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Diffstat (limited to 'ed25519.c')
| -rw-r--r-- | ed25519.c | 2030 |
1 files changed, 2030 insertions, 0 deletions
diff --git a/ed25519.c b/ed25519.c new file mode 100644 index 0000000..0e167ae --- /dev/null +++ b/ed25519.c @@ -0,0 +1,2030 @@ +/* $OpenBSD: ed25519.c,v 1.4 2023/01/15 23:05:32 djm Exp $ */ + +/* + * Public Domain, Authors: + * - Daniel J. Bernstein + * - Niels Duif + * - Tanja Lange + * - lead: Peter Schwabe + * - Bo-Yin Yang + */ + +#include "includes.h" + +#include <string.h> + +#include "crypto_api.h" + +#define int8 crypto_int8 +#define uint8 crypto_uint8 +#define int16 crypto_int16 +#define uint16 crypto_uint16 +#define int32 crypto_int32 +#define uint32 crypto_uint32 +#define int64 crypto_int64 +#define uint64 crypto_uint64 + +/* from supercop-20221122/crypto_verify/32/ref/verify.c */ + +static int crypto_verify_32(const unsigned char *x,const unsigned char *y) +{ + unsigned int differentbits = 0; +#define F(i) differentbits |= x[i] ^ y[i]; + F(0) + F(1) + F(2) + F(3) + F(4) + F(5) + F(6) + F(7) + F(8) + F(9) + F(10) + F(11) + F(12) + F(13) + F(14) + F(15) + F(16) + F(17) + F(18) + F(19) + F(20) + F(21) + F(22) + F(23) + F(24) + F(25) + F(26) + F(27) + F(28) + F(29) + F(30) + F(31) + return (1 & ((differentbits - 1) >> 8)) - 1; +} +/* from supercop-20221122/crypto_sign/ed25519/ref/fe25519.h */ +#ifndef FE25519_H +#define FE25519_H + + +#define fe25519 crypto_sign_ed25519_ref_fe25519 +#define fe25519_freeze crypto_sign_ed25519_ref_fe25519_freeze +#define fe25519_unpack crypto_sign_ed25519_ref_fe25519_unpack +#define fe25519_pack crypto_sign_ed25519_ref_fe25519_pack +#define fe25519_iszero crypto_sign_ed25519_ref_fe25519_iszero +#define fe25519_iseq_vartime crypto_sign_ed25519_ref_fe25519_iseq_vartime +#define fe25519_cmov crypto_sign_ed25519_ref_fe25519_cmov +#define fe25519_setone crypto_sign_ed25519_ref_fe25519_setone +#define fe25519_setzero crypto_sign_ed25519_ref_fe25519_setzero +#define fe25519_neg crypto_sign_ed25519_ref_fe25519_neg +#define fe25519_getparity crypto_sign_ed25519_ref_fe25519_getparity +#define fe25519_add crypto_sign_ed25519_ref_fe25519_add +#define fe25519_sub crypto_sign_ed25519_ref_fe25519_sub +#define fe25519_mul crypto_sign_ed25519_ref_fe25519_mul +#define fe25519_square crypto_sign_ed25519_ref_fe25519_square +#define fe25519_invert crypto_sign_ed25519_ref_fe25519_invert +#define fe25519_pow2523 crypto_sign_ed25519_ref_fe25519_pow2523 + +typedef struct +{ + crypto_uint32 v[32]; +} +fe25519; + +static void fe25519_freeze(fe25519 *r); + +static void fe25519_unpack(fe25519 *r, const unsigned char x[32]); + +static void fe25519_pack(unsigned char r[32], const fe25519 *x); + +static int fe25519_iszero(const fe25519 *x); + +static int fe25519_iseq_vartime(const fe25519 *x, const fe25519 *y); + +static void fe25519_cmov(fe25519 *r, const fe25519 *x, unsigned char b); + +static void fe25519_setone(fe25519 *r); + +static void fe25519_setzero(fe25519 *r); + +static void fe25519_neg(fe25519 *r, const fe25519 *x); + +unsigned char fe25519_getparity(const fe25519 *x); + +static void fe25519_add(fe25519 *r, const fe25519 *x, const fe25519 *y); + +static void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y); + +static void fe25519_mul(fe25519 *r, const fe25519 *x, const fe25519 *y); + +static void fe25519_square(fe25519 *r, const fe25519 *x); + +static void fe25519_invert(fe25519 *r, const fe25519 *x); + +static void fe25519_pow2523(fe25519 *r, const fe25519 *x); + +#endif +/* from supercop-20221122/crypto_sign/ed25519/ref/fe25519.c */ +#define WINDOWSIZE 1 /* Should be 1,2, or 4 */ +#define WINDOWMASK ((1<<WINDOWSIZE)-1) + + +static crypto_uint32 fe25519_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 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 crypto_uint32 times19(crypto_uint32 a) +{ + return (a << 4) + (a << 1) + a; +} + +static crypto_uint32 times38(crypto_uint32 a) +{ + return (a << 5) + (a << 2) + (a << 1); +} + +static void fe25519_reduce_add_sub(fe25519 *r) +{ + crypto_uint32 t; + int i,rep; + + for(rep=0;rep<4;rep++) + { + 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 void reduce_mul(fe25519 *r) +{ + crypto_uint32 t; + int i,rep; + + for(rep=0;rep<2;rep++) + { + 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 void fe25519_freeze(fe25519 *r) +{ + int i; + crypto_uint32 m = fe25519_equal(r->v[31],127); + for(i=30;i>0;i--) + m &= fe25519_equal(r->v[i],255); + m &= ge(r->v[0],237); + + m = -m; + + r->v[31] -= m&127; + for(i=30;i>0;i--) + r->v[i] -= m&255; + r->v[0] -= m&237; +} + +static 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 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 int fe25519_iszero(const fe25519 *x) +{ + int i; + int r; + fe25519 t = *x; + fe25519_freeze(&t); + r = fe25519_equal(t.v[0],0); + for(i=1;i<32;i++) + r &= fe25519_equal(t.v[i],0); + return r; +} + +static 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 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]); +} + +unsigned char fe25519_getparity(const fe25519 *x) +{ + fe25519 t = *x; + fe25519_freeze(&t); + return t.v[0] & 1; +} + +static void fe25519_setone(fe25519 *r) +{ + int i; + r->v[0] = 1; + for(i=1;i<32;i++) r->v[i]=0; +} + +static void fe25519_setzero(fe25519 *r) +{ + int i; + for(i=0;i<32;i++) r->v[i]=0; +} + +static 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 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]; + fe25519_reduce_add_sub(r); +} + +static 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]; + fe25519_reduce_add_sub(r); +} + +static 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 void fe25519_square(fe25519 *r, const fe25519 *x) +{ + fe25519_mul(r, x, x); +} + +static 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 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); +} +/* from supercop-20221122/crypto_sign/ed25519/ref/sc25519.h */ +#ifndef SC25519_H +#define SC25519_H + + +#define sc25519 crypto_sign_ed25519_ref_sc25519 +#define shortsc25519 crypto_sign_ed25519_ref_shortsc25519 +#define sc25519_from32bytes crypto_sign_ed25519_ref_sc25519_from32bytes +#define sc25519_from64bytes crypto_sign_ed25519_ref_sc25519_from64bytes +#define sc25519_to32bytes crypto_sign_ed25519_ref_sc25519_to32bytes +#define sc25519_add crypto_sign_ed25519_ref_sc25519_add +#define sc25519_mul crypto_sign_ed25519_ref_sc25519_mul +#define sc25519_window3 crypto_sign_ed25519_ref_sc25519_window3 +#define sc25519_2interleave2 crypto_sign_ed25519_ref_sc25519_2interleave2 + +typedef struct +{ + crypto_uint32 v[32]; +} +sc25519; + +typedef struct +{ + crypto_uint32 v[16]; +} +shortsc25519; + +static void sc25519_from32bytes(sc25519 *r, const unsigned char x[32]); + + +static void sc25519_from64bytes(sc25519 *r, const unsigned char x[64]); + + +static void sc25519_to32bytes(unsigned char r[32], const sc25519 *x); + + + + +static void sc25519_add(sc25519 *r, const sc25519 *x, const sc25519 *y); + + +static void sc25519_mul(sc25519 *r, const sc25519 *x, const sc25519 *y); + + +/* Convert s into a representation of the form \sum_{i=0}^{84}r[i]2^3 + * with r[i] in {-4,...,3} + */ +static void sc25519_window3(signed char r[85], const sc25519 *s); + +/* Convert s into a representation of the form \sum_{i=0}^{50}r[i]2^5 + * with r[i] in {-16,...,15} + */ + +static void sc25519_2interleave2(unsigned char r[127], const sc25519 *s1, const sc25519 *s2); + +#endif +/* from supercop-20221122/crypto_sign/ed25519/ref/sc25519.c */ + +/*Arithmetic modulo the group order m = 2^252 + 27742317777372353535851937790883648493 = 7237005577332262213973186563042994240857116359379907606001950938285454250989 */ + +static const crypto_uint32 sc25519_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 sc25519_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 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 sc25519_reduce_add_sub */ +static void sc25519_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 += sc25519_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 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 carry; + crypto_uint32 pb = 0; + crypto_uint32 b; + + 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] += sc25519_mu[i]*x[j+31]; + carry = q2[31] >> 8; + q2[32] += carry; + carry = q2[32] >> 8; + q2[33] += carry; + + 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] += sc25519_m[i]*q3[j]; + + for(i=0;i<32;i++) + { + carry = r2[i] >> 8; + r2[i+1] += carry; + r2[i] &= 0xff; + } + + for(i=0;i<32;i++) + { + pb += r2[i]; + 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! + */ + + sc25519_reduce_add_sub(r); + sc25519_reduce_add_sub(r); +} + +static 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 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 void sc25519_to32bytes(unsigned char r[32], const sc25519 *x) +{ + int i; + for(i=0;i<32;i++) r[i] = x->v[i]; +} + + + + +static void sc25519_add(sc25519 *r, const sc25519 *x, const sc25519 *y) +{ + int i, carry; + for(i=0;i<32;i++) r->v[i] = x->v[i] + y->v[i]; + for(i=0;i<31;i++) + { + carry = r->v[i] >> 8; + r->v[i+1] += carry; + r->v[i] &= 0xff; + } + sc25519_reduce_add_sub(r); +} + + +static void sc25519_mul(sc25519 *r, const sc25519 *x, const sc25519 *y) +{ + int i,j,carry; + 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]; + + /* Reduce coefficients */ + for(i=0;i<63;i++) + { + carry = t[i] >> 8; + t[i+1] += carry; + t[i] &= 0xff; + } + + barrett_reduce(r, t); +} + + +static 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 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); +} +/* from supercop-20221122/crypto_sign/ed25519/ref/ge25519.h */ +#ifndef GE25519_H +#define GE25519_H + + +#define ge25519 crypto_sign_ed25519_ref_ge25519 +#define ge25519_base crypto_sign_ed25519_ref_ge25519_base +#define ge25519_unpackneg_vartime crypto_sign_ed25519_ref_unpackneg_vartime +#define ge25519_pack crypto_sign_ed25519_ref_pack +#define ge25519_isneutral_vartime crypto_sign_ed25519_ref_isneutral_vartime +#define ge25519_double_scalarmult_vartime crypto_sign_ed25519_ref_double_scalarmult_vartime +#define ge25519_scalarmult_base crypto_sign_ed25519_ref_scalarmult_base + +typedef struct +{ + fe25519 x; + fe25519 y; + fe25519 z; + fe25519 t; +} ge25519; + +const ge25519 ge25519_base; + +int ge25519_unpackneg_vartime(ge25519 *r, const unsigned char p[32]); + +static void ge25519_pack(unsigned char r[32], const ge25519 *p); + +int ge25519_isneutral_vartime(const ge25519 *p); + +static void ge25519_double_scalarmult_vartime(ge25519 *r, const ge25519 *p1, const sc25519 *s1, const ge25519 *p2, const sc25519 *s2); + +static void ge25519_scalarmult_base(ge25519 *r, const sc25519 *s); + +#endif +/* from supercop-20221122/crypto_sign/ed25519/ref/ge25519.c */ + +/* + * 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] = { +{{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 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, 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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 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; +} + +static 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 */ +static 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); + } +} + +static 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); + } +} +/* from supercop-20221122/crypto_sign/ed25519/ref/keypair.c */ + +int crypto_sign_ed25519_keypair(unsigned char *pk,unsigned char *sk) +{ + unsigned char az[64]; + sc25519 scsk; + ge25519 gepk; + + randombytes(sk,32); + crypto_hash_sha512(az,sk,32); + az[0] &= 248; + az[31] &= 127; + az[31] |= 64; + + sc25519_from32bytes(&scsk,az); + + ge25519_scalarmult_base(&gepk, &scsk); + ge25519_pack(pk, &gepk); + memmove(sk + 32,pk,32); + return 0; +} +/* from supercop-20221122/crypto_sign/ed25519/ref/sign.c */ + +int crypto_sign_ed25519( + unsigned char *sm,unsigned long long *smlen, + const unsigned char *m,unsigned long long mlen, + const unsigned char *sk + ) +{ + unsigned char pk[32]; + unsigned char az[64]; + unsigned char nonce[64]; + unsigned char hram[64]; + sc25519 sck, scs, scsk; + ge25519 ger; + + memmove(pk,sk + 32,32); + /* pk: 32-byte public key A */ + + crypto_hash_sha512(az,sk,32); + az[0] &= 248; + az[31] &= 127; + az[31] |= 64; + /* az: 32-byte scalar a, 32-byte randomizer z */ + + *smlen = mlen + 64; + memmove(sm + 64,m,mlen); + memmove(sm + 32,az + 32,32); + /* sm: 32-byte uninit, 32-byte z, mlen-byte m */ + + crypto_hash_sha512(nonce, sm+32, mlen+32); + /* nonce: 64-byte H(z,m) */ + + sc25519_from64bytes(&sck, nonce); + ge25519_scalarmult_base(&ger, &sck); + ge25519_pack(sm, &ger); + /* sm: 32-byte R, 32-byte z, mlen-byte m */ + + memmove(sm + 32,pk,32); + /* sm: 32-byte R, 32-byte A, mlen-byte m */ + + crypto_hash_sha512(hram,sm,mlen + 64); + /* hram: 64-byte H(R,A,m) */ + + sc25519_from64bytes(&scs, hram); + sc25519_from32bytes(&scsk, az); + sc25519_mul(&scs, &scs, &scsk); + sc25519_add(&scs, &scs, &sck); + /* scs: S = nonce + H(R,A,m)a */ + + sc25519_to32bytes(sm + 32,&scs); + /* sm: 32-byte R, 32-byte S, mlen-byte m */ + + return 0; +} +/* from supercop-20221122/crypto_sign/ed25519/ref/open.c */ + +int crypto_sign_ed25519_open( + unsigned char *m,unsigned long long *mlen, + const unsigned char *sm,unsigned long long smlen, + const unsigned char *pk + ) +{ + unsigned char pkcopy[32]; + unsigned char rcopy[32]; + unsigned char hram[64]; + unsigned char rcheck[32]; + ge25519 get1, get2; + sc25519 schram, scs; + + if (smlen < 64) goto badsig; + if (sm[63] & 224) goto badsig; + if (ge25519_unpackneg_vartime(&get1,pk)) goto badsig; + + memmove(pkcopy,pk,32); + memmove(rcopy,sm,32); + + sc25519_from32bytes(&scs, sm+32); + + memmove(m,sm,smlen); + memmove(m + 32,pkcopy,32); + crypto_hash_sha512(hram,m,smlen); + + sc25519_from64bytes(&schram, hram); + + ge25519_double_scalarmult_vartime(&get2, &get1, &schram, &ge25519_base, &scs); + ge25519_pack(rcheck, &get2); + + if (crypto_verify_32(rcopy,rcheck) == 0) { + memmove(m,m + 64,smlen - 64); + memset(m + smlen - 64,0,64); + *mlen = smlen - 64; + return 0; + } + +badsig: + *mlen = (unsigned long long) -1; + memset(m,0,smlen); + return -1; +} |