120 lines
3.6 KiB
C
120 lines
3.6 KiB
C
#include "fe.h"
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/*
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Preconditions:
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|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
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Write p=2^255-19; q=floor(h/p).
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Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
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Proof:
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Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
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Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
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Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
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Then 0<y<1.
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Write r=h-pq.
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Have 0<=r<=p-1=2^255-20.
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Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
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Write x=r+19(2^-255)r+y.
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Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
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Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
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so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
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*/
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void fe_tobytes(unsigned char *s,const fe h)
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{
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int32_t h0 = h[0];
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int32_t h1 = h[1];
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int32_t h2 = h[2];
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int32_t h3 = h[3];
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int32_t h4 = h[4];
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int32_t h5 = h[5];
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int32_t h6 = h[6];
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int32_t h7 = h[7];
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int32_t h8 = h[8];
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int32_t h9 = h[9];
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int32_t q;
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int32_t carry0;
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int32_t carry1;
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int32_t carry2;
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int32_t carry3;
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int32_t carry4;
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int32_t carry5;
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int32_t carry6;
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int32_t carry7;
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int32_t carry8;
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int32_t carry9;
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q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
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q = (h0 + q) >> 26;
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q = (h1 + q) >> 25;
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q = (h2 + q) >> 26;
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q = (h3 + q) >> 25;
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q = (h4 + q) >> 26;
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q = (h5 + q) >> 25;
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q = (h6 + q) >> 26;
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q = (h7 + q) >> 25;
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q = (h8 + q) >> 26;
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q = (h9 + q) >> 25;
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/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
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h0 += 19 * q;
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/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
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carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
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carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
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carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
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carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
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carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
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carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
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carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
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carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
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carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
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carry9 = h9 >> 25; h9 -= carry9 << 25;
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/* h10 = carry9 */
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/*
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Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
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Have h0+...+2^230 h9 between 0 and 2^255-1;
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evidently 2^255 h10-2^255 q = 0.
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Goal: Output h0+...+2^230 h9.
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*/
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s[0] = (unsigned char) (h0 >> 0);
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s[1] = (unsigned char) (h0 >> 8);
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s[2] = (unsigned char) (h0 >> 16);
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s[3] = (unsigned char) ((h0 >> 24) | (h1 << 2));
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s[4] = (unsigned char) (h1 >> 6);
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s[5] = (unsigned char) (h1 >> 14);
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s[6] = (unsigned char) ((h1 >> 22) | (h2 << 3));
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s[7] = (unsigned char) (h2 >> 5);
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s[8] = (unsigned char) (h2 >> 13);
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s[9] = (unsigned char) ((h2 >> 21) | (h3 << 5));
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s[10] = (unsigned char) (h3 >> 3);
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s[11] = (unsigned char) (h3 >> 11);
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s[12] = (unsigned char) ((h3 >> 19) | (h4 << 6));
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s[13] = (unsigned char) (h4 >> 2);
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s[14] = (unsigned char) (h4 >> 10);
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s[15] = (unsigned char) (h4 >> 18);
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s[16] = (unsigned char) (h5 >> 0);
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s[17] = (unsigned char) (h5 >> 8);
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s[18] = (unsigned char) (h5 >> 16);
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s[19] = (unsigned char) ((h5 >> 24) | (h6 << 1));
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s[20] = (unsigned char) (h6 >> 7);
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s[21] = (unsigned char) (h6 >> 15);
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s[22] = (unsigned char) ((h6 >> 23) | (h7 << 3));
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s[23] = (unsigned char) (h7 >> 5);
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s[24] = (unsigned char) (h7 >> 13);
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s[25] = (unsigned char) ((h7 >> 21) | (h8 << 4));
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s[26] = (unsigned char) (h8 >> 4);
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s[27] = (unsigned char) (h8 >> 12);
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s[28] = (unsigned char) ((h8 >> 20) | (h9 << 6));
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s[29] = (unsigned char) (h9 >> 2);
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s[30] = (unsigned char) (h9 >> 10);
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s[31] = (unsigned char) (h9 >> 18);
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}
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