#include "ge.h" #include "crypto_uint32.h" 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 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 x; } static inline void cmov(ge_precomp *t,ge_precomp *u,unsigned char b) { fe_cmov(t->yplusx,u->yplusx,b); fe_cmov(t->yminusx,u->yminusx,b); fe_cmov(t->xy2d,u->xy2d,b); } /* base[i][j] = (j+1)*256^i*B */ static ge_precomp base[32][8] = { #include "base.h" } ; static inline void select_ed25519(ge_precomp *t,int pos,signed char b) { ge_precomp minust; unsigned char bnegative = negative(b); unsigned char babs = b - (((-bnegative) & b) << 1); ge_precomp_0(t); cmov(t,&base[pos][0],equal(babs,1)); cmov(t,&base[pos][1],equal(babs,2)); cmov(t,&base[pos][2],equal(babs,3)); cmov(t,&base[pos][3],equal(babs,4)); cmov(t,&base[pos][4],equal(babs,5)); cmov(t,&base[pos][5],equal(babs,6)); cmov(t,&base[pos][6],equal(babs,7)); cmov(t,&base[pos][7],equal(babs,8)); fe_copy(minust.yplusx,t->yminusx); fe_copy(minust.yminusx,t->yplusx); fe_neg(minust.xy2d,t->xy2d); cmov(t,&minust,bnegative); } /* h = a * B where a = a[0]+256*a[1]+...+256^31 a[31] B is the Ed25519 base point (x,4/5) with x positive. Preconditions: a[31] <= 127 */ static inline void ge_scalarmult_base(ge_p3 *h,const unsigned char *a) { signed char e[64]; signed char carry; ge_p1p1 r; ge_p2 s; ge_precomp t; int i; for (i = 0;i < 32;++i) { e[2 * i + 0] = (a[i] >> 0) & 15; e[2 * i + 1] = (a[i] >> 4) & 15; } /* each e[i] is between 0 and 15 */ /* e[63] is between 0 and 7 */ carry = 0; for (i = 0;i < 63;++i) { e[i] += carry; carry = e[i] + 8; carry >>= 4; e[i] -= carry << 4; } e[63] += carry; /* each e[i] is between -8 and 8 */ ge_p3_0(h); for (i = 1;i < 64;i += 2) { select_ed25519(&t,i / 2,e[i]); ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r); } ge_p3_dbl(&r,h); ge_p1p1_to_p2(&s,&r); ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r); ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r); ge_p2_dbl(&r,&s); ge_p1p1_to_p3(h,&r); for (i = 0;i < 64;i += 2) { select_ed25519(&t,i / 2,e[i]); ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r); } }