120 lines
3.1 KiB
C
120 lines
3.1 KiB
C
|
#include "fe.h"
|
||
|
|
|
||
|
|
/*
|
||
|
|
Preconditions:
|
||
|
|
|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
|
||
|
|
|
||
|
|
Write p=2^255-19; q=floor(h/p).
|
||
|
|
Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
|
||
|
|
|
||
|
|
Proof:
|
||
|
|
Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
|
||
|
|
Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
|
||
|
|
|
||
|
|
Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
|
||
|
|
Then 0<y<1.
|
||
|
|
|
||
|
|
Write r=h-pq.
|
||
|
|
Have 0<=r<=p-1=2^255-20.
|
||
|
|
Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
|
||
|
|
|
||
|
|
Write x=r+19(2^-255)r+y.
|
||
|
|
Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
|
||
|
|
|
||
|
|
Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
|
||
|
|
so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
|
||
|
|
*/
|
||
|
|
|
||
|
|
void fe_tobytes(unsigned char *s,const fe h)
|
||
|
|
{
|
||
|
|
crypto_int32 h0 = h[0];
|
||
|
|
crypto_int32 h1 = h[1];
|
||
|
|
crypto_int32 h2 = h[2];
|
||
|
|
crypto_int32 h3 = h[3];
|
||
|
|
crypto_int32 h4 = h[4];
|
||
|
|
crypto_int32 h5 = h[5];
|
||
|
|
crypto_int32 h6 = h[6];
|
||
|
|
crypto_int32 h7 = h[7];
|
||
|
|
crypto_int32 h8 = h[8];
|
||
|
|
crypto_int32 h9 = h[9];
|
||
|
|
crypto_int32 q;
|
||
|
|
crypto_int32 carry0;
|
||
|
|
crypto_int32 carry1;
|
||
|
|
crypto_int32 carry2;
|
||
|
|
crypto_int32 carry3;
|
||
|
|
crypto_int32 carry4;
|
||
|
|
crypto_int32 carry5;
|
||
|
|
crypto_int32 carry6;
|
||
|
|
crypto_int32 carry7;
|
||
|
|
crypto_int32 carry8;
|
||
|
|
crypto_int32 carry9;
|
||
|
|
|
||
|
|
q = (19 * h9 + (((crypto_int32) 1) << 24)) >> 25;
|
||
|
|
q = (h0 + q) >> 26;
|
||
|
|
q = (h1 + q) >> 25;
|
||
|
|
q = (h2 + q) >> 26;
|
||
|
|
q = (h3 + q) >> 25;
|
||
|
|
q = (h4 + q) >> 26;
|
||
|
|
q = (h5 + q) >> 25;
|
||
|
|
q = (h6 + q) >> 26;
|
||
|
|
q = (h7 + q) >> 25;
|
||
|
|
q = (h8 + q) >> 26;
|
||
|
|
q = (h9 + q) >> 25;
|
||
|
|
|
||
|
|
/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
|
||
|
|
h0 += 19 * q;
|
||
|
|
/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
|
||
|
|
|
||
|
|
carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
|
||
|
|
carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
|
||
|
|
carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
|
||
|
|
carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
|
||
|
|
carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
|
||
|
|
carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
|
||
|
|
carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
|
||
|
|
carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
|
||
|
|
carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
|
||
|
|
carry9 = h9 >> 25; h9 -= carry9 << 25;
|
||
|
|
/* h10 = carry9 */
|
||
|
|
|
||
|
|
/*
|
||
|
|
Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
|
||
|
|
Have h0+...+2^230 h9 between 0 and 2^255-1;
|
||
|
|
evidently 2^255 h10-2^255 q = 0.
|
||
|
|
Goal: Output h0+...+2^230 h9.
|
||
|
|
*/
|
||
|
|
|
||
|
|
s[0] = h0 >> 0;
|
||
|
|
s[1] = h0 >> 8;
|
||
|
|
s[2] = h0 >> 16;
|
||
|
|
s[3] = (h0 >> 24) | (h1 << 2);
|
||
|
|
s[4] = h1 >> 6;
|
||
|
|
s[5] = h1 >> 14;
|
||
|
|
s[6] = (h1 >> 22) | (h2 << 3);
|
||
|
|
s[7] = h2 >> 5;
|
||
|
|
s[8] = h2 >> 13;
|
||
|
|
s[9] = (h2 >> 21) | (h3 << 5);
|
||
|
|
s[10] = h3 >> 3;
|
||
|
|
s[11] = h3 >> 11;
|
||
|
|
s[12] = (h3 >> 19) | (h4 << 6);
|
||
|
|
s[13] = h4 >> 2;
|
||
|
|
s[14] = h4 >> 10;
|
||
|
|
s[15] = h4 >> 18;
|
||
|
|
s[16] = h5 >> 0;
|
||
|
|
s[17] = h5 >> 8;
|
||
|
|
s[18] = h5 >> 16;
|
||
|
|
s[19] = (h5 >> 24) | (h6 << 1);
|
||
|
|
s[20] = h6 >> 7;
|
||
|
|
s[21] = h6 >> 15;
|
||
|
|
s[22] = (h6 >> 23) | (h7 << 3);
|
||
|
|
s[23] = h7 >> 5;
|
||
|
|
s[24] = h7 >> 13;
|
||
|
|
s[25] = (h7 >> 21) | (h8 << 4);
|
||
|
|
s[26] = h8 >> 4;
|
||
|
|
s[27] = h8 >> 12;
|
||
|
|
s[28] = (h8 >> 20) | (h9 << 6);
|
||
|
|
s[29] = h9 >> 2;
|
||
|
|
s[30] = h9 >> 10;
|
||
|
|
s[31] = h9 >> 18;
|
||
|
|
}
|