diff options
| author | Nagi5Yeq <nagi5yeq@gmail.com> | 2019-07-04 23:55:21 +0800 |
|---|---|---|
| committer | Nagi5Yeq <nagi5yeq@gmail.com> | 2019-07-04 23:55:21 +0800 |
| commit | 28bc016fb0dc11bf2a4c3e157daac24b2d9482f6 (patch) | |
| tree | 187edb3f152852940610e0cd09a5b2d16f83cc99 | |
| parent | 22aca24950b45892a70aef77a5f197e521fc11b5 (diff) | |
add ge448 and data
| -rw-r--r-- | fe448.c | 61 | ||||
| -rw-r--r-- | fe448.h | 2 | ||||
| -rw-r--r-- | ge448.c | 272 | ||||
| -rw-r--r-- | ge448.h | 34 | ||||
| -rw-r--r-- | ge448_base.data | 1490 | ||||
| -rw-r--r-- | ge448_gen.c | 99 | ||||
| -rw-r--r-- | sc448.c | 131 | ||||
| -rw-r--r-- | sc448.h | 13 |
8 files changed, 2006 insertions, 96 deletions
@@ -342,4 +342,65 @@ void fe448_invert(fe448 *r, const fe448 *x) /* pow(2**446-2**222-1) */ void fe448_pow446(fe448 *r, const fe448 *x) { + fe448 t0; + fe448 t1; + fe448 t2; + int i; + + fe448_square(&t0, x); + fe448_mul(&t0, &t0, x); /* 2^2 - 1 */ + fe448_square(&t0, &t0); /* 2^3 - 2 */ + fe448_mul(&t1, &t0, x); /* 2^3 - 1 */ + fe448_square(&t0, &t1); /* 2^4 - 2^1 */ + for (i = 0; i < 2; i++) + { + fe448_square(&t0, &t0); + } /* 2^6 - 2^3 */ + fe448_mul(&t1, &t1, &t0); /* 2^6 - 1 */ + fe448_square(&t0, &t1); /* 2^7 - 2^1 */ + for (i = 0; i < 5; i++) + { + fe448_square(&t0, &t0); + } /* 2^12 - 2^6 */ + fe448_mul(&t1, &t1, &t0); /* 2^12 - 1 */ + fe448_square(&t1, &t1); /* 2^13 - 2^1 */ + fe448_mul(&t1, &t1, x); /* 2^13 - 1 */ + fe448_square(&t0, &t1); /* 2^14 - 2^1 */ + for (i = 0; i < 12; i++) + { + fe448_square(&t0, &t0); + } /* 2^26 - 2^13 */ + fe448_mul(&t1, &t1, &t0); /* 2^26 - 1 */ + fe448_square(&t1, &t1); /* 2^26 - 2^1 */ + fe448_mul(&t1, &t1, x); /* 2^27 - 1 */ + fe448_square(&t0, &t1); /* 2^28 - 2^1 */ + for (i = 0; i < 26; i++) + { + fe448_square(&t0, &t0); + } /* 2^54 - 2^27 */ + fe448_mul(&t1, &t1, &t0); /* 2^54 - 1 */ + fe448_square(&t1, &t1); /* 2^55 - 2^1 */ + fe448_mul(&t1, &t1, x); /* 2^55 - 1 */ + fe448_square(&t0, &t1); /* 2^56 - 2^1 */ + for (i = 0; i < 54; i++) + { + fe448_square(&t0, &t0); + } /* 2^110 - 2^55 */ + fe448_mul(&t1, &t1, &t0); /* 2^110 - 1 */ + fe448_square(&t1, &t1); /* 2^111 - 2^1 */ + fe448_mul(&t1, &t1, x); /* 2^111 - 1 */ + fe448_square(&t0, &t1); /* 2^112 - 2^1 */ + for (i = 0; i < 110; i++) + { + fe448_square(&t0, &t0); + } /* 2^222 - 2^111 */ + fe448_mul(&t2, &t1, &t0); /* 2^222 - 1 */ + fe448_square(&t1, &t2); /* 2^223 - 2^1 */ + fe448_mul(&t1, &t1, x); /* 2^223 - 1 */ + fe448_square(&t0, &t1); /* 2^224 - 2^1 */ + for (i = 0; i < 222; i++) + { + fe448_square(&t0, &t0); + } /* 2^446 - 2^223 */ + fe448_mul(r, &t2, &t0); /* 2^446 - 2^222 - 1 */ } @@ -19,7 +19,7 @@ #define fe448_mul crypto_sign_ed448_ref_fe448_mul #define fe448_square crypto_sign_ed448_ref_fe448_square #define fe448_invert crypto_sign_ed448_ref_fe448_invert -#define fe448_pow2523 crypto_sign_ed448_ref_fe448_pow2523 +#define fe448_pow446 crypto_sign_ed448_ref_fe448_pow446 typedef struct { @@ -0,0 +1,272 @@ +#include "fe448.h" +#include "sc448.h" +#include "ge448.h" + +/* + * Ed448-Goldilocks: x^2 + y^2 = 1 + dx^2y^2 + * with d = -39081 + */ + +/* d */ +static const fe448 ge448_ecd = {{0x56, 0x67, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x00}}; + +#define ge448_p3 ge448 /* use projective coordinates only */ + +typedef struct +{ + fe448 x; + fe448 y; +} ge448_aff; + +/* Packed coordinates of the base point */ +const ge448 ge448_base = {{{0x5E, 0xC0, 0x0C, 0xC7, 0x2B, 0xA8, 0x26, 0x26, 0x8E, 0x93, 0x00, 0x8B, 0xE1, 0x80, 0x3B, 0x43, + 0x11, 0x65, 0xB6, 0x2A, 0xF7, 0x1A, 0xAE, 0x12, 0x64, 0xA4, 0xD3, 0xA3, 0x24, 0xE3, 0x6D, 0xEA, + 0x67, 0x17, 0x0F, 0x47, 0x70, 0x65, 0x14, 0x9E, 0xDA, 0x36, 0xBF, 0x22, 0xA6, 0x15, 0x1D, 0x22, + 0xED, 0x0D, 0xED, 0x6B, 0xC6, 0x70, 0x19, 0x4F, 0x00}}, + {{0x14, 0xFA, 0x30, 0xF2, 0x5B, 0x79, 0x08, 0x98, 0xAD, 0xC8, 0xD7, 0x4E, 0x2C, 0x13, 0xBD, 0xFD, + 0xC4, 0x39, 0x7C, 0xE6, 0x1C, 0xFF, 0xD3, 0x3A, 0xD7, 0xC2, 0xA0, 0x05, 0x1E, 0x9C, 0x78, 0x87, + 0x40, 0x98, 0xA3, 0x6C, 0x73, 0x73, 0xEA, 0x4B, 0x62, 0xC7, 0xC9, 0x56, 0x37, 0x20, 0x76, 0x88, + 0x24, 0xBC, 0xB6, 0x6E, 0x71, 0x46, 0x3F, 0x69, 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, + 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}}}; + +/* Multiples of the base point in affine representation */ +static const ge448_aff ge448_base_multiples_affine[745] = { +#include "ge448_base.data" +}; + +/* point addition from rfc8032 */ +static void ge25519_mixadd2(ge448_p3 *r, const ge448_aff *q) +{ + fe448 a, b, c, d, e, f, g, h; + a = r->z; /* A=Z1*Z2 (Z2=1) */ + fe448_square(&b, &a); /* B=A^2 */ + fe448_mul(&c, &r->x, &q->x); /* C=X1*X2 */ + fe448_mul(&d, &r->y, &q->y); /* D=Y1*Y2 */ + fe448_mul(&e, &c, &d); + fe448_mul(&e, &e, &ge448_ecd); /* E=d*C*D */ + fe448_sub(&f, &b, &e); /* F=B-E */ + fe448_add(&g, &b, &e); /* G=B+E */ + fe448_add(&b, &r->x, &r->y); + fe448_add(&h, &q->x, &q->y); + fe448_mul(&h, &b, &h); /* H=(X1+Y1)*(X2+Y2) */ + fe448_sub(&h, &h, &c); + fe448_sub(&h, &h, &d); + fe448_mul(&h, &h, &f); + fe448_mul(&r->x, &a, &h); /* X3=A*F*(H-C-D) */ + fe448_sub(&d, &d, &c); + fe448_mul(&d, &d, &g); + fe448_mul(&r->y, &a, &d); /* Y3=A*G*(D-C) */ + fe448_mul(&r->z, &f, &g); /* Z3=F*G */ +} + +static void add_p3(ge448_p3 *r, const ge448_p3 *p, const ge448_p3 *q) +{ + fe448 a, b, c, d, e, f, g, h; + fe448_mul(&a, &p->z, &q->z); /* A=Z1*Z2 */ + fe448_square(&b, &a); /* B=A^2 */ + fe448_mul(&c, &p->x, &q->x); /* C=X1*X2 */ + fe448_mul(&d, &p->y, &q->y); /* D=Y1*Y2 */ + fe448_mul(&e, &c, &d); + fe448_mul(&e, &e, &ge448_ecd); /* E=d*C*D */ + fe448_sub(&f, &b, &e); /* F=B-E */ + fe448_add(&g, &b, &e); /* G=B+E */ + fe448_add(&b, &p->x, &p->y); + fe448_add(&h, &q->x, &q->y); + fe448_mul(&h, &b, &h); /* H=(X1+Y1)*(X2+Y2) */ + fe448_sub(&h, &h, &c); + fe448_sub(&h, &h, &d); + fe448_mul(&h, &h, &f); + fe448_mul(&r->x, &a, &h); /* X3=A*F*(H-C-D) */ + fe448_sub(&d, &d, &c); + fe448_mul(&d, &d, &g); + fe448_mul(&r->y, &a, &d); /* Y3=A*G*(D-C) */ + fe448_mul(&r->z, &f, &g); /* Z3=F*G */ +} + +/* point doubling from rfc8032 */ +static void dbl_p3(ge448_p3 *r, const ge448_p3 *p) +{ + fe448 b, c, d, e, h, j; + fe448_add(&b, &p->x, &p->y); + fe448_square(&b, &b); /* B=(X1+Y1)^2 */ + fe448_square(&c, &p->x); /* C=X1^2 */ + fe448_square(&d, &p->y); /* D=Y1^2 */ + fe448_add(&e, &c, &d); /* E=C+D */ + fe448_square(&h, &p->z); /* H=Z1^2 */ + fe448_sub(&j, &e, &h); + fe448_sub(&j, &j, &h); /* J=E-2*H */ + fe448_sub(&h, &b, &e); + fe448_mul(&r->x, &h, &j); /* X3=(B-E)*J */ + fe448_sub(&h, &c, &d); + fe448_mul(&r->y, &e, &h); /* Y3=E*(C-D) */ + fe448_mul(&r->z, &e, &j); /* Z3=E*J */ +} + +/* Constant-time version of: if(b) r = p */ +static void cmov_aff(ge448_aff *r, const ge448_aff *p, unsigned char b) +{ + fe448_cmov(&r->x, &p->x, b); + fe448_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(ge448_aff *t, unsigned long long pos, signed char b) +{ + /* constant time */ + fe448 v; + *t = ge448_base_multiples_affine[5 * pos + 0]; + cmov_aff(t, &ge448_base_multiples_affine[5 * pos + 1], equal(b, 1) | equal(b, -1)); + cmov_aff(t, &ge448_base_multiples_affine[5 * pos + 2], equal(b, 2) | equal(b, -2)); + cmov_aff(t, &ge448_base_multiples_affine[5 * pos + 3], equal(b, 3) | equal(b, -3)); + cmov_aff(t, &ge448_base_multiples_affine[5 * pos + 4], equal(b, -4)); + fe448_neg(&v, &t->x); + fe448_cmov(&t->x, &v, negative(b)); +} + +static void setneutral(ge448 *r) +{ + fe448_setzero(&r->x); + fe448_setone(&r->y); + fe448_setone(&r->z); +} + +/* ******************************************************************** + * EXPORTED FUNCTIONS + ******************************************************************** */ + +/* return 0 on success, -1 otherwise */ +int ge448_unpackneg_vartime(ge448_p3 *r, const unsigned char p[57]) +{ + unsigned char par; + fe448 t, chk, num, num2, den, den2, n3d; + fe448_setone(&r->z); + par = p[56] >> 7; + fe448_unpack(&r->y, p); + fe448_square(&num, &r->y); /* x = y^2 */ + fe448_mul(&den, &num, &ge448_ecd); /* den = dy^2 */ + fe448_sub(&num, &num, &r->z); /* x = y^2-1 */ + fe448_sub(&den, &r->z, &den); /* den = dy^2-1 */ + + /* Computation of sqrt(num/den) */ + /* 1.: computation of num^3 * den */ + fe448_square(&num2, &num); + fe448_mul(&n3d, &num2, &num); + fe448_mul(&n3d, &n3d, &den); + + /* 2. computation of r->x = n3d * (num^5*den^3)^((p-3)/4) */ + fe448_square(&den2, &den); + fe448_mul(&t, &n3d, &den2); + fe448_mul(&t, &t, &num2); + fe448_pow446(&t, &t); + fe448_mul(&r->x, &t, &n3d); + + /* 3. Check whether square root exists */ + fe448_square(&chk, &r->x); + fe448_mul(&chk, &chk, &den); + if (!fe448_iseq_vartime(&chk, &num)) + return -1; + + /* 4. Choose the desired square root according to parity: */ + if (fe448_getparity(&r->x) != (1 - par)) + fe448_neg(&r->x, &r->x); + return 0; +} + +void ge448_pack(unsigned char r[57], const ge448_p3 *p) +{ + fe448 tx, ty, zi; + fe448_invert(&zi, &p->z); + fe448_mul(&tx, &p->x, &zi); + fe448_mul(&ty, &p->y, &zi); + fe448_pack(r, &ty); + r[56] ^= fe448_getparity(&tx) << 7; +} + +int ge448_isneutral_vartime(const ge448_p3 *p) +{ + int ret = 1; + if (!fe448_iszero(&p->x)) + ret = 0; + if (!fe448_iseq_vartime(&p->y, &p->z)) + ret = 0; + return ret; +} + +/* computes [s1]p1 + [s2]p2 */ +void ge448_double_scalarmult_vartime(ge448_p3 *r, const ge448_p3 *p1, const sc448 *s1, const ge448_p3 *p2, const sc448 *s2) +{ + ge448_p3 pre[16]; + unsigned char b[223]; + int i; + + /* precomputation s2 s1 */ + setneutral(pre); /* 00 00 */ + pre[1] = *p1; /* 00 01 */ + dbl_p3(&pre[2], p1); /* 00 10 */ + add_p3(&pre[3], &pre[1], &pre[2]); /* 00 11 */ + pre[4] = *p2; /* 01 00 */ + add_p3(&pre[5], &pre[1], &pre[4]); /* 01 01 */ + add_p3(&pre[6], &pre[2], &pre[4]); /* 01 10 */ + add_p3(&pre[7], &pre[3], &pre[4]); /* 01 11 */ + dbl_p3(&pre[8], p2); /* 10 00 */ + add_p3(&pre[9], &pre[1], &pre[8]); /* 10 01 */ + dbl_p3(&pre[10], &pre[5]); /* 10 10 */ + add_p3(&pre[11], &pre[3], &pre[8]); /* 10 11 */ + add_p3(&pre[12], &pre[4], &pre[8]); /* 11 00 */ + add_p3(&pre[13], &pre[1], &pre[12]); /* 11 01 */ + add_p3(&pre[14], &pre[2], &pre[12]); /* 11 10 */ + add_p3(&pre[15], &pre[3], &pre[12]); /* 11 11 */ + + sc448_2interleave2(b, s1, s2); + + /* scalar multiplication */ + *r = pre[b[222]]; + for (i = 125; i >= 0; i--) + { + dbl_p3(r, r); + dbl_p3(r, r); + if (b[i] != 0) + { + add_p3(r, r, &pre[b[i]]); + } + } +} + +void ge448_scalarmult_base(ge448_p3 *r, const sc448 *s) +{ + signed char b[149]; + int i; + ge448_aff t; + sc448_window3(b, s); + + choose_t((ge448_aff *)r, 0, b[0]); + fe448_setone(&r->z); + for (i = 1; i < 149; i++) + { + choose_t(&t, (unsigned long long)i, b[i]); + ge25519_mixadd2(r, &t); + } +} @@ -0,0 +1,34 @@ +#ifndef GE448_H +#define GE448_H + +#include "fe448.h" +#include "sc448.h" + +#define ge448 crypto_sign_ed448_ref_ge448 +#define ge448_base crypto_sign_ed448_ref_ge448_base +#define ge448_unpackneg_vartime crypto_sign_ed448_ref_unpackneg_vartime +#define ge448_pack crypto_sign_ed448_ref_pack +#define ge448_isneutral_vartime crypto_sign_ed448_ref_isneutral_vartime +#define ge448_double_scalarmult_vartime crypto_sign_ed448_ref_double_scalarmult_vartime +#define ge448_scalarmult_base crypto_sign_ed448_ref_scalarmult_base + +typedef struct +{ + fe448 x; + fe448 y; + fe448 z; +} ge448; + +extern const ge448 ge448_base; + +int ge448_unpackneg_vartime(ge448 *r, const unsigned char p[57]); + +void ge448_pack(unsigned char r[57], const ge448 *p); + +int ge448_isneutral_vartime(const ge448 *p); + +void ge448_double_scalarmult_vartime(ge448 *r, const ge448 *p1, const sc448 *s1, const ge448 *p2, const sc448 *s2); + +void ge448_scalarmult_base(ge448 *r, const sc448 *s); + +#endif diff --git a/ge448_base.data b/ge448_base.data new file mode 100644 index 0000000..9afd629 --- /dev/null +++ b/ge448_base.data @@ -0,0 +1,1490 @@ +{{{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, 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, 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}}}, +{{{0x5e, 0xc0, 0x0c, 0xc7, 0x2b, 0xa8, 0x26, 0x26, 0x8e, 0x93, 0x00, 0x8b, 0xe1, 0x80, 0x3b, 0x43, 0x11, 0x65, 0xb6, 0x2a, 0xf7, 0x1a, 0xae, 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0x5a, 0x9c, 0x92, 0xb2, 0xce, 0xd4, 0x84, 0xa8, 0xd5, 0x6c, 0x61, 0xf7, 0x48, 0xc1, 0xe5, 0xfe, 0xd2, 0x67, 0x58, 0x17, 0xcf, 0x3c, 0xb5, 0xe5, 0x1a, 0x70, 0x60, 0x44, 0xb2, 0x75, 0x8d, 0x4d, 0x4e, 0x26, 0x00}}, + {{0x28, 0x8e, 0xf5, 0x5b, 0xee, 0x73, 0x6b, 0xd7, 0x28, 0xd1, 0x81, 0x3c, 0x67, 0xcd, 0x4f, 0xd6, 0x46, 0xd2, 0x07, 0x41, 0xfd, 0xa4, 0x2b, 0xe4, 0xb9, 0xfb, 0xcb, 0x9e, 0xa7, 0x7f, 0xe9, 0x42, 0xa1, 0x82, 0x8a, 0x7b, 0x70, 0x5e, 0xc4, 0x11, 0x30, 0x8b, 0x40, 0xbe, 0x16, 0x00, 0x3d, 0x6f, 0xd7, 0x14, 0x64, 0xa1, 0xc0, 0x0f, 0xda, 0x74, 0x00}}}, +{{{0x48, 0x2d, 0x0f, 0x00, 0xc5, 0x65, 0x10, 0x94, 0x79, 0x79, 0x1b, 0x48, 0x32, 0x9a, 0xa2, 0x44, 0x68, 0xed, 0xcf, 0xde, 0x33, 0xfb, 0xaf, 0xa2, 0xfc, 0x4a, 0x29, 0x40, 0xd5, 0x36, 0x31, 0x43, 0xf4, 0x57, 0xae, 0x87, 0xcc, 0x7d, 0x3c, 0xc2, 0xd7, 0x44, 0xc7, 0x44, 0xe1, 0x42, 0x52, 0x88, 0x82, 0x78, 0xb7, 0x65, 0x17, 0xb5, 0xc7, 0xd7, 0x00}}, + {{0x55, 0xe4, 0x74, 0xb7, 0xb0, 0x5e, 0x26, 0x7c, 0xd9, 0x30, 0x60, 0x68, 0xa3, 0xfc, 0xc0, 0xe5, 0x02, 0xf1, 0x57, 0x9f, 0x6a, 0x4d, 0x74, 0xa3, 0xc4, 0xa7, 0x20, 0x15, 0x50, 0x90, 0x2f, 0xc8, 0x43, 0x86, 0x2f, 0x77, 0x9f, 0xca, 0xd7, 0x19, 0xa9, 0xe8, 0xe8, 0x26, 0x7a, 0x8f, 0xa1, 0xb6, 0xc2, 0x2d, 0x46, 0x3c, 0x69, 0xfd, 0xe8, 0x31, 0x00}}}, +{{{0x73, 0x80, 0xa7, 0xca, 0xf3, 0x4a, 0x87, 0x8d, 0x8c, 0xa8, 0x8b, 0x32, 0x4d, 0x3e, 0x0d, 0x70, 0xf1, 0x96, 0x96, 0x8e, 0x25, 0x8c, 0xd4, 0xcb, 0x17, 0xa0, 0xa2, 0xce, 0x69, 0x43, 0xe3, 0x36, 0x35, 0xf8, 0x0e, 0x5e, 0x4a, 0x24, 0x32, 0xf3, 0x0e, 0x39, 0x2f, 0x08, 0x4c, 0x5d, 0x04, 0xca, 0x50, 0x91, 0x59, 0x7c, 0x9c, 0xd9, 0x7b, 0x01, 0x00}}, + {{0xdd, 0xe6, 0x9e, 0xae, 0xa2, 0x88, 0x7a, 0x73, 0x50, 0xed, 0x0c, 0xc3, 0x24, 0x31, 0x67, 0x80, 0x7f, 0x5b, 0xab, 0x22, 0x56, 0xa4, 0x11, 0x56, 0x6e, 0xfe, 0x69, 0x27, 0x51, 0x4b, 0x58, 0x13, 0xb6, 0xd2, 0x85, 0xf3, 0xbf, 0xf0, 0xc0, 0x9d, 0x32, 0xf3, 0x54, 0x05, 0x59, 0x53, 0xe5, 0xcc, 0xac, 0x50, 0xfc, 0x49, 0xf2, 0x74, 0x2d, 0x16, 0x00}}}, +{{{0x4b, 0x3d, 0x88, 0xc3, 0x92, 0x8a, 0x14, 0x69, 0xe9, 0x16, 0xdf, 0x38, 0xde, 0xb0, 0xe5, 0x92, 0xcf, 0x60, 0xab, 0xe2, 0x6b, 0xed, 0x9d, 0xf6, 0x51, 0x75, 0x5a, 0x79, 0x34, 0xa8, 0xac, 0x0a, 0xb3, 0x1d, 0xb3, 0xf5, 0xb3, 0x0d, 0x35, 0xa8, 0x66, 0x66, 0xfc, 0x6e, 0x8d, 0xec, 0x53, 0x22, 0x7a, 0xa0, 0x8a, 0x64, 0xa9, 0xa1, 0xd6, 0x17, 0x00}}, + {{0x48, 0x41, 0xb5, 0xd7, 0x1c, 0x62, 0x99, 0x63, 0x8b, 0xef, 0x25, 0x44, 0x03, 0xa1, 0x43, 0xc0, 0xe5, 0xf2, 0x04, 0x90, 0x63, 0x3a, 0x0a, 0x6f, 0x09, 0x47, 0x12, 0x99, 0x5b, 0x04, 0xd6, 0xdd, 0xaa, 0xe8, 0x89, 0x32, 0x49, 0xdc, 0x9d, 0x91, 0x50, 0x3f, 0x64, 0xf3, 0xd2, 0xfd, 0xa5, 0x9c, 0xdb, 0xf1, 0xde, 0x9c, 0x94, 0x2d, 0xcf, 0xb9, 0x00}}}, +{{{0x81, 0x68, 0x4a, 0xbc, 0x3b, 0xd3, 0x48, 0x00, 0x61, 0xfb, 0x79, 0x0f, 0xf9, 0x8c, 0xc9, 0x7c, 0xe9, 0xf0, 0x67, 0x10, 0x0c, 0xe4, 0x6b, 0xa1, 0x78, 0x1c, 0x30, 0xf7, 0x0e, 0x8d, 0xe9, 0x45, 0xf4, 0xc6, 0x8c, 0x9b, 0x63, 0x8c, 0x6c, 0xf4, 0xbc, 0x3c, 0xec, 0xb9, 0xb9, 0x22, 0xbe, 0xad, 0x0d, 0xf1, 0x56, 0xbd, 0xcd, 0x6e, 0x9e, 0x4a, 0x00}}, + {{0x2f, 0x79, 0xd7, 0xf4, 0x36, 0x8c, 0x14, 0x2e, 0x21, 0x97, 0x4c, 0x8e, 0x54, 0x28, 0x36, 0x27, 0xc2, 0xdb, 0x9f, 0x54, 0x6d, 0xee, 0x11, 0xf4, 0xeb, 0x2d, 0xa9, 0x5e, 0x75, 0x10, 0xbd, 0xdb, 0xaf, 0x6e, 0x01, 0x9d, 0xa2, 0xb2, 0x67, 0x46, 0x93, 0x96, 0x8e, 0x07, 0x98, 0xb4, 0x06, 0x2c, 0x08, 0x63, 0xe6, 0x2f, 0xb8, 0x62, 0x1f, 0x8f, 0x00}}}, +{{{0x6c, 0x29, 0x6c, 0x91, 0x2c, 0x65, 0x9f, 0xb1, 0xff, 0x91, 0x1a, 0x8e, 0x6a, 0x6b, 0xf9, 0x5b, 0x25, 0xf7, 0x34, 0x41, 0x87, 0x6c, 0xa2, 0x25, 0x10, 0x0d, 0x75, 0x7d, 0xd4, 0xd1, 0xdb, 0x82, 0x8b, 0xed, 0x77, 0x80, 0x15, 0xb7, 0x0f, 0xba, 0x7d, 0x9a, 0x69, 0x75, 0xae, 0xe7, 0xdc, 0xbd, 0x57, 0x8b, 0x94, 0xbf, 0xa6, 0x62, 0x3a, 0xa9, 0x00}}, + {{0xc7, 0x36, 0xc1, 0x36, 0xf7, 0xd0, 0x66, 0x79, 0xaf, 0xbb, 0x21, 0xa3, 0xb4, 0x82, 0x58, 0x09, 0x28, 0x3c, 0x6c, 0x8c, 0xcb, 0xff, 0xcb, 0xd3, 0xd6, 0xd1, 0xcf, 0x63, 0x91, 0x4a, 0xb2, 0xbc, 0x4e, 0x3b, 0x0b, 0x97, 0x4f, 0xe0, 0xda, 0x30, 0x3a, 0x58, 0xb5, 0x56, 0x14, 0xad, 0x47, 0x04, 0x72, 0xda, 0xad, 0x64, 0x2e, 0xd9, 0xb4, 0x0d, 0x00}}}, +{{{0x01, 0xcb, 0xa2, 0x8f, 0xe9, 0x01, 0xe0, 0x19, 0xa5, 0xc3, 0xa3, 0x58, 0x84, 0x83, 0xe1, 0x58, 0x80, 0xe9, 0x1f, 0x06, 0xc4, 0x6b, 0xec, 0xf8, 0x02, 0x10, 0x67, 0xac, 0x05, 0x3e, 0x24, 0x83, 0xff, 0xd5, 0x45, 0x01, 0xf9, 0xab, 0x5f, 0xce, 0x55, 0x73, 0xac, 0x70, 0x5a, 0x96, 0x26, 0x93, 0xd9, 0xdb, 0x32, 0xd8, 0x0f, 0x9a, 0x92, 0x4a, 0x00}}, + {{0x21, 0x16, 0x60, 0x99, 0xf1, 0x73, 0x76, 0x65, 0x55, 0x39, 0x59, 0x16, 0x83, 0x7c, 0x23, 0x2d, 0x61, 0x0c, 0x3f, 0x82, 0x09, 0xe9, 0x42, 0x9e, 0x7a, 0x0e, 0x4b, 0x41, 0xa2, 0xe0, 0x83, 0x5c, 0x77, 0x98, 0x74, 0x52, 0x01, 0xcd, 0x65, 0x34, 0xa2, 0x05, 0xc3, 0xbf, 0xcb, 0xf4, 0x07, 0x46, 0x65, 0x5d, 0xc7, 0xb1, 0xd1, 0x3e, 0xea, 0x4d, 0x00}}}
\ No newline at end of file diff --git a/ge448_gen.c b/ge448_gen.c new file mode 100644 index 0000000..dfe5ed3 --- /dev/null +++ b/ge448_gen.c @@ -0,0 +1,99 @@ +#include "ge448.h" +#include <stdio.h> +#include <assert.h> + +const ge448 ge448_base = {{{0x5E, 0xC0, 0x0C, 0xC7, 0x2B, 0xA8, 0x26, 0x26, 0x8E, 0x93, 0x00, 0x8B, 0xE1, 0x80, 0x3B, 0x43, + 0x11, 0x65, 0xB6, 0x2A, 0xF7, 0x1A, 0xAE, 0x12, 0x64, 0xA4, 0xD3, 0xA3, 0x24, 0xE3, 0x6D, 0xEA, + 0x67, 0x17, 0x0F, 0x47, 0x70, 0x65, 0x14, 0x9E, 0xDA, 0x36, 0xBF, 0x22, 0xA6, 0x15, 0x1D, 0x22, + 0xED, 0x0D, 0xED, 0x6B, 0xC6, 0x70, 0x19, 0x4F, 0x00}}, + {{0x14, 0xFA, 0x30, 0xF2, 0x5B, 0x79, 0x08, 0x98, 0xAD, 0xC8, 0xD7, 0x4E, 0x2C, 0x13, 0xBD, 0xFD, + 0xC4, 0x39, 0x7C, 0xE6, 0x1C, 0xFF, 0xD3, 0x3A, 0xD7, 0xC2, 0xA0, 0x05, 0x1E, 0x9C, 0x78, 0x87, + 0x40, 0x98, 0xA3, 0x6C, 0x73, 0x73, 0xEA, 0x4B, 0x62, 0xC7, 0xC9, 0x56, 0x37, 0x20, 0x76, 0x88, + 0x24, 0xBC, 0xB6, 0x6E, 0x71, 0x46, 0x3F, 0x69, 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, + 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}}}; + +#define ge448_p3 ge448 /* use projective coordinates only */ + +static const fe448 ge448_ecd = {{0x56, 0x67, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x00}}; + +static void add_p3(ge448_p3 *r, const ge448_p3 *p, const ge448_p3 *q) +{ + fe448 a, b, c, d, e, f, g, h; + fe448_mul(&a, &p->z, &q->z); /* A=Z1*Z2 */ + fe448_square(&b, &a); /* B=A^2 */ + fe448_mul(&c, &p->x, &q->x); /* C=X1*X2 */ + fe448_mul(&d, &p->y, &q->y); /* D=Y1*Y2 */ + fe448_mul(&e, &c, &d); + fe448_mul(&e, &e, &ge448_ecd); /* E=d*C*D */ + fe448_sub(&f, &b, &e); /* F=B-E */ + fe448_add(&g, &b, &e); /* G=B+E */ + fe448_add(&b, &p->x, &p->y); + fe448_add(&h, &q->x, &q->y); + fe448_mul(&h, &b, &h); /* H=(X1+Y1)*(X2+Y2) */ + fe448_sub(&h, &h, &c); + fe448_sub(&h, &h, &d); + fe448_mul(&h, &h, &f); + fe448_mul(&r->x, &a, &h); /* X3=A*F*(H-C-D) */ + fe448_sub(&d, &d, &c); + fe448_mul(&d, &d, &g); + fe448_mul(&r->y, &a, &d); /* Y3=A*G*(D-C) */ + fe448_mul(&r->z, &f, &g); /* Z3=F*G */ +} + +static void output(ge448_p3 *p) +{ + int i, printed; + fe448 tx, ty, zi; + unsigned char px[57], py[57]; + char buffer[4000]; + fe448_invert(&zi, &p->z); + fe448_mul(&tx, &p->x, &zi); + fe448_mul(&ty, &p->y, &zi); + fe448_pack(px, &tx); + fe448_pack(py, &ty); + printed = 0; + printed += sprintf(buffer + printed, "{{{0x%02x", px[0]); + for (i = 1; i < 57; i++) + { + printed += sprintf(buffer + printed, ", 0x%02x", px[i]); + } + printed += sprintf(buffer + printed, "}},\n"); + printed += sprintf(buffer + printed, " {{0x%02x", py[0]); + for (i = 1; i < 57; i++) + { + printed += sprintf(buffer + printed, ", 0x%02x", py[i]); + } + printed += sprintf(buffer + printed, "}}}"); + assert(fwrite(buffer, 1, printed, stdout) == printed); +} + +int main() +{ + int i; + ge448 neutral = {{{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, + 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, + 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, + 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}}}; + output(&neutral); + for (i = 1; i < 745; i++) + { + add_p3(&neutral, &neutral, &ge448_base); + puts(","); + output(&neutral); + } + return 0; +}
\ No newline at end of file @@ -198,94 +198,55 @@ void sc448_mul(sc448 *r, const sc448 *x, const sc448 *y) barrett_reduce(r, t); } - /* not implemented yet */ -#if 0 -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; -} -void sc25519_window5(signed char r[51], const sc25519 *s) +void sc448_window3(signed char r[149], const sc448 *s) { - char carry; - int i; - for (i = 0; i < 6; i++) - { - r[8 * i + 0] = s->v[5 * i + 0] & 31; - r[8 * i + 1] = (s->v[5 * i + 0] >> 5) & 31; - r[8 * i + 1] ^= (s->v[5 * i + 1] << 3) & 31; - r[8 * i + 2] = (s->v[5 * i + 1] >> 2) & 31; - r[8 * i + 3] = (s->v[5 * i + 1] >> 7) & 31; - r[8 * i + 3] ^= (s->v[5 * i + 2] << 1) & 31; - r[8 * i + 4] = (s->v[5 * i + 2] >> 4) & 31; - r[8 * i + 4] ^= (s->v[5 * i + 3] << 4) & 31; - r[8 * i + 5] = (s->v[5 * i + 3] >> 1) & 31; - r[8 * i + 6] = (s->v[5 * i + 3] >> 6) & 31; - r[8 * i + 6] ^= (s->v[5 * i + 4] << 2) & 31; - r[8 * i + 7] = (s->v[5 * i + 4] >> 3) & 31; - } - r[8 * i + 0] = s->v[5 * i + 0] & 31; - r[8 * i + 1] = (s->v[5 * i + 0] >> 5) & 31; - r[8 * i + 1] ^= (s->v[5 * i + 1] << 3) & 31; - r[8 * i + 2] = (s->v[5 * i + 1] >> 2) & 31; - - /* Making it signed */ - carry = 0; - for (i = 0; i < 50; i++) - { - r[i] += carry; - r[i + 1] += r[i] >> 5; - r[i] &= 31; - carry = r[i] >> 4; - r[i] -= carry << 5; - } - r[50] += carry; + char carry; + int i; + for (i = 0; i < 18; 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 < 148; i++) + { + r[i] += carry; + r[i + 1] += r[i] >> 3; + r[i] &= 7; + carry = r[i] >> 2; + r[i] -= carry << 3; + } + r[148] += carry; } -void sc25519_2interleave2(unsigned char r[127], const sc25519 *s1, const sc25519 *s2) +void sc448_2interleave2(unsigned char r[223], const sc448 *s1, const sc448 *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); + int i; + for (i = 0; i < 55; 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[220] = (s1->v[55] & 3) ^ ((s2->v[55] & 3) << 2); + r[221] = ((s1->v[55] >> 2) & 3) ^ (((s2->v[55] >> 2) & 3) << 2); + r[222] = ((s1->v[55] >> 4) & 3) ^ (((s2->v[55] >> 4) & 3) << 2); } -#endif @@ -14,7 +14,6 @@ #define sc448_sub_nored crypto_sign_ed448_ref_sc448_sub_nored #define sc448_mul crypto_sign_ed448_ref_sc448_mul #define sc448_window3 crypto_sign_ed448_ref_sc448_window3 -#define sc448_window5 crypto_sign_ed448_ref_sc448_window5 #define sc448_2interleave2 crypto_sign_ed448_ref_sc448_2interleave2 typedef struct @@ -41,17 +40,11 @@ void sc448_sub_nored(sc448 *r, const sc448 *x, const sc448 *y); void sc448_mul(sc448 *r, const sc448 *x, const sc448 *y); -#if 0 /* Convert s into a representation of the form \sum_{i=0}^{84}r[i]2^3 * with r[i] in {-4,...,3} */ -void sc448_window3(signed char r[85], const sc448 *s); +void sc448_window3(signed char r[149], const sc448 *s); -/* Convert s into a representation of the form \sum_{i=0}^{50}r[i]2^5 - * with r[i] in {-16,...,15} - */ -void sc448_window5(signed char r[51], const sc448 *s); +void sc448_2interleave2(unsigned char r[223], const sc448 *s1, const sc448 *s2); -void sc448_2interleave2(unsigned char r[127], const sc448 *s1, const sc448 *s2); -#endif -#endif +#endif
\ No newline at end of file |
