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| -rw-r--r-- | ge25519.c | 321 |
1 files changed, 321 insertions, 0 deletions
diff --git a/ge25519.c b/ge25519.c new file mode 100644 index 0000000..dfe3849 --- /dev/null +++ b/ge25519.c @@ -0,0 +1,321 @@ +/* $OpenBSD: ge25519.c,v 1.3 2013/12/09 11:03:45 markus Exp $ */ + +/* + * Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange, + * Peter Schwabe, Bo-Yin Yang. + * Copied from supercop-20130419/crypto_sign/ed25519/ref/ge25519.c + */ + +#include "includes.h" + +#include "fe25519.h" +#include "sc25519.h" +#include "ge25519.h" + +/* + * Arithmetic on the twisted Edwards curve -x^2 + y^2 = 1 + dx^2y^2 + * with d = -(121665/121666) = 37095705934669439343138083508754565189542113879843219016388785533085940283555 + * Base point: (15112221349535400772501151409588531511454012693041857206046113283949847762202,46316835694926478169428394003475163141307993866256225615783033603165251855960); + */ + +/* 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}}; + +#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; + + +/* Packed coordinates of the base point */ +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] = { +#include "ge25519_base.data" +}; + +static 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 void p1p1_to_p3(ge25519_p3 *r, const ge25519_p1p1 *p) +{ + p1p1_to_p2((ge25519_p2 *)r, p); + fe25519_mul(&r->t, &p->x, &p->y); +} + +static 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 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 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 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 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 y; +} + +static unsigned char negative(signed char b) +{ + unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */ + x >>= 63; /* 1: yes; 0: no */ + return x; +} + +static 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 void setneutral(ge25519 *r) +{ + fe25519_setzero(&r->x); + fe25519_setone(&r->y); + fe25519_setone(&r->z); + fe25519_setzero(&r->t); +} + +/* ******************************************************************** + * EXPORTED FUNCTIONS + ******************************************************************** */ + +/* return 0 on success, -1 otherwise */ +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; +} + +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; +} + +int ge25519_isneutral_vartime(const ge25519_p3 *p) +{ + int ret = 1; + if(!fe25519_iszero(&p->x)) ret = 0; + if(!fe25519_iseq_vartime(&p->y, &p->z)) ret = 0; + return ret; +} + +/* computes [s1]p1 + [s2]p2 */ +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]; + 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 *)&pre[5]); 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); + } +} + +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); + } +} |