release/src/router/libsodium/src/libsodium/crypto_sign/ed25519/ref10/fe_tobytes.c

   1 #include "fe.h"
   2
   3 /*
   4 Preconditions:
   5   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
   6
   7 Write p=2^255-19; q=floor(h/p).
   8 Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
   9
  10 Proof:
  11   Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
  12   Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
  13
  14   Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
  15   Then 0<y<1.
  16
  17   Write r=h-pq.
  18   Have 0<=r<=p-1=2^255-20.
  19   Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
  20
  21   Write x=r+19(2^-255)r+y.
  22   Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
  23
  24   Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
  25   so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
  26 */
  27
  28 void fe_tobytes(unsigned char *s,const fe h)
  29 {
  30   crypto_int32 h0 = h[0];
  31   crypto_int32 h1 = h[1];
  32   crypto_int32 h2 = h[2];
  33   crypto_int32 h3 = h[3];
  34   crypto_int32 h4 = h[4];
  35   crypto_int32 h5 = h[5];
  36   crypto_int32 h6 = h[6];
  37   crypto_int32 h7 = h[7];
  38   crypto_int32 h8 = h[8];
  39   crypto_int32 h9 = h[9];
  40   crypto_int32 q;
  41   crypto_int32 carry0;
  42   crypto_int32 carry1;
  43   crypto_int32 carry2;
  44   crypto_int32 carry3;
  45   crypto_int32 carry4;
  46   crypto_int32 carry5;
  47   crypto_int32 carry6;
  48   crypto_int32 carry7;
  49   crypto_int32 carry8;
  50   crypto_int32 carry9;
  51
  52   q = (19 * h9 + (((crypto_int32) 1) << 24)) >> 25;
  53   q = (h0 + q) >> 26;
  54   q = (h1 + q) >> 25;
  55   q = (h2 + q) >> 26;
  56   q = (h3 + q) >> 25;
  57   q = (h4 + q) >> 26;
  58   q = (h5 + q) >> 25;
  59   q = (h6 + q) >> 26;
  60   q = (h7 + q) >> 25;
  61   q = (h8 + q) >> 26;
  62   q = (h9 + q) >> 25;
  63
  64   /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
  65   h0 += 19 * q;
  66   /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
  67
  68   carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
  69   carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
  70   carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
  71   carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
  72   carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
  73   carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
  74   carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
  75   carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
  76   carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
  77   carry9 = h9 >> 25;               h9 -= carry9 << 25;
  78                   /* h10 = carry9 */
  79
  80   /*
  81   Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
  82   Have h0+...+2^230 h9 between 0 and 2^255-1;
  83   evidently 2^255 h10-2^255 q = 0.
  84   Goal: Output h0+...+2^230 h9.
  85   */
  86
  87   s[0] = h0 >> 0;
  88   s[1] = h0 >> 8;
  89   s[2] = h0 >> 16;
  90   s[3] = (h0 >> 24) | (h1 << 2);
  91   s[4] = h1 >> 6;
  92   s[5] = h1 >> 14;
  93   s[6] = (h1 >> 22) | (h2 << 3);
  94   s[7] = h2 >> 5;
  95   s[8] = h2 >> 13;
  96   s[9] = (h2 >> 21) | (h3 << 5);
  97   s[10] = h3 >> 3;
  98   s[11] = h3 >> 11;
  99   s[12] = (h3 >> 19) | (h4 << 6);
 100   s[13] = h4 >> 2;
 101   s[14] = h4 >> 10;
 102   s[15] = h4 >> 18;
 103   s[16] = h5 >> 0;
 104   s[17] = h5 >> 8;
 105   s[18] = h5 >> 16;
 106   s[19] = (h5 >> 24) | (h6 << 1);
 107   s[20] = h6 >> 7;
 108   s[21] = h6 >> 15;
 109   s[22] = (h6 >> 23) | (h7 << 3);
 110   s[23] = h7 >> 5;
 111   s[24] = h7 >> 13;
 112   s[25] = (h7 >> 21) | (h8 << 4);
 113   s[26] = h8 >> 4;
 114   s[27] = h8 >> 12;
 115   s[28] = (h8 >> 20) | (h9 << 6);
 116   s[29] = h9 >> 2;
 117   s[30] = h9 >> 10;
 118   s[31] = h9 >> 18;
 119 }