/* version 20081011 Matthew Dempsky Public domain. Derived from public domain code by D. J. Bernstein. 20140216 tweak: Mask top bit of point input. */ static void add(unsigned int out[32],const unsigned int a[32],const unsigned int b[32]) { unsigned int j; unsigned int u; u = 0; for (j = 0;j < 31;++j) { u += a[j] + b[j]; out[j] = u & 255; u >>= 8; } u += a[31] + b[31]; out[31] = u; } static void sub(unsigned int out[32],const unsigned int a[32],const unsigned int b[32]) { unsigned int j; unsigned int u; u = 218; for (j = 0;j < 31;++j) { u += a[j] + 65280 - b[j]; out[j] = u & 255; u >>= 8; } u += a[31] - b[31]; out[31] = u; } static void squeeze(unsigned int a[32]) { unsigned int j; unsigned int u; u = 0; for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; } u += a[31]; a[31] = u & 127; u = 19 * (u >> 7); for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; } u += a[31]; a[31] = u; } static const unsigned int minusp[32] = { 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128 } ; static void freeze(unsigned int a[32]) { unsigned int aorig[32]; unsigned int j; unsigned int negative; for (j = 0;j < 32;++j) aorig[j] = a[j]; add(a,a,minusp); negative = -((a[31] >> 7) & 1); for (j = 0;j < 32;++j) a[j] ^= negative & (aorig[j] ^ a[j]); } static void mult(unsigned int out[32],const unsigned int a[32],const unsigned int b[32]) { unsigned int i; unsigned int j; unsigned int u; for (i = 0;i < 32;++i) { u = 0; for (j = 0;j <= i;++j) u += a[j] * b[i - j]; for (j = i + 1;j < 32;++j) u += 38 * a[j] * b[i + 32 - j]; out[i] = u; } squeeze(out); } static void mult121665(unsigned int out[32],const unsigned int a[32]) { unsigned int j; unsigned int u; u = 0; for (j = 0;j < 31;++j) { u += 121665 * a[j]; out[j] = u & 255; u >>= 8; } u += 121665 * a[31]; out[31] = u & 127; u = 19 * (u >> 7); for (j = 0;j < 31;++j) { u += out[j]; out[j] = u & 255; u >>= 8; } u += out[j]; out[j] = u; } static void square(unsigned int out[32],const unsigned int a[32]) { unsigned int i; unsigned int j; unsigned int u; for (i = 0;i < 32;++i) { u = 0; for (j = 0;j < i - j;++j) u += a[j] * a[i - j]; for (j = i + 1;j < i + 32 - j;++j) u += 38 * a[j] * a[i + 32 - j]; u *= 2; if ((i & 1) == 0) { u += a[i / 2] * a[i / 2]; u += 38 * a[i / 2 + 16] * a[i / 2 + 16]; } out[i] = u; } squeeze(out); } static void select(unsigned int p[64],unsigned int q[64],const unsigned int r[64],const unsigned int s[64],unsigned int b) { unsigned int j; unsigned int t; unsigned int bminus1; bminus1 = b - 1; for (j = 0;j < 64;++j) { t = bminus1 & (r[j] ^ s[j]); p[j] = s[j] ^ t; q[j] = r[j] ^ t; } } static void mainloop(unsigned int work[64],const unsigned char e[32]) { unsigned int xzm1[64]; unsigned int xzm[64]; unsigned int xzmb[64]; unsigned int xzm1b[64]; unsigned int xznb[64]; unsigned int xzn1b[64]; unsigned int a0[64]; unsigned int a1[64]; unsigned int b0[64]; unsigned int b1[64]; unsigned int c1[64]; unsigned int r[32]; unsigned int s[32]; unsigned int t[32]; unsigned int u[32]; unsigned int i; unsigned int j; unsigned int b; int pos; for (j = 0;j < 32;++j) xzm1[j] = work[j]; xzm1[32] = 1; for (j = 33;j < 64;++j) xzm1[j] = 0; xzm[0] = 1; for (j = 1;j < 64;++j) xzm[j] = 0; for (pos = 254;pos >= 0;--pos) { b = e[pos / 8] >> (pos & 7); b &= 1; select(xzmb,xzm1b,xzm,xzm1,b); add(a0,xzmb,xzmb + 32); sub(a0 + 32,xzmb,xzmb + 32); add(a1,xzm1b,xzm1b + 32); sub(a1 + 32,xzm1b,xzm1b + 32); square(b0,a0); square(b0 + 32,a0 + 32); mult(b1,a1,a0 + 32); mult(b1 + 32,a1 + 32,a0); add(c1,b1,b1 + 32); sub(c1 + 32,b1,b1 + 32); square(r,c1 + 32); sub(s,b0,b0 + 32); mult121665(t,s); add(u,t,b0); mult(xznb,b0,b0 + 32); mult(xznb + 32,s,u); square(xzn1b,c1); mult(xzn1b + 32,r,work); select(xzm,xzm1,xznb,xzn1b,b); } for (j = 0;j < 64;++j) work[j] = xzm[j]; } static void recip(unsigned int out[32],const unsigned int z[32]) { unsigned int z2[32]; unsigned int z9[32]; unsigned int z11[32]; unsigned int z2_5_0[32]; unsigned int z2_10_0[32]; unsigned int z2_20_0[32]; unsigned int z2_50_0[32]; unsigned int z2_100_0[32]; unsigned int t0[32]; unsigned int t1[32]; int i; /* 2 */ square(z2,z); /* 4 */ square(t1,z2); /* 8 */ square(t0,t1); /* 9 */ mult(z9,t0,z); /* 11 */ mult(z11,z9,z2); /* 22 */ square(t0,z11); /* 2^5 - 2^0 = 31 */ mult(z2_5_0,t0,z9); /* 2^6 - 2^1 */ square(t0,z2_5_0); /* 2^7 - 2^2 */ square(t1,t0); /* 2^8 - 2^3 */ square(t0,t1); /* 2^9 - 2^4 */ square(t1,t0); /* 2^10 - 2^5 */ square(t0,t1); /* 2^10 - 2^0 */ mult(z2_10_0,t0,z2_5_0); /* 2^11 - 2^1 */ square(t0,z2_10_0); /* 2^12 - 2^2 */ square(t1,t0); /* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t0,t1); square(t1,t0); } /* 2^20 - 2^0 */ mult(z2_20_0,t1,z2_10_0); /* 2^21 - 2^1 */ square(t0,z2_20_0); /* 2^22 - 2^2 */ square(t1,t0); /* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { square(t0,t1); square(t1,t0); } /* 2^40 - 2^0 */ mult(t0,t1,z2_20_0); /* 2^41 - 2^1 */ square(t1,t0); /* 2^42 - 2^2 */ square(t0,t1); /* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t1,t0); square(t0,t1); } /* 2^50 - 2^0 */ mult(z2_50_0,t0,z2_10_0); /* 2^51 - 2^1 */ square(t0,z2_50_0); /* 2^52 - 2^2 */ square(t1,t0); /* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); } /* 2^100 - 2^0 */ mult(z2_100_0,t1,z2_50_0); /* 2^101 - 2^1 */ square(t1,z2_100_0); /* 2^102 - 2^2 */ square(t0,t1); /* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { square(t1,t0); square(t0,t1); } /* 2^200 - 2^0 */ mult(t1,t0,z2_100_0); /* 2^201 - 2^1 */ square(t0,t1); /* 2^202 - 2^2 */ square(t1,t0); /* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); } /* 2^250 - 2^0 */ mult(t0,t1,z2_50_0); /* 2^251 - 2^1 */ square(t1,t0); /* 2^252 - 2^2 */ square(t0,t1); /* 2^253 - 2^3 */ square(t1,t0); /* 2^254 - 2^4 */ square(t0,t1); /* 2^255 - 2^5 */ square(t1,t0); /* 2^255 - 21 */ mult(out,t1,z11); } int crypto_scalarmult(unsigned char *q, const unsigned char *n, const unsigned char *p) { unsigned int work[96]; unsigned char e[32]; unsigned int i; for (i = 0;i < 32;++i) e[i] = n[i]; e[0] &= 248; e[31] &= 127; e[31] |= 64; for (i = 0;i < 32;++i) work[i] = p[i]; work[31] &= 127; mainloop(work,e); recip(work + 32,work + 32); mult(work + 64,work,work + 32); freeze(work + 64); for (i = 0;i < 32;++i) q[i] = work[64 + i]; return 0; } static const unsigned char basepoint[32] = {9}; int crypto_scalarmult_base(unsigned char *q,const unsigned char *n) { return crypto_scalarmult(q,n,basepoint); } int main (void) { unsigned char *x, *y; *x = 8; *y = 8; crypto_scalarmult_base (x, y); }