1#include "fe.h"
2
3/*
4Preconditions:
5 |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
6
7Write p=2^255-19; q=floor(h/p).
8Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
9
10Proof:
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
28void 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}
120