product doesn't increase the degree of its input. */ freduce_coefficients(zzz); /* |zzz[i]| < 2^26 */ fsum(zzz, xx); /* |zzz[i]| < 2^27 */ fproduct(z2, zz, zzz); /* |z2[i]| < 14*2^(26+27) */ freduce_degree(z2); freduce_coefficients(z2); /* |z2|i| < 2^26 */ } static inline void swap_conditional(limb a[19], limb b[19], limb iswap) { unsigned i; const s32 swap = (s32) -iswap; for (i = 0; i < 10; ++i) { const s32 x = swap & ( ((s32)a[i]) ^ ((s32)b[i]) ); a[i] = ((s32)a[i]) ^ x; b[i] = ((s32)b[i]) ^ x; } } static inline void cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q) { limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0}; limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t; limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1}; limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h; unsigned i, j; memcpy(nqpqx, q, sizeof(limb) * 10); for (i = 0; i < 32; ++i) { u8 byte = n[31 - i]; for (j = 0; j < 8; ++j) { const limb bit = byte >> 7; swap_conditional(nqx, nqpqx, bit); swap_conditional(nqz, nqpqz, bit); fmonty(nqx2, nqz2, nqpqx2, nqpqz2, nqx, nqz, nqpqx, nqpqz, q); swap_conditional(nqx2, nqpqx2, bit); swap_conditional(nqz2, nqpqz2, bit); t = nqx; nqx = nqx2; nqx2 = t; t = nqz; nqz = nqz2; nqz2 = t; t = nqpqx; nqpqx = nqpqx2; nqpqx2 = t; t = nqpqz; nqpqz = nqpqz2; nqpqz2 = t; byte <<= 1; } } memcpy(resultx, nqx, sizeof(limb) * 10); memcpy(resultz, nqz, sizeof(limb) * 10); } static inline void crecip(limb *out, const limb *z) { limb z2[10]; limb z9[10]; limb z11[10]; limb z2_5_0[10]; limb z2_10_0[10]; limb z2_20_0[10]; limb z2_50_0[10]; limb z2_100_0[10]; limb t0[10]; limb t1[10]; int i; /* 2 */ fsquare(z2,z); /* 4 */ fsquare(t1,z2); /* 8 */ fsquare(t0,t1); /* 9 */ fmul(z9,t0,z); /* 11 */ fmul(z11,z9,z2); /* 22 */ fsquare(t0,z11); /* 2^5 - 2^0 = 31 */ fmul(z2_5_0,t0,z9); /* 2^6 - 2^1 */ fsquare(t0,z2_5_0); /* 2^7 - 2^2 */ fsquare(t1,t0); /* 2^8 - 2^3 */ fsquare(t0,t1); /* 2^9 - 2^4 */ fsquare(t1,t0); /* 2^10 - 2^5 */ fsquare(t0,t1); /* 2^10 - 2^0 */ fmul(z2_10_0,t0,z2_5_0); /* 2^11 - 2^1 */ fsquare(t0,z2_10_0); /* 2^12 - 2^2 */ fsquare(t1,t0); /* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } /* 2^20 - 2^0 */ fmul(z2_20_0,t1,z2_10_0); /* 2^21 - 2^1 */ fsquare(t0,z2_20_0); /* 2^22 - 2^2 */ fsquare(t1,t0); /* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } /* 2^40 - 2^0 */ fmul(t0,t1,z2_20_0); /* 2^41 - 2^1 */ fsquare(t1,t0); /* 2^42 - 2^2 */ fsquare(t0,t1); /* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t1,t0); fsquare(t0,t1); } /* 2^50 - 2^0 */ fmul(z2_50_0,t0,z2_10_0); /* 2^51 - 2^1 */ fsquare(t0,z2_50_0); /* 2^52 - 2^2 */ fsquare(t1,t0); /* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } /* 2^100 - 2^0 */ fmul(z2_100_0,t1,z2_50_0); /* 2^101 - 2^1 */ fsquare(t1,z2_100_0); /* 2^102 - 2^2 */ fsquare(t0,t1); /* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fsquare(t1,t0); fsquare(t0,t1); } /* 2^200 - 2^0 */ fmul(t1,t0,z2_100_0); /* 2^201 - 2^1 */ fsquare(t0,t1); /* 2^202 - 2^2 */ fsquare(t1,t0); /* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } /* 2^250 - 2^0 */ fmul(t0,t1,z2_50_0); /* 2^251 - 2^1 */ fsquare(t1,t0); /* 2^252 - 2^2 */ fsquare(t0,t1); /* 2^253 - 2^3 */ fsquare(t1,t0); /* 2^254 - 2^4 */ fsquare(t0,t1); /* 2^255 - 2^5 */ fsquare(t1,t0); /* 2^255 - 21 */ fmul(out,t1,z11); } static void crypto_scalarmult(u8 *mypublic, const u8 *secret, const u8 *basepoint) { limb bp[10], x[10], z[11], zmone[10]; uint8_t e[32]; int i; for (i = 0; i < 32; ++i) e[i] = secret[i]; e[0] &= 248; e[31] &= 127; e[31] |= 64; fexpand(bp, basepoint); cmult(x, z, e, bp); crecip(zmone, z); fmul(z, x, zmone); fcontract(mypublic, z); } static const unsigned char base[32] = {9}; static inline void crypto_scalarmult_base(unsigned char *q,const unsigned char *n) { crypto_scalarmult(q,n,base); } ////////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////////// // Ed25519 ref from: http://bench.cr.yp.to/supercop.html typedef struct { crypto_uint32 v[32]; } fe25519; typedef struct { crypto_uint32 v[32]; } sc25519; typedef struct { crypto_uint32 v[16]; } shortsc25519; typedef struct { fe25519 x; fe25519 y; fe25519 z; fe25519 t; } ge25519; #define ge25519_p3 ge25519 typedef struct { fe25519 x; fe25519 z; fe25519 y; fe25519 t; } ge25519_p1p1; typedef struct { fe25519 x; fe25519 y; fe25519 z; } ge25519_p2; typedef struct { fe25519 x; fe25519 y; } ge25519_aff; static inline void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y); static inline crypto_uint32 equal(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */ { crypto_uint32 x = a ^ b; /* 0: yes; 1..65535: no */ x -= 1; /* 4294967295: yes; 0..65534: no */ x >>= 31; /* 1: yes; 0: no */ return x; } static inline crypto_uint32 ge(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */ { unsigned int x = a; x -= (unsigned int) b; /* 0..65535: yes; 4294901761..4294967295: no */ x >>= 31; /* 0: yes; 1: no */ x ^= 1; /* 1: yes; 0: no */ return x; } static inline crypto_uint32 times19(crypto_uint32 a) { return (a << 4) + (a << 1) + a; } static inline crypto_uint32 times38(crypto_uint32 a) { return (a << 5) + (a << 2) + (a << 1); } static inline void reduce_add_sub(fe25519 *r) { int i,rep; for(rep=0;rep<4;rep++) { crypto_uint32 t = r->v[31] >> 7; r->v[31] &= 127; t = times19(t); r->v[0] += t; for(i=0;i<31;i++) { t = r->v[i] >> 8; r->v[i+1] += t; r->v[i] &= 255; } } } static inline void reduce_mul(fe25519 *r) { int i,rep; for(rep=0;rep<2;rep++) { crypto_uint32 t = r->v[31] >> 7; r->v[31] &= 127; t = times19(t); r->v[0] += t; for(i=0;i<31;i++) { t = r->v[i] >> 8; r->v[i+1] += t; r->v[i] &= 255; } } } /* reduction modulo 2^255-19 */ static inline void fe25519_freeze(fe25519 *r) { int i; crypto_uint32 mm = equal(r->v[31],127); for(i=30;i>0;i--) mm &= equal(r->v[i],255); mm &= ge(r->v[0],237); mm = -mm; r->v[31] -= mm&127; for(i=30;i>0;i--) r->v[i] -= mm&255; r->v[0] -= mm&237; } static inline void fe25519_unpack(fe25519 *r, const unsigned char x[32]) { int i; for(i=0;i<32;i++) r->v[i] = x[i]; r->v[31] &= 127; } /* Assumes input x being reduced below 2^255 */ static inline void fe25519_pack(unsigned char r[32], const fe25519 *x) { int i; fe25519 y = *x; fe25519_freeze(&y); for(i=0;i<32;i++) r[i] = y.v[i]; } static inline int fe25519_iseq_vartime(const fe25519 *x, const fe25519 *y) { int i; fe25519 t1 = *x; fe25519 t2 = *y; fe25519_freeze(&t1); fe25519_freeze(&t2); for(i=0;i<32;i++) if(t1.v[i] != t2.v[i]) return 0; return 1; } static inline void fe25519_cmov(fe25519 *r, const fe25519 *x, unsigned char b) { int i; crypto_uint32 mask = b; mask = -mask; for(i=0;i<32;i++) r->v[i] ^= mask & (x->v[i] ^ r->v[i]); } static inline unsigned char fe25519_getparity(const fe25519 *x) { fe25519 t = *x; fe25519_freeze(&t); return t.v[0] & 1; } static inline void fe25519_setone(fe25519 *r) { int i; r->v[0] = 1; for(i=1;i<32;i++) r->v[i]=0; } static inline void fe25519_setzero(fe25519 *r) { int i; for(i=0;i<32;i++) r->v[i]=0; } static inline void fe25519_neg(fe25519 *r, const fe25519 *x) { fe25519 t; int i; for(i=0;i<32;i++) t.v[i]=x->v[i]; fe25519_setzero(r); fe25519_sub(r, r, &t); } static inline void fe25519_add(fe25519 *r, const fe25519 *x, const fe25519 *y) { int i; for(i=0;i<32;i++) r->v[i] = x->v[i] + y->v[i]; reduce_add_sub(r); } static inline void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y) { int i; crypto_uint32 t[32]; t[0] = x->v[0] + 0x1da; t[31] = x->v[31] + 0xfe; for(i=1;i<31;i++) t[i] = x->v[i] + 0x1fe; for(i=0;i<32;i++) r->v[i] = t[i] - y->v[i]; reduce_add_sub(r); } static inline void fe25519_mul(fe25519 *r, const fe25519 *x, const fe25519 *y) { int i,j; crypto_uint32 t[63]; for(i=0;i<63;i++)t[i] = 0; for(i=0;i<32;i++) for(j=0;j<32;j++) t[i+j] += x->v[i] * y->v[j]; for(i=32;i<63;i++) r->v[i-32] = t[i-32] + times38(t[i]); r->v[31] = t[31]; /* result now in r[0]...r[31] */ reduce_mul(r); } static inline void fe25519_square(fe25519 *r, const fe25519 *x) { fe25519_mul(r, x, x); } static inline void fe25519_invert(fe25519 *r, const fe25519 *x) { fe25519 z2; fe25519 z9; fe25519 z11; fe25519 z2_5_0; fe25519 z2_10_0; fe25519 z2_20_0; fe25519 z2_50_0; fe25519 z2_100_0; fe25519 t0; fe25519 t1; int i; /* 2 */ fe25519_square(&z2,x); /* 4 */ fe25519_square(&t1,&z2); /* 8 */ fe25519_square(&t0,&t1); /* 9 */ fe25519_mul(&z9,&t0,x); /* 11 */ fe25519_mul(&z11,&z9,&z2); /* 22 */ fe25519_square(&t0,&z11); /* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0,&t0,&z9); /* 2^6 - 2^1 */ fe25519_square(&t0,&z2_5_0); /* 2^7 - 2^2 */ fe25519_square(&t1,&t0); /* 2^8 - 2^3 */ fe25519_square(&t0,&t1); /* 2^9 - 2^4 */ fe25519_square(&t1,&t0); /* 2^10 - 2^5 */ fe25519_square(&t0,&t1); /* 2^10 - 2^0 */ fe25519_mul(&z2_10_0,&t0,&z2_5_0); /* 2^11 - 2^1 */ fe25519_square(&t0,&z2_10_0); /* 2^12 - 2^2 */ fe25519_square(&t1,&t0); /* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); } /* 2^20 - 2^0 */ fe25519_mul(&z2_20_0,&t1,&z2_10_0); /* 2^21 - 2^1 */ fe25519_square(&t0,&z2_20_0); /* 2^22 - 2^2 */ fe25519_square(&t1,&t0); /* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); } /* 2^40 - 2^0 */ fe25519_mul(&t0,&t1,&z2_20_0); /* 2^41 - 2^1 */ fe25519_square(&t1,&t0); /* 2^42 - 2^2 */ fe25519_square(&t0,&t1); /* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fe25519_square(&t1,&t0); fe25519_square(&t0,&t1); } /* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t0,&z2_10_0); /* 2^51 - 2^1 */ fe25519_square(&t0,&z2_50_0); /* 2^52 - 2^2 */ fe25519_square(&t1,&t0); /* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); } /* 2^100 - 2^0 */ fe25519_mul(&z2_100_0,&t1,&z2_50_0); /* 2^101 - 2^1 */ fe25519_square(&t1,&z2_100_0); /* 2^102 - 2^2 */ fe25519_square(&t0,&t1); /* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fe25519_square(&t1,&t0); fe25519_square(&t0,&t1); } /* 2^200 - 2^0 */ fe25519_mul(&t1,&t0,&z2_100_0); /* 2^201 - 2^1 */ fe25519_square(&t0,&t1); /* 2^202 - 2^2 */ fe25519_square(&t1,&t0); /* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); } /* 2^250 - 2^0 */ fe25519_mul(&t0,&t1,&z2_50_0); /* 2^251 - 2^1 */ fe25519_square(&t1,&t0); /* 2^252 - 2^2 */ fe25519_square(&t0,&t1); /* 2^253 - 2^3 */ fe25519_square(&t1,&t0); /* 2^254 - 2^4 */ fe25519_square(&t0,&t1); /* 2^255 - 2^5 */ fe25519_square(&t1,&t0); /* 2^255 - 21 */ fe25519_mul(r,&t1,&z11); } static inline void fe25519_pow2523(fe25519 *r, const fe25519 *x) { fe25519 z2; fe25519 z9; fe25519 z11; fe25519 z2_5_0; fe25519 z2_10_0; fe25519 z2_20_0; fe25519 z2_50_0; fe25519 z2_100_0; fe25519 t; int i; /* 2 */ fe25519_square(&z2,x); /* 4 */ fe25519_square(&t,&z2); /* 8 */ fe25519_square(&t,&t); /* 9 */ fe25519_mul(&z9,&t,x); /* 11 */ fe25519_mul(&z11,&z9,&z2); /* 22 */ fe25519_square(&t,&z11); /* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0,&t,&z9); /* 2^6 - 2^1 */ fe25519_square(&t,&z2_5_0); /* 2^10 - 2^5 */ for (i = 1;i < 5;i++) { fe25519_square(&t,&t); } /* 2^10 - 2^0 */ fe25519_mul(&z2_10_0,&t,&z2_5_0); /* 2^11 - 2^1 */ fe25519_square(&t,&z2_10_0); /* 2^20 - 2^10 */ for (i = 1;i < 10;i++) { fe25519_square(&t,&t); } /* 2^20 - 2^0 */ fe25519_mul(&z2_20_0,&t,&z2_10_0); /* 2^21 - 2^1 */ fe25519_square(&t,&z2_20_0); /* 2^40 - 2^20 */ for (i = 1;i < 20;i++) { fe25519_square(&t,&t); } /* 2^40 - 2^0 */ fe25519_mul(&t,&t,&z2_20_0); /* 2^41 - 2^1 */ fe25519_square(&t,&t); /* 2^50 - 2^10 */ for (i = 1;i < 10;i++) { fe25519_square(&t,&t); } /* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t,&z2_10_0); /* 2^51 - 2^1 */ fe25519_square(&t,&z2_50_0); /* 2^100 - 2^50 */ for (i = 1;i < 50;i++) { fe25519_square(&t,&t); } /* 2^100 - 2^0 */ fe25519_mul(&z2_100_0,&t,&z2_50_0); /* 2^101 - 2^1 */ fe25519_square(&t,&z2_100_0); /* 2^200 - 2^100 */ for (i = 1;i < 100;i++) { fe25519_square(&t,&t); } /* 2^200 - 2^0 */ fe25519_mul(&t,&t,&z2_100_0); /* 2^201 - 2^1 */ fe25519_square(&t,&t); /* 2^250 - 2^50 */ for (i = 1;i < 50;i++) { fe25519_square(&t,&t); } /* 2^250 - 2^0 */ fe25519_mul(&t,&t,&z2_50_0); /* 2^251 - 2^1 */ fe25519_square(&t,&t); /* 2^252 - 2^2 */ fe25519_square(&t,&t); /* 2^252 - 3 */ fe25519_mul(r,&t,x); } static const crypto_uint32 m[32] = {0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2, 0xDE, 0xF9, 0xDE, 0x14, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10}; static const crypto_uint32 mu[33] = {0x1B, 0x13, 0x2C, 0x0A, 0xA3, 0xE5, 0x9C, 0xED, 0xA7, 0x29, 0x63, 0x08, 0x5D, 0x21, 0x06, 0x21, 0xEB, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0F}; static inline crypto_uint32 lt(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */ { unsigned int x = a; x -= (unsigned int) b; /* 0..65535: no; 4294901761..4294967295: yes */ x >>= 31; /* 0: no; 1: yes */ return x; } /* Reduce coefficients of r before calling reduce_add_sub */ static inline void reduce_add_sub(sc25519 *r) { crypto_uint32 pb = 0; crypto_uint32 b; crypto_uint32 mask; int i; unsigned char t[32]; for(i=0;i<32;i++) { pb += m[i]; b = lt(r->v[i],pb); t[i] = r->v[i]-pb+(b<<8); pb = b; } mask = b - 1; for(i=0;i<32;i++) r->v[i] ^= mask & (r->v[i] ^ t[i]); } /* Reduce coefficients of x before calling barrett_reduce */ static inline void barrett_reduce(sc25519 *r, const crypto_uint32 x[64]) { /* See HAC, Alg. 14.42 */ int i,j; crypto_uint32 q2[66]; crypto_uint32 *q3 = q2 + 33; crypto_uint32 r1[33]; crypto_uint32 r2[33]; crypto_uint32 pb = 0; for (i = 0;i < 66;++i) q2[i] = 0; for (i = 0;i < 33;++i) r2[i] = 0; for(i=0;i<33;i++) for(j=0;j<33;j++) if(i+j >= 31) q2[i+j] += mu[i]*x[j+31]; q2[32] += (q2[31] >> 8); q2[33] += (q2[32] >> 8); for(i=0;i<33;i++)r1[i] = x[i]; for(i=0;i<32;i++) for(j=0;j<33;j++) if(i+j < 33) r2[i+j] += m[i]*q3[j]; for(i=0;i<32;i++) { r2[i+1] += (r2[i] >> 8); r2[i] &= 0xff; } for(i=0;i<32;i++) { pb += r2[i]; crypto_uint32 b = lt(r1[i],pb); r->v[i] = r1[i]-pb+(b<<8); pb = b; } /* XXX: Can it really happen that r<0?, See HAC, Alg 14.42, Step 3 * If so: Handle it here! */ reduce_add_sub(r); reduce_add_sub(r); } static inline void sc25519_from32bytes(sc25519 *r, const unsigned char x[32]) { int i; crypto_uint32 t[64]; for(i=0;i<32;i++) t[i] = x[i]; for(i=32;i<64;++i) t[i] = 0; barrett_reduce(r, t); } static inline void sc25519_from64bytes(sc25519 *r, const unsigned char x[64]) { int i; crypto_uint32 t[64]; for(i=0;i<64;i++) t[i] = x[i]; barrett_reduce(r, t); } static inline void sc25519_to32bytes(unsigned char r[32], const sc25519 *x) { int i; for(i=0;i<32;i++) r[i] = x->v[i]; } static inline void sc25519_add(sc25519 *r, const sc25519 *x, const sc25519 *y) { int i; for(i=0;i<32;i++) r->v[i] = x->v[i] + y->v[i]; for(i=0;i<31;i++) { r->v[i+1] += (r->v[i] >> 8); r->v[i] &= 0xff; } reduce_add_sub(r); } static inline void sc25519_mul(sc25519 *r, const sc25519 *x, const sc25519 *y) { int i,j; crypto_uint32 t[64]; for(i=0;i<64;i++)t[i] = 0; for(i=0;i<32;i++) for(j=0;j<32;j++) t[i+j] += x->v[i] * y->v[j]; for(i=0;i<63;i++) { t[i+1] += (t[i] >> 8); t[i] &= 0xff; } barrett_reduce(r, t); } static inline void sc25519_window3(signed char r[85], const sc25519 *s) { char carry; int i; for(i=0;i<10;i++) { r[8*i+0] = s->v[3*i+0] & 7; r[8*i+1] = (s->v[3*i+0] >> 3) & 7; r[8*i+2] = (s->v[3*i+0] >> 6) & 7; r[8*i+2] ^= (s->v[3*i+1] << 2) & 7; r[8*i+3] = (s->v[3*i+1] >> 1) & 7; r[8*i+4] = (s->v[3*i+1] >> 4) & 7; r[8*i+5] = (s->v[3*i+1] >> 7) & 7; r[8*i+5] ^= (s->v[3*i+2] << 1) & 7; r[8*i+6] = (s->v[3*i+2] >> 2) & 7; r[8*i+7] = (s->v[3*i+2] >> 5) & 7; } r[8*i+0] = s->v[3*i+0] & 7; r[8*i+1] = (s->v[3*i+0] >> 3) & 7; r[8*i+2] = (s->v[3*i+0] >> 6) & 7; r[8*i+2] ^= (s->v[3*i+1] << 2) & 7; r[8*i+3] = (s->v[3*i+1] >> 1) & 7; r[8*i+4] = (s->v[3*i+1] >> 4) & 7; /* Making it signed */ carry = 0; for(i=0;i<84;i++) { r[i] += carry; r[i+1] += r[i] >> 3; r[i] &= 7; carry = r[i] >> 2; r[i] -= carry<<3; } r[84] += carry; } static inline void sc25519_2interleave2(unsigned char r[127], const sc25519 *s1, const sc25519 *s2) { int i; for(i=0;i<31;i++) { r[4*i] = ( s1->v[i] & 3) ^ (( s2->v[i] & 3) << 2); r[4*i+1] = ((s1->v[i] >> 2) & 3) ^ (((s2->v[i] >> 2) & 3) << 2); r[4*i+2] = ((s1->v[i] >> 4) & 3) ^ (((s2->v[i] >> 4) & 3) << 2); r[4*i+3] = ((s1->v[i] >> 6) & 3) ^ (((s2->v[i] >> 6) & 3) << 2); } r[124] = ( s1->v[31] & 3) ^ (( s2->v[31] & 3) << 2); r[125] = ((s1->v[31] >> 2) & 3) ^ (((s2->v[31] >> 2) & 3) << 2); r[126] = ((s1->v[31] >> 4) & 3) ^ (((s2->v[31] >> 4) & 3) << 2); } /* d */ static const fe25519 ge25519_ecd = {{0xA3, 0x78, 0x59, 0x13, 0xCA, 0x4D, 0xEB, 0x75, 0xAB, 0xD8, 0x41, 0x41, 0x4D, 0x0A, 0x70, 0x00, 0x98, 0xE8, 0x79, 0x77, 0x79, 0x40, 0xC7, 0x8C, 0x73, 0xFE, 0x6F, 0x2B, 0xEE, 0x6C, 0x03, 0x52}}; /* 2*d */ static const fe25519 ge25519_ec2d = {{0x59, 0xF1, 0xB2, 0x26, 0x94, 0x9B, 0xD6, 0xEB, 0x56, 0xB1, 0x83, 0x82, 0x9A, 0x14, 0xE0, 0x00, 0x30, 0xD1, 0xF3, 0xEE, 0xF2, 0x80, 0x8E, 0x19, 0xE7, 0xFC, 0xDF, 0x56, 0xDC, 0xD9, 0x06, 0x24}}; /* sqrt(-1) */ static const fe25519 ge25519_sqrtm1 = {{0xB0, 0xA0, 0x0E, 0x4A, 0x27, 0x1B, 0xEE, 0xC4, 0x78, 0xE4, 0x2F, 0xAD, 0x06, 0x18, 0x43, 0x2F, 0xA7, 0xD7, 0xFB, 0x3D, 0x99, 0x00, 0x4D, 0x2B, 0x0B, 0xDF, 0xC1, 0x4F, 0x80, 0x24, 0x83, 0x2B}}; /* Packed coordinates of the base point */ static const ge25519 ge25519_base = {{{0x1A, 0xD5, 0x25, 0x8F, 0x60, 0x2D, 0x56, 0xC9, 0xB2, 0xA7, 0x25, 0x95, 0x60, 0xC7, 0x2C, 0x69, 0x5C, 0xDC, 0xD6, 0xFD, 0x31, 0xE2, 0xA4, 0xC0, 0xFE, 0x53, 0x6E, 0xCD, 0xD3, 0x36, 0x69, 0x21}}, {{0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66}}, {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, {{0xA3, 0xDD, 0xB7, 0xA5, 0xB3, 0x8A, 0xDE, 0x6D, 0xF5, 0x52, 0x51, 0x77, 0x80, 0x9F, 0xF0, 0x20, 0x7D, 0xE3, 0xAB, 0x64, 0x8E, 0x4E, 0xEA, 0x66, 0x65, 0x76, 0x8B, 0xD7, 0x0F, 0x5F, 0x87, 0x67}}}; /* Multiples of the base point in affine representation */ static const ge25519_aff ge25519_base_multiples_affine[425] = { {{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}}, {{{0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95, 0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0, 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21}} , {{0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66}}}, {{{0x0e, 0xce, 0x43, 0x28, 0x4e, 0xa1, 0xc5, 0x83, 0x5f, 0xa4, 0xd7, 0x15, 0x45, 0x8e, 0x0d, 0x08, 0xac, 0xe7, 0x33, 0x18, 0x7d, 0x3b, 0x04, 0x3d, 0x6c, 0x04, 0x5a, 0x9f, 0x4c, 0x38, 0xab, 0x36}} , {{0xc9, 0xa3, 0xf8, 0x6a, 0xae, 0x46, 0x5f, 0x0e, 0x56, 0x51, 0x38, 0x64, 0x51, 0x0f, 0x39, 0x97, 0x56, 0x1f, 0xa2, 0xc9, 0xe8, 0x5e, 0xa2, 0x1d, 0xc2, 0x29, 0x23, 0x09, 0xf3, 0xcd, 0x60, 0x22}}}, {{{0x5c, 0xe2, 0xf8, 0xd3, 0x5f, 0x48, 0x62, 0xac, 0x86, 0x48, 0x62, 0x81, 0x19, 0x98, 0x43, 0x63, 0x3a, 0xc8, 0xda, 0x3e, 0x74, 0xae, 0xf4, 0x1f, 0x49, 0x8f, 0x92, 0x22, 0x4a, 0x9c, 0xae, 0x67}} , {{0xd4, 0xb4, 0xf5, 0x78, 0x48, 0x68, 0xc3, 0x02, 0x04, 0x03, 0x24, 0x67, 0x17, 0xec, 0x16, 0x9f, 0xf7, 0x9e, 0x26, 0x60, 0x8e, 0xa1, 0x26, 0xa1, 0xab, 0x69, 0xee, 0x77, 0xd1, 0xb1, 0x67, 0x12}}}, {{{0x70, 0xf8, 0xc9, 0xc4, 0x57, 0xa6, 0x3a, 0x49, 0x47, 0x15, 0xce, 0x93, 0xc1, 0x9e, 0x73, 0x1a, 0xf9, 0x20, 0x35, 0x7a, 0xb8, 0xd4, 0x25, 0x83, 0x46, 0xf1, 0xcf, 0x56, 0xdb, 0xa8, 0x3d, 0x20}} , {{0x2f, 0x11, 0x32, 0xca, 0x61, 0xab, 0x38, 0xdf, 0xf0, 0x0f, 0x2f, 0xea, 0x32, 0x28, 0xf2, 0x4c, 0x6c, 0x71, 0xd5, 0x80, 0x85, 0xb8, 0x0e, 0x47, 0xe1, 0x95, 0x15, 0xcb, 0x27, 0xe8, 0xd0, 0x47}}}, {{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}}, {{{0xc8, 0x84, 0xa5, 0x08, 0xbc, 0xfd, 0x87, 0x3b, 0x99, 0x8b, 0x69, 0x80, 0x7b, 0xc6, 0x3a, 0xeb, 0x93, 0xcf, 0x4e, 0xf8, 0x5c, 0x2d, 0x86, 0x42, 0xb6, 0x71, 0xd7, 0x97, 0x5f, 0xe1, 0x42, 0x67}} , {{0xb4, 0xb9, 0x37, 0xfc, 0xa9, 0x5b, 0x2f, 0x1e, 0x93, 0xe4, 0x1e, 0x62, 0xfc, 0x3c, 0x78, 0x81, 0x8f, 0xf3, 0x8a, 0x66, 0x09, 0x6f, 0xad, 0x6e, 0x79, 0x73, 0xe5, 0xc9, 0x00, 0x06, 0xd3, 0x21}}}, {{{0xf8, 0xf9, 0x28, 0x6c, 0x6d, 0x59, 0xb2, 0x59, 0x74, 0x23, 0xbf, 0xe7, 0x33, 0x8d, 0x57, 0x09, 0x91, 0x9c, 0x24, 0x08, 0x15, 0x2b, 0xe2, 0xb8, 0xee, 0x3a, 0xe5, 0x27, 0x06, 0x86, 0xa4, 0x23}} , {{0xeb, 0x27, 0x67, 0xc1, 0x37, 0xab, 0x7a, 0xd8, 0x27, 0x9c, 0x07, 0x8e, 0xff, 0x11, 0x6a, 0xb0, 0x78, 0x6e, 0xad, 0x3a, 0x2e, 0x0f, 0x98, 0x9f, 0x72, 0xc3, 0x7f, 0x82, 0xf2, 0x96, 0x96, 0x70}}}, {{{0x81, 0x6b, 0x88, 0xe8, 0x1e, 0xc7, 0x77, 0x96, 0x0e, 0xa1, 0xa9, 0x52, 0xe0, 0xd8, 0x0e, 0x61, 0x9e, 0x79, 0x2d, 0x95, 0x9c, 0x8d, 0x96, 0xe0, 0x06, 0x40, 0x5d, 0x87, 0x28, 0x5f, 0x98, 0x70}} , {{0xf1, 0x79, 0x7b, 0xed, 0x4f, 0x44, 0xb2, 0xe7, 0x08, 0x0d, 0xc2, 0x08, 0x12, 0xd2, 0x9f, 0xdf, 0xcd, 0x93, 0x20, 0x8a, 0xcf, 0x33, 0xca, 0x6d, 0x89, 0xb9, 0x77, 0xc8, 0x93, 0x1b, 0x4e, 0x60}}}, {{{0x26, 0x4f, 0x7e, 0x97, 0xf6, 0x40, 0xdd, 0x4f, 0xfc, 0x52, 0x78, 0xf9, 0x90, 0x31, 0x03, 0xe6, 0x7d, 0x56, 0x39, 0x0b, 0x1d, 0x56, 0x82, 0x85, 0xf9, 0x1a, 0x42, 0x17, 0x69, 0x6c, 0xcf, 0x39}} , {{0x69, 0xd2, 0x06, 0x3a, 0x4f, 0x39, 0x2d, 0xf9, 0x38, 0x40, 0x8c, 0x4c, 0xe7, 0x05, 0x12, 0xb4, 0x78, 0x8b, 0xf8, 0xc0, 0xec, 0x93, 0xde, 0x7a, 0x6b, 0xce, 0x2c, 0xe1, 0x0e, 0xa9, 0x34, 0x44}}}, {{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}}, {{{0x0b, 0xa4, 0x3c, 0xb0, 0x0f, 0x7a, 0x51, 0xf1, 0x78, 0xd6, 0xd9, 0x6a, 0xfd, 0x46, 0xe8, 0xb8, 0xa8, 0x79, 0x1d, 0x87, 0xf9, 0x90, 0xf2, 0x9c, 0x13, 0x29, 0xf8, 0x0b, 0x20, 0x64, 0xfa, 0x05}} , {{0x26, 0x09, 0xda, 0x17, 0xaf, 0x95, 0xd6, 0xfb, 0x6a, 0x19, 0x0d, 0x6e, 0x5e, 0x12, 0xf1, 0x99, 0x4c, 0xaa, 0xa8, 0x6f, 0x79, 0x86, 0xf4, 0x72, 0x28, 0x00, 0x26, 0xf9, 0xea, 0x9e, 0x19, 0x3d}}}, {{{0x87, 0xdd, 0xcf, 0xf0, 0x5b, 0x49, 0xa2, 0x5d, 0x40, 0x7a, 0x23, 0x26, 0xa4, 0x7a, 0x83, 0x8a, 0xb7, 0x8b, 0xd2, 0x1a, 0xbf, 0xea, 0x02, 0x24, 0x08, 0x5f, 0x7b, 0xa9, 0xb1, 0xbe, 0x9d, 0x37}} , {{0xfc, 0x86, 0x4b, 0x08, 0xee, 0xe7, 0xa0, 0xfd, 0x21, 0x45, 0x09, 0x34, 0xc1, 0x61, 0x32, 0x23, 0xfc, 0x9b, 0x55, 0x48, 0x53, 0x99, 0xf7, 0x63, 0xd0, 0x99, 0xce, 0x01, 0xe0, 0x9f, 0xeb, 0x28}}}, {{{0x47, 0xfc, 0xab, 0x5a, 0x17, 0xf0, 0x85, 0x56, 0x3a, 0x30, 0x86, 0x20, 0x28, 0x4b, 0x8e, 0x44, 0x74, 0x3a, 0x6e, 0x02, 0xf1, 0x32, 0x8f, 0x9f, 0x3f, 0x08, 0x35, 0xe9, 0xca, 0x16, 0x5f, 0x6e}} , {{0x1c, 0x59, 0x1c, 0x65, 0x5d, 0x34, 0xa4, 0x09, 0xcd, 0x13, 0x9c, 0x70, 0x7d, 0xb1, 0x2a, 0xc5, 0x88, 0xaf, 0x0b, 0x60, 0xc7, 0x9f, 0x34, 0x8d, 0xd6, 0xb7, 0x7f, 0xea, 0x78, 0x65, 0x8d, 0x77}}}, {{{0x56, 0xa5, 0xc2, 0x0c, 0xdd, 0xbc, 0xb8, 0x20, 0x6d, 0x57, 0x61, 0xb5, 0xfb, 0x78, 0xb5, 0xd4, 0x49, 0x54, 0x90, 0x26, 0xc1, 0xcb, 0xe9, 0xe6, 0xbf, 0xec, 0x1d, 0x4e, 0xed, 0x07, 0x7e, 0x5e}} , {{0xc7, 0xf6, 0x6c, 0x56, 0x31, 0x20, 0x14, 0x0e, 0xa8, 0xd9, 0x27, 0xc1, 0x9a, 0x3d, 0x1b, 0x7d, 0x0e, 0x26, 0xd3, 0x81, 0xaa, 0xeb, 0xf5, 0x6b, 0x79, 0x02, 0xf1, 0x51, 0x5c, 0x75, 0x55, 0x0f}}}, {{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}}, {{{0x0a, 0x34, 0xcd, 0x82, 0x3c, 0x33, 0x09, 0x54, 0xd2, 0x61, 0x39, 0x30, 0x9b, 0xfd, 0xef, 0x21, 0x26, 0xd4, 0x70, 0xfa, 0xee, 0xf9, 0x31, 0x33, 0x73, 0x84, 0xd0, 0xb3, 0x81, 0xbf, 0xec, 0x2e}} , {{0xe8, 0x93, 0x8b, 0x00, 0x64, 0xf7, 0x9c, 0xb8, 0x74, 0xe0, 0xe6, 0x49, 0x48, 0x4d, 0x4d, 0x48, 0xb6, 0x19, 0xa1, 0x40, 0xb7, 0xd9, 0x32, 0x41, 0x7c, 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0x55, 0x1f, 0x60, 0x5a}}}, {{{0xe5, 0x89, 0x8a, 0x76, 0x6c, 0xdb, 0x4d, 0x0a, 0x5b, 0x72, 0x9d, 0x59, 0x6e, 0x63, 0x63, 0x18, 0x7c, 0xe3, 0xfa, 0xe2, 0xdb, 0xa1, 0x8d, 0xf4, 0xa5, 0xd7, 0x16, 0xb2, 0xd0, 0xb3, 0x3f, 0x39}} , {{0xce, 0x60, 0x09, 0x6c, 0xf5, 0x76, 0x17, 0x24, 0x80, 0x3a, 0x96, 0xc7, 0x94, 0x2e, 0xf7, 0x6b, 0xef, 0xb5, 0x05, 0x96, 0xef, 0xd3, 0x7b, 0x51, 0xda, 0x05, 0x44, 0x67, 0xbc, 0x07, 0x21, 0x4e}}}, {{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}}, {{{0xe9, 0x73, 0x6f, 0x21, 0xb9, 0xde, 0x22, 0x7d, 0xeb, 0x97, 0x31, 0x10, 0xa3, 0xea, 0xe1, 0xc6, 0x37, 0xeb, 0x8f, 0x43, 0x58, 0xde, 0x41, 0x64, 0x0e, 0x3e, 0x07, 0x99, 0x3d, 0xf1, 0xdf, 0x1e}} , {{0xf8, 0xad, 0x43, 0xc2, 0x17, 0x06, 0xe2, 0xe4, 0xa9, 0x86, 0xcd, 0x18, 0xd7, 0x78, 0xc8, 0x74, 0x66, 0xd2, 0x09, 0x18, 0xa5, 0xf1, 0xca, 0xa6, 0x62, 0x92, 0xc1, 0xcb, 0x00, 0xeb, 0x42, 0x2e}}}, {{{0x7b, 0x34, 0x24, 0x4c, 0xcf, 0x38, 0xe5, 0x6c, 0x0a, 0x01, 0x2c, 0x22, 0x0b, 0x24, 0x38, 0xad, 0x24, 0x7e, 0x19, 0xf0, 0x6c, 0xf9, 0x31, 0xf4, 0x35, 0x11, 0xf6, 0x46, 0x33, 0x3a, 0x23, 0x59}} , {{0x20, 0x0b, 0xa1, 0x08, 0x19, 0xad, 0x39, 0x54, 0xea, 0x3e, 0x23, 0x09, 0xb6, 0xe2, 0xd2, 0xbc, 0x4d, 0xfc, 0x9c, 0xf0, 0x13, 0x16, 0x22, 0x3f, 0xb9, 0xd2, 0x11, 0x86, 0x90, 0x55, 0xce, 0x3c}}}, {{{0xc4, 0x0b, 0x4b, 0x62, 0x99, 0x37, 0x84, 0x3f, 0x74, 0xa2, 0xf9, 0xce, 0xe2, 0x0b, 0x0f, 0x2a, 0x3d, 0xa3, 0xe3, 0xdb, 0x5a, 0x9d, 0x93, 0xcc, 0xa5, 0xef, 0x82, 0x91, 0x1d, 0xe6, 0x6c, 0x68}} , {{0xa3, 0x64, 0x17, 0x9b, 0x8b, 0xc8, 0x3a, 0x61, 0xe6, 0x9d, 0xc6, 0xed, 0x7b, 0x03, 0x52, 0x26, 0x9d, 0x3a, 0xb3, 0x13, 0xcc, 0x8a, 0xfd, 0x2c, 0x1a, 0x1d, 0xed, 0x13, 0xd0, 0x55, 0x57, 0x0e}}}, {{{0x1a, 0xea, 0xbf, 0xfd, 0x4a, 0x3c, 0x8e, 0xec, 0x29, 0x7e, 0x77, 0x77, 0x12, 0x99, 0xd7, 0x84, 0xf9, 0x55, 0x7f, 0xf1, 0x8b, 0xb4, 0xd2, 0x95, 0xa3, 0x8d, 0xf0, 0x8a, 0xa7, 0xeb, 0x82, 0x4b}} , {{0x2c, 0x28, 0xf4, 0x3a, 0xf6, 0xde, 0x0a, 0xe0, 0x41, 0x44, 0x23, 0xf8, 0x3f, 0x03, 0x64, 0x9f, 0xc3, 0x55, 0x4c, 0xc6, 0xc1, 0x94, 0x1c, 0x24, 0x5d, 0x5f, 0x92, 0x45, 0x96, 0x57, 0x37, 0x14}}}, {{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}}, {{{0xc1, 0xcd, 0x90, 0x66, 0xb9, 0x76, 0xa0, 0x5b, 0xa5, 0x85, 0x75, 0x23, 0xf9, 0x89, 0xa5, 0x82, 0xb2, 0x6f, 0xb1, 0xeb, 0xc4, 0x69, 0x6f, 0x18, 0x5a, 0xed, 0x94, 0x3d, 0x9d, 0xd9, 0x2c, 0x1a}} , {{0x35, 0xb0, 0xe6, 0x73, 0x06, 0xb7, 0x37, 0xe0, 0xf8, 0xb0, 0x22, 0xe8, 0xd2, 0xed, 0x0b, 0xef, 0xe6, 0xc6, 0x5a, 0x99, 0x9e, 0x1a, 0x9f, 0x04, 0x97, 0xe4, 0x4d, 0x0b, 0xbe, 0xba, 0x44, 0x40}}}, {{{0xc1, 0x56, 0x96, 0x91, 0x5f, 0x1f, 0xbb, 0x54, 0x6f, 0x88, 0x89, 0x0a, 0xb2, 0xd6, 0x41, 0x42, 0x6a, 0x82, 0xee, 0x14, 0xaa, 0x76, 0x30, 0x65, 0x0f, 0x67, 0x39, 0xa6, 0x51, 0x7c, 0x49, 0x24}} , {{0x35, 0xa3, 0x78, 0xd1, 0x11, 0x0f, 0x75, 0xd3, 0x70, 0x46, 0xdb, 0x20, 0x51, 0xcb, 0x92, 0x80, 0x54, 0x10, 0x74, 0x36, 0x86, 0xa9, 0xd7, 0xa3, 0x08, 0x78, 0xf1, 0x01, 0x29, 0xf8, 0x80, 0x3b}}}, {{{0xdb, 0xa7, 0x9d, 0x9d, 0xbf, 0xa0, 0xcc, 0xed, 0x53, 0xa2, 0xa2, 0x19, 0x39, 0x48, 0x83, 0x19, 0x37, 0x58, 0xd1, 0x04, 0x28, 0x40, 0xf7, 0x8a, 0xc2, 0x08, 0xb7, 0xa5, 0x42, 0xcf, 0x53, 0x4c}} , {{0xa7, 0xbb, 0xf6, 0x8e, 0xad, 0xdd, 0xf7, 0x90, 0xdd, 0x5f, 0x93, 0x89, 0xae, 0x04, 0x37, 0xe6, 0x9a, 0xb7, 0xe8, 0xc0, 0xdf, 0x16, 0x2a, 0xbf, 0xc4, 0x3a, 0x3c, 0x41, 0xd5, 0x89, 0x72, 0x5a}}}, {{{0x1f, 0x96, 0xff, 0x34, 0x2c, 0x13, 0x21, 0xcb, 0x0a, 0x89, 0x85, 0xbe, 0xb3, 0x70, 0x9e, 0x1e, 0xde, 0x97, 0xaf, 0x96, 0x30, 0xf7, 0x48, 0x89, 0x40, 0x8d, 0x07, 0xf1, 0x25, 0xf0, 0x30, 0x58}} , {{0x1e, 0xd4, 0x93, 0x57, 0xe2, 0x17, 0xe7, 0x9d, 0xab, 0x3c, 0x55, 0x03, 0x82, 0x2f, 0x2b, 0xdb, 0x56, 0x1e, 0x30, 0x2e, 0x24, 0x47, 0x6e, 0xe6, 0xff, 0x33, 0x24, 0x2c, 0x75, 0x51, 0xd4, 0x67}}}, {{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}}, {{{0x2b, 0x06, 0xd9, 0xa1, 0x5d, 0xe1, 0xf4, 0xd1, 0x1e, 0x3c, 0x9a, 0xc6, 0x29, 0x2b, 0x13, 0x13, 0x78, 0xc0, 0xd8, 0x16, 0x17, 0x2d, 0x9e, 0xa9, 0xc9, 0x79, 0x57, 0xab, 0x24, 0x91, 0x92, 0x19}} , {{0x69, 0xfb, 0xa1, 0x9c, 0xa6, 0x75, 0x49, 0x7d, 0x60, 0x73, 0x40, 0x42, 0xc4, 0x13, 0x0a, 0x95, 0x79, 0x1e, 0x04, 0x83, 0x94, 0x99, 0x9b, 0x1e, 0x0c, 0xe8, 0x1f, 0x54, 0xef, 0xcb, 0xc0, 0x52}}}, {{{0x14, 0x89, 0x73, 0xa1, 0x37, 0x87, 0x6a, 0x7a, 0xcf, 0x1d, 0xd9, 0x2e, 0x1a, 0x67, 0xed, 0x74, 0xc0, 0xf0, 0x9c, 0x33, 0xdd, 0xdf, 0x08, 0xbf, 0x7b, 0xd1, 0x66, 0xda, 0xe6, 0xc9, 0x49, 0x08}} , {{0xe9, 0xdd, 0x5e, 0x55, 0xb0, 0x0a, 0xde, 0x21, 0x4c, 0x5a, 0x2e, 0xd4, 0x80, 0x3a, 0x57, 0x92, 0x7a, 0xf1, 0xc4, 0x2c, 0x40, 0xaf, 0x2f, 0xc9, 0x92, 0x03, 0xe5, 0x5a, 0xbc, 0xdc, 0xf4, 0x09}}}, {{{0xf3, 0xe1, 0x2b, 0x7c, 0x05, 0x86, 0x80, 0x93, 0x4a, 0xad, 0xb4, 0x8f, 0x7e, 0x99, 0x0c, 0xfd, 0xcd, 0xef, 0xd1, 0xff, 0x2c, 0x69, 0x34, 0x13, 0x41, 0x64, 0xcf, 0x3b, 0xd0, 0x90, 0x09, 0x1e}} , {{0x9d, 0x45, 0xd6, 0x80, 0xe6, 0x45, 0xaa, 0xf4, 0x15, 0xaa, 0x5c, 0x34, 0x87, 0x99, 0xa2, 0x8c, 0x26, 0x84, 0x62, 0x7d, 0xb6, 0x29, 0xc0, 0x52, 0xea, 0xf5, 0x81, 0x18, 0x0f, 0x35, 0xa9, 0x0e}}}, {{{0xe7, 0x20, 0x72, 0x7c, 0x6d, 0x94, 0x5f, 0x52, 0x44, 0x54, 0xe3, 0xf1, 0xb2, 0xb0, 0x36, 0x46, 0x0f, 0xae, 0x92, 0xe8, 0x70, 0x9d, 0x6e, 0x79, 0xb1, 0xad, 0x37, 0xa9, 0x5f, 0xc0, 0xde, 0x03}} , {{0x15, 0x55, 0x37, 0xc6, 0x1c, 0x27, 0x1c, 0x6d, 0x14, 0x4f, 0xca, 0xa4, 0xc4, 0x88, 0x25, 0x46, 0x39, 0xfc, 0x5a, 0xe5, 0xfe, 0x29, 0x11, 0x69, 0xf5, 0x72, 0x84, 0x4d, 0x78, 0x9f, 0x94, 0x15}}}, {{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}}, {{{0xec, 0xd3, 0xff, 0x57, 0x0b, 0xb0, 0xb2, 0xdc, 0xf8, 0x4f, 0xe2, 0x12, 0xd5, 0x36, 0xbe, 0x6b, 0x09, 0x43, 0x6d, 0xa3, 0x4d, 0x90, 0x2d, 0xb8, 0x74, 0xe8, 0x71, 0x45, 0x19, 0x8b, 0x0c, 0x6a}} , {{0xb8, 0x42, 0x1c, 0x03, 0xad, 0x2c, 0x03, 0x8e, 0xac, 0xd7, 0x98, 0x29, 0x13, 0xc6, 0x02, 0x29, 0xb5, 0xd4, 0xe7, 0xcf, 0xcc, 0x8b, 0x83, 0xec, 0x35, 0xc7, 0x9c, 0x74, 0xb7, 0xad, 0x85, 0x5f}}}, {{{0x78, 0x84, 0xe1, 0x56, 0x45, 0x69, 0x68, 0x5a, 0x4f, 0xb8, 0xb1, 0x29, 0xff, 0x33, 0x03, 0x31, 0xb7, 0xcb, 0x96, 0x25, 0xe6, 0xe6, 0x41, 0x98, 0x1a, 0xbb, 0x03, 0x56, 0xf2, 0xb2, 0x91, 0x34}} , {{0x2c, 0x6c, 0xf7, 0x66, 0xa4, 0x62, 0x6b, 0x39, 0xb3, 0xba, 0x65, 0xd3, 0x1c, 0xf8, 0x11, 0xaa, 0xbe, 0xdc, 0x80, 0x59, 0x87, 0xf5, 0x7b, 0xe5, 0xe3, 0xb3, 0x3e, 0x39, 0xda, 0xbe, 0x88, 0x09}}}, {{{0x8b, 0xf1, 0xa0, 0xf5, 0xdc, 0x29, 0xb4, 0xe2, 0x07, 0xc6, 0x7a, 0x00, 0xd0, 0x89, 0x17, 0x51, 0xd4, 0xbb, 0xd4, 0x22, 0xea, 0x7e, 0x7d, 0x7c, 0x24, 0xea, 0xf2, 0xe8, 0x22, 0x12, 0x95, 0x06}} , {{0xda, 0x7c, 0xa4, 0x0c, 0xf4, 0xba, 0x6e, 0xe1, 0x89, 0xb5, 0x59, 0xca, 0xf1, 0xc0, 0x29, 0x36, 0x09, 0x44, 0xe2, 0x7f, 0xd1, 0x63, 0x15, 0x99, 0xea, 0x25, 0xcf, 0x0c, 0x9d, 0xc0, 0x44, 0x6f}}}, {{{0x1d, 0x86, 0x4e, 0xcf, 0xf7, 0x37, 0x10, 0x25, 0x8f, 0x12, 0xfb, 0x19, 0xfb, 0xe0, 0xed, 0x10, 0xc8, 0xe2, 0xf5, 0x75, 0xb1, 0x33, 0xc0, 0x96, 0x0d, 0xfb, 0x15, 0x6c, 0x0d, 0x07, 0x5f, 0x05}} , {{0x69, 0x3e, 0x47, 0x97, 0x2c, 0xaf, 0x52, 0x7c, 0x78, 0x83, 0xad, 0x1b, 0x39, 0x82, 0x2f, 0x02, 0x6f, 0x47, 0xdb, 0x2a, 0xb0, 0xe1, 0x91, 0x99, 0x55, 0xb8, 0x99, 0x3a, 0xa0, 0x44, 0x11, 0x51}}} }; static inline void p1p1_to_p2(ge25519_p2 *r, const ge25519_p1p1 *p) { fe25519_mul(&r->x, &p->x, &p->t); fe25519_mul(&r->y, &p->y, &p->z); fe25519_mul(&r->z, &p->z, &p->t); } static inline void p1p1_to_p2_2(ge25519_p3 *r, const ge25519_p1p1 *p) { fe25519_mul(&r->x, &p->x, &p->t); fe25519_mul(&r->y, &p->y, &p->z); fe25519_mul(&r->z, &p->z, &p->t); } static inline void p1p1_to_p3(ge25519_p3 *r, const ge25519_p1p1 *p) { p1p1_to_p2_2(r, p); fe25519_mul(&r->t, &p->x, &p->y); } static inline void ge25519_mixadd2(ge25519_p3 *r, const ge25519_aff *q) { fe25519 a,b,t1,t2,c,d,e,f,g,h,qt; fe25519_mul(&qt, &q->x, &q->y); fe25519_sub(&a, &r->y, &r->x); /* A = (Y1-X1)*(Y2-X2) */ fe25519_add(&b, &r->y, &r->x); /* B = (Y1+X1)*(Y2+X2) */ fe25519_sub(&t1, &q->y, &q->x); fe25519_add(&t2, &q->y, &q->x); fe25519_mul(&a, &a, &t1); fe25519_mul(&b, &b, &t2); fe25519_sub(&e, &b, &a); /* E = B-A */ fe25519_add(&h, &b, &a); /* H = B+A */ fe25519_mul(&c, &r->t, &qt); /* C = T1*k*T2 */ fe25519_mul(&c, &c, &ge25519_ec2d); fe25519_add(&d, &r->z, &r->z); /* D = Z1*2 */ fe25519_sub(&f, &d, &c); /* F = D-C */ fe25519_add(&g, &d, &c); /* G = D+C */ fe25519_mul(&r->x, &e, &f); fe25519_mul(&r->y, &h, &g); fe25519_mul(&r->z, &g, &f); fe25519_mul(&r->t, &e, &h); } static inline void add_p1p1(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_p3 *q) { fe25519 a, b, c, d, t; fe25519_sub(&a, &p->y, &p->x); /* A = (Y1-X1)*(Y2-X2) */ fe25519_sub(&t, &q->y, &q->x); fe25519_mul(&a, &a, &t); fe25519_add(&b, &p->x, &p->y); /* B = (Y1+X1)*(Y2+X2) */ fe25519_add(&t, &q->x, &q->y); fe25519_mul(&b, &b, &t); fe25519_mul(&c, &p->t, &q->t); /* C = T1*k*T2 */ fe25519_mul(&c, &c, &ge25519_ec2d); fe25519_mul(&d, &p->z, &q->z); /* D = Z1*2*Z2 */ fe25519_add(&d, &d, &d); fe25519_sub(&r->x, &b, &a); /* E = B-A */ fe25519_sub(&r->t, &d, &c); /* F = D-C */ fe25519_add(&r->z, &d, &c); /* G = D+C */ fe25519_add(&r->y, &b, &a); /* H = B+A */ } /* See http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#doubling-dbl-2008-hwcd */ static inline void dbl_p1p1(ge25519_p1p1 *r, const ge25519_p2 *p) { fe25519 a,b,c,d; fe25519_square(&a, &p->x); fe25519_square(&b, &p->y); fe25519_square(&c, &p->z); fe25519_add(&c, &c, &c); fe25519_neg(&d, &a); fe25519_add(&r->x, &p->x, &p->y); fe25519_square(&r->x, &r->x); fe25519_sub(&r->x, &r->x, &a); fe25519_sub(&r->x, &r->x, &b); fe25519_add(&r->z, &d, &b); fe25519_sub(&r->t, &r->z, &c); fe25519_sub(&r->y, &d, &b); } /* Constant-time version of: if(b) r = p */ static inline void cmov_aff(ge25519_aff *r, const ge25519_aff *p, unsigned char b) { fe25519_cmov(&r->x, &p->x, b); fe25519_cmov(&r->y, &p->y, b); } static inline unsigned char equal(signed char b,signed char c) { unsigned char ub = b; unsigned char uc = c; unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */ crypto_uint32 y = x; /* 0: yes; 1..255: no */ y -= 1; /* 4294967295: yes; 0..254: no */ y >>= 31; /* 1: yes; 0: no */ return (unsigned char)y; } static inline unsigned char negative(signed char b) { unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */ x >>= 63; /* 1: yes; 0: no */ return (unsigned char)x; } static inline void choose_t(ge25519_aff *t, unsigned long long pos, signed char b) { /* constant time */ fe25519 v; *t = ge25519_base_multiples_affine[5*pos+0]; cmov_aff(t, &ge25519_base_multiples_affine[5*pos+1],equal(b,1) | equal(b,-1)); cmov_aff(t, &ge25519_base_multiples_affine[5*pos+2],equal(b,2) | equal(b,-2)); cmov_aff(t, &ge25519_base_multiples_affine[5*pos+3],equal(b,3) | equal(b,-3)); cmov_aff(t, &ge25519_base_multiples_affine[5*pos+4],equal(b,-4)); fe25519_neg(&v, &t->x); fe25519_cmov(&t->x, &v, negative(b)); } static inline void setneutral(ge25519 *r) { fe25519_setzero(&r->x); fe25519_setone(&r->y); fe25519_setone(&r->z); fe25519_setzero(&r->t); } /* return 0 on success, -1 otherwise */ static inline int ge25519_unpackneg_vartime(ge25519_p3 *r, const unsigned char p[32]) { unsigned char par; fe25519 t, chk, num, den, den2, den4, den6; fe25519_setone(&r->z); par = p[31] >> 7; fe25519_unpack(&r->y, p); fe25519_square(&num, &r->y); /* x = y^2 */ fe25519_mul(&den, &num, &ge25519_ecd); /* den = dy^2 */ fe25519_sub(&num, &num, &r->z); /* x = y^2-1 */ fe25519_add(&den, &r->z, &den); /* den = dy^2+1 */ /* Computation of sqrt(num/den) */ /* 1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8) */ fe25519_square(&den2, &den); fe25519_square(&den4, &den2); fe25519_mul(&den6, &den4, &den2); fe25519_mul(&t, &den6, &num); fe25519_mul(&t, &t, &den); fe25519_pow2523(&t, &t); /* 2. computation of r->x = t * num * den^3 */ fe25519_mul(&t, &t, &num); fe25519_mul(&t, &t, &den); fe25519_mul(&t, &t, &den); fe25519_mul(&r->x, &t, &den); /* 3. Check whether sqrt computation gave correct result, multiply by sqrt(-1) if not: */ fe25519_square(&chk, &r->x); fe25519_mul(&chk, &chk, &den); if (!fe25519_iseq_vartime(&chk, &num)) fe25519_mul(&r->x, &r->x, &ge25519_sqrtm1); /* 4. Now we have one of the two square roots, except if input was not a square */ fe25519_square(&chk, &r->x); fe25519_mul(&chk, &chk, &den); if (!fe25519_iseq_vartime(&chk, &num)) return -1; /* 5. Choose the desired square root according to parity: */ if(fe25519_getparity(&r->x) != (1-par)) fe25519_neg(&r->x, &r->x); fe25519_mul(&r->t, &r->x, &r->y); return 0; } static inline void ge25519_pack(unsigned char r[32], const ge25519_p3 *p) { fe25519 tx, ty, zi; fe25519_invert(&zi, &p->z); fe25519_mul(&tx, &p->x, &zi); fe25519_mul(&ty, &p->y, &zi); fe25519_pack(r, &ty); r[31] ^= fe25519_getparity(&tx) << 7; } /* computes [s1]p1 + [s2]p2 */ static inline void ge25519_double_scalarmult_vartime(ge25519_p3 *r, const ge25519_p3 *p1, const sc25519 *s1, const ge25519_p3 *p2, const sc25519 *s2) { ge25519_p1p1 tp1p1; ge25519_p3 pre[16]; char *pre5 = (char *)(&(pre[5])); // eliminate type punning warning unsigned char b[127]; int i; /* precomputation s2 s1 */ setneutral(pre); /* 00 00 */ pre[1] = *p1; /* 00 01 */ dbl_p1p1(&tp1p1,(ge25519_p2 *)p1); p1p1_to_p3( &pre[2], &tp1p1); /* 00 10 */ add_p1p1(&tp1p1,&pre[1], &pre[2]); p1p1_to_p3( &pre[3], &tp1p1); /* 00 11 */ pre[4] = *p2; /* 01 00 */ add_p1p1(&tp1p1,&pre[1], &pre[4]); p1p1_to_p3( &pre[5], &tp1p1); /* 01 01 */ add_p1p1(&tp1p1,&pre[2], &pre[4]); p1p1_to_p3( &pre[6], &tp1p1); /* 01 10 */ add_p1p1(&tp1p1,&pre[3], &pre[4]); p1p1_to_p3( &pre[7], &tp1p1); /* 01 11 */ dbl_p1p1(&tp1p1,(ge25519_p2 *)p2); p1p1_to_p3( &pre[8], &tp1p1); /* 10 00 */ add_p1p1(&tp1p1,&pre[1], &pre[8]); p1p1_to_p3( &pre[9], &tp1p1); /* 10 01 */ dbl_p1p1(&tp1p1,(ge25519_p2 *)pre5); p1p1_to_p3(&pre[10], &tp1p1); /* 10 10 */ add_p1p1(&tp1p1,&pre[3], &pre[8]); p1p1_to_p3(&pre[11], &tp1p1); /* 10 11 */ add_p1p1(&tp1p1,&pre[4], &pre[8]); p1p1_to_p3(&pre[12], &tp1p1); /* 11 00 */ add_p1p1(&tp1p1,&pre[1],&pre[12]); p1p1_to_p3(&pre[13], &tp1p1); /* 11 01 */ add_p1p1(&tp1p1,&pre[2],&pre[12]); p1p1_to_p3(&pre[14], &tp1p1); /* 11 10 */ add_p1p1(&tp1p1,&pre[3],&pre[12]); p1p1_to_p3(&pre[15], &tp1p1); /* 11 11 */ sc25519_2interleave2(b,s1,s2); /* scalar multiplication */ *r = pre[b[126]]; for(i=125;i>=0;i--) { dbl_p1p1(&tp1p1, (ge25519_p2 *)r); p1p1_to_p2((ge25519_p2 *) r, &tp1p1); dbl_p1p1(&tp1p1, (ge25519_p2 *)r); if(b[i]!=0) { p1p1_to_p3(r, &tp1p1); add_p1p1(&tp1p1, r, &pre[b[i]]); } if(i != 0) p1p1_to_p2((ge25519_p2 *)r, &tp1p1); else p1p1_to_p3(r, &tp1p1); } } static inline void ge25519_scalarmult_base(ge25519_p3 *r, const sc25519 *s) { signed char b[85]; int i; ge25519_aff t; sc25519_window3(b,s); choose_t((ge25519_aff *)r, 0, b[0]); fe25519_setone(&r->z); fe25519_mul(&r->t, &r->x, &r->y); for(i=1;i<85;i++) { choose_t(&t, (unsigned long long) i, b[i]); ge25519_mixadd2(r, &t); } } static inline void get_hram(unsigned char *hram, const unsigned char *sm, const unsigned char *pk, unsigned char *playground, unsigned long long smlen) { unsigned long long i; for (i = 0;i < 32;++i) playground[i] = sm[i]; for (i = 32;i < 64;++i) playground[i] = pk[i-32]; for (i = 64;i < smlen;++i) playground[i] = sm[i]; ZeroTier::SHA512(hram,playground,(unsigned int)smlen); } ////////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////////// } // anonymous namespace namespace ZeroTier { void C25519::agree(const C25519::Private &mine,const C25519::Public &their,void *keybuf,unsigned int keylen) { unsigned char rawkey[32]; unsigned char digest[64]; crypto_scalarmult(rawkey,mine.data,their.data); SHA512(digest,rawkey,32); for(unsigned int i=0,k=0;i