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/* $OpenBSD: smult_curve25519_ref.c,v 1.1 2014/08/27 10:28:57 reyk Exp $ */ |
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/* |
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version 20081011 |
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Matthew Dempsky |
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Public domain. |
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Derived from public domain code by D. J. Bernstein. |
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*/ |
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int crypto_scalarmult_curve25519(unsigned char *, const unsigned char *, const unsigned char *); |
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static void add(unsigned int out[32],const unsigned int a[32],const unsigned int b[32]) |
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{ |
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unsigned int j; |
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unsigned int u; |
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u = 0; |
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for (j = 0;j < 31;++j) { u += a[j] + b[j]; out[j] = u & 255; u >>= 8; } |
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u += a[31] + b[31]; out[31] = u; |
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} |
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static void sub(unsigned int out[32],const unsigned int a[32],const unsigned int b[32]) |
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{ |
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unsigned int j; |
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unsigned int u; |
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u = 218; |
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for (j = 0;j < 31;++j) { |
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u += a[j] + 65280 - b[j]; |
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out[j] = u & 255; |
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u >>= 8; |
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} |
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u += a[31] - b[31]; |
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out[31] = u; |
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} |
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static void squeeze(unsigned int a[32]) |
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{ |
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unsigned int j; |
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unsigned int u; |
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u = 0; |
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for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; } |
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u += a[31]; a[31] = u & 127; |
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u = 19 * (u >> 7); |
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for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; } |
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u += a[31]; a[31] = u; |
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} |
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static const unsigned int minusp[32] = { |
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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 |
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} ; |
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static void freeze(unsigned int a[32]) |
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{ |
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unsigned int aorig[32]; |
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unsigned int j; |
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unsigned int negative; |
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for (j = 0;j < 32;++j) aorig[j] = a[j]; |
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add(a,a,minusp); |
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negative = -((a[31] >> 7) & 1); |
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for (j = 0;j < 32;++j) a[j] ^= negative & (aorig[j] ^ a[j]); |
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} |
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static void mult(unsigned int out[32],const unsigned int a[32],const unsigned int b[32]) |
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{ |
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unsigned int i; |
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unsigned int j; |
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unsigned int u; |
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for (i = 0;i < 32;++i) { |
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u = 0; |
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for (j = 0;j <= i;++j) u += a[j] * b[i - j]; |
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for (j = i + 1;j < 32;++j) u += 38 * a[j] * b[i + 32 - j]; |
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out[i] = u; |
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} |
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squeeze(out); |
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} |
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static void mult121665(unsigned int out[32],const unsigned int a[32]) |
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{ |
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unsigned int j; |
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unsigned int u; |
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u = 0; |
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for (j = 0;j < 31;++j) { u += 121665 * a[j]; out[j] = u & 255; u >>= 8; } |
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u += 121665 * a[31]; out[31] = u & 127; |
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u = 19 * (u >> 7); |
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for (j = 0;j < 31;++j) { u += out[j]; out[j] = u & 255; u >>= 8; } |
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u += out[j]; out[j] = u; |
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} |
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static void square(unsigned int out[32],const unsigned int a[32]) |
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{ |
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unsigned int i; |
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unsigned int j; |
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unsigned int u; |
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for (i = 0;i < 32;++i) { |
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u = 0; |
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for (j = 0;j < i - j;++j) u += a[j] * a[i - j]; |
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for (j = i + 1;j < i + 32 - j;++j) u += 38 * a[j] * a[i + 32 - j]; |
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u *= 2; |
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if ((i & 1) == 0) { |
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u += a[i / 2] * a[i / 2]; |
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u += 38 * a[i / 2 + 16] * a[i / 2 + 16]; |
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} |
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out[i] = u; |
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} |
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squeeze(out); |
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} |
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static void select(unsigned int p[64],unsigned int q[64],const unsigned int r[64],const unsigned int s[64],unsigned int b) |
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{ |
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unsigned int j; |
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unsigned int t; |
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unsigned int bminus1; |
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bminus1 = b - 1; |
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for (j = 0;j < 64;++j) { |
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t = bminus1 & (r[j] ^ s[j]); |
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p[j] = s[j] ^ t; |
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q[j] = r[j] ^ t; |
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} |
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} |
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static void mainloop(unsigned int work[64],const unsigned char e[32]) |
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{ |
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unsigned int xzm1[64]; |
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unsigned int xzm[64]; |
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unsigned int xzmb[64]; |
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unsigned int xzm1b[64]; |
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unsigned int xznb[64]; |
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unsigned int xzn1b[64]; |
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unsigned int a0[64]; |
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unsigned int a1[64]; |
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unsigned int b0[64]; |
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unsigned int b1[64]; |
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unsigned int c1[64]; |
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unsigned int r[32]; |
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unsigned int s[32]; |
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unsigned int t[32]; |
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unsigned int u[32]; |
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unsigned int j; |
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unsigned int b; |
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int pos; |
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for (j = 0;j < 32;++j) xzm1[j] = work[j]; |
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xzm1[32] = 1; |
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for (j = 33;j < 64;++j) xzm1[j] = 0; |
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xzm[0] = 1; |
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for (j = 1;j < 64;++j) xzm[j] = 0; |
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for (pos = 254;pos >= 0;--pos) { |
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b = e[pos / 8] >> (pos & 7); |
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b &= 1; |
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select(xzmb,xzm1b,xzm,xzm1,b); |
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add(a0,xzmb,xzmb + 32); |
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sub(a0 + 32,xzmb,xzmb + 32); |
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add(a1,xzm1b,xzm1b + 32); |
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sub(a1 + 32,xzm1b,xzm1b + 32); |
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square(b0,a0); |
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square(b0 + 32,a0 + 32); |
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mult(b1,a1,a0 + 32); |
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mult(b1 + 32,a1 + 32,a0); |
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add(c1,b1,b1 + 32); |
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sub(c1 + 32,b1,b1 + 32); |
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square(r,c1 + 32); |
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sub(s,b0,b0 + 32); |
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mult121665(t,s); |
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add(u,t,b0); |
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mult(xznb,b0,b0 + 32); |
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mult(xznb + 32,s,u); |
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square(xzn1b,c1); |
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mult(xzn1b + 32,r,work); |
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select(xzm,xzm1,xznb,xzn1b,b); |
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} |
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for (j = 0;j < 64;++j) work[j] = xzm[j]; |
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} |
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static void recip(unsigned int out[32],const unsigned int z[32]) |
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{ |
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unsigned int z2[32]; |
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unsigned int z9[32]; |
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unsigned int z11[32]; |
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unsigned int z2_5_0[32]; |
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unsigned int z2_10_0[32]; |
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unsigned int z2_20_0[32]; |
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unsigned int z2_50_0[32]; |
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unsigned int z2_100_0[32]; |
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unsigned int t0[32]; |
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unsigned int t1[32]; |
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int i; |
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/* 2 */ square(z2,z); |
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/* 4 */ square(t1,z2); |
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/* 8 */ square(t0,t1); |
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/* 9 */ mult(z9,t0,z); |
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/* 11 */ mult(z11,z9,z2); |
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/* 22 */ square(t0,z11); |
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/* 2^5 - 2^0 = 31 */ mult(z2_5_0,t0,z9); |
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/* 2^6 - 2^1 */ square(t0,z2_5_0); |
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/* 2^7 - 2^2 */ square(t1,t0); |
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/* 2^8 - 2^3 */ square(t0,t1); |
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/* 2^9 - 2^4 */ square(t1,t0); |
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/* 2^10 - 2^5 */ square(t0,t1); |
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/* 2^10 - 2^0 */ mult(z2_10_0,t0,z2_5_0); |
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/* 2^11 - 2^1 */ square(t0,z2_10_0); |
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/* 2^12 - 2^2 */ square(t1,t0); |
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/* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t0,t1); square(t1,t0); } |
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/* 2^20 - 2^0 */ mult(z2_20_0,t1,z2_10_0); |
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/* 2^21 - 2^1 */ square(t0,z2_20_0); |
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/* 2^22 - 2^2 */ square(t1,t0); |
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/* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { square(t0,t1); square(t1,t0); } |
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/* 2^40 - 2^0 */ mult(t0,t1,z2_20_0); |
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/* 2^41 - 2^1 */ square(t1,t0); |
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/* 2^42 - 2^2 */ square(t0,t1); |
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/* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t1,t0); square(t0,t1); } |
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/* 2^50 - 2^0 */ mult(z2_50_0,t0,z2_10_0); |
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/* 2^51 - 2^1 */ square(t0,z2_50_0); |
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/* 2^52 - 2^2 */ square(t1,t0); |
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/* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); } |
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/* 2^100 - 2^0 */ mult(z2_100_0,t1,z2_50_0); |
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/* 2^101 - 2^1 */ square(t1,z2_100_0); |
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/* 2^102 - 2^2 */ square(t0,t1); |
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/* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { square(t1,t0); square(t0,t1); } |
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/* 2^200 - 2^0 */ mult(t1,t0,z2_100_0); |
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/* 2^201 - 2^1 */ square(t0,t1); |
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/* 2^202 - 2^2 */ square(t1,t0); |
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/* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); } |
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/* 2^250 - 2^0 */ mult(t0,t1,z2_50_0); |
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/* 2^251 - 2^1 */ square(t1,t0); |
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/* 2^252 - 2^2 */ square(t0,t1); |
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/* 2^253 - 2^3 */ square(t1,t0); |
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/* 2^254 - 2^4 */ square(t0,t1); |
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/* 2^255 - 2^5 */ square(t1,t0); |
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/* 2^255 - 21 */ mult(out,t1,z11); |
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} |
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int crypto_scalarmult_curve25519(unsigned char *q, |
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const unsigned char *n, |
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const unsigned char *p) |
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{ |
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unsigned int work[96]; |
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unsigned char e[32]; |
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unsigned int i; |
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for (i = 0;i < 32;++i) e[i] = n[i]; |
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e[0] &= 248; |
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e[31] &= 127; |
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e[31] |= 64; |
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for (i = 0;i < 32;++i) work[i] = p[i]; |
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mainloop(work,e); |
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recip(work + 32,work + 32); |
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mult(work + 64,work,work + 32); |
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freeze(work + 64); |
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for (i = 0;i < 32;++i) q[i] = work[64 + i]; |
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return 0; |
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} |