release/src/router/libsodium/src/libsodium/crypto_sign/edwards25519sha512batch/ref/ge25519_edwards25519sha512batch.c

   1 #include "fe25519.h"
   2 #include "sc25519.h"
   3 #include "ge25519.h"
   4
   5 /*
   6  * Arithmetic on the twisted Edwards curve -x^2 + y^2 = 1 + dx^2y^2
   7  * with d = -(121665/121666) = 37095705934669439343138083508754565189542113879843219016388785533085940283555
   8  * Base point: (15112221349535400772501151409588531511454012693041857206046113283949847762202,46316835694926478169428394003475163141307993866256225615783033603165251855960);
   9  */
  10
  11 typedef struct
  12 {
  13   fe25519 x;
  14   fe25519 z;
  15   fe25519 y;
  16   fe25519 t;
  17 } ge25519_p1p1;
  18
  19 typedef struct
  20 {
  21   fe25519 x;
  22   fe25519 y;
  23   fe25519 z;
  24 } ge25519_p2;
  25
  26 #define ge25519_p3 ge25519
  27
  28 /* Windowsize for fixed-window scalar multiplication */
  29 #define WINDOWSIZE 2                      /* Should be 1,2, or 4 */
  30 #define WINDOWMASK ((1<<WINDOWSIZE)-1)
  31
  32 /* packed parameter d in the Edwards curve equation */
  33 static const unsigned char ecd[32] = {0xA3, 0x78, 0x59, 0x13, 0xCA, 0x4D, 0xEB, 0x75, 0xAB, 0xD8, 0x41, 0x41, 0x4D, 0x0A, 0x70, 0x00,
  34                                       0x98, 0xE8, 0x79, 0x77, 0x79, 0x40, 0xC7, 0x8C, 0x73, 0xFE, 0x6F, 0x2B, 0xEE, 0x6C, 0x03, 0x52};
  35
  36 /* Packed coordinates of the base point */
  37 static const unsigned char ge25519_base_x[32] = {0x1A, 0xD5, 0x25, 0x8F, 0x60, 0x2D, 0x56, 0xC9, 0xB2, 0xA7, 0x25, 0x95, 0x60, 0xC7, 0x2C, 0x69,
  38                                                  0x5C, 0xDC, 0xD6, 0xFD, 0x31, 0xE2, 0xA4, 0xC0, 0xFE, 0x53, 0x6E, 0xCD, 0xD3, 0x36, 0x69, 0x21};
  39 static const unsigned char ge25519_base_y[32] = {0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
  40                                                  0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66};
  41 static const unsigned char ge25519_base_z[32] = {1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
  42 static const unsigned char ge25519_base_t[32] = {0xA3, 0xDD, 0xB7, 0xA5, 0xB3, 0x8A, 0xDE, 0x6D, 0xF5, 0x52, 0x51, 0x77, 0x80, 0x9F, 0xF0, 0x20,
  43                                                  0x7D, 0xE3, 0xAB, 0x64, 0x8E, 0x4E, 0xEA, 0x66, 0x65, 0x76, 0x8B, 0xD7, 0x0F, 0x5F, 0x87, 0x67};
  44
  45 /* Packed coordinates of the neutral element */
  46 static const unsigned char ge25519_neutral_x[32] = {0};
  47 static const unsigned char ge25519_neutral_y[32] = {1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
  48 static const unsigned char ge25519_neutral_z[32] = {1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
  49 static const unsigned char ge25519_neutral_t[32] = {0};
  50
  51 static void p1p1_to_p2(ge25519_p2 *r, const ge25519_p1p1 *p)
  52 {
  53   fe25519_mul(&r->x, &p->x, &p->t);
  54   fe25519_mul(&r->y, &p->y, &p->z);
  55   fe25519_mul(&r->z, &p->z, &p->t);
  56 }
  57
  58 static void p1p1_to_p3(ge25519_p3 *r, const ge25519_p1p1 *p)
  59 {
  60   p1p1_to_p2((ge25519_p2 *)r, p);
  61   fe25519_mul(&r->t, &p->x, &p->y);
  62 }
  63
  64 /* Constant-time version of: if(b) r = p */
  65 static void cmov_p3(ge25519_p3 *r, const ge25519_p3 *p, unsigned char b)
  66 {
  67   fe25519_cmov(&r->x, &p->x, b);
  68   fe25519_cmov(&r->y, &p->y, b);
  69   fe25519_cmov(&r->z, &p->z, b);
  70   fe25519_cmov(&r->t, &p->t, b);
  71 }
  72
  73 /* See http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#doubling-dbl-2008-hwcd */
  74 static void dbl_p1p1(ge25519_p1p1 *r, const ge25519_p2 *p)
  75 {
  76   fe25519 a,b,c,d;
  77   fe25519_square(&a, &p->x);
  78   fe25519_square(&b, &p->y);
  79   fe25519_square(&c, &p->z);
  80   fe25519_add(&c, &c, &c);
  81   fe25519_neg(&d, &a);
  82
  83   fe25519_add(&r->x, &p->x, &p->y);
  84   fe25519_square(&r->x, &r->x);
  85   fe25519_sub(&r->x, &r->x, &a);
  86   fe25519_sub(&r->x, &r->x, &b);
  87   fe25519_add(&r->z, &d, &b);
  88   fe25519_sub(&r->t, &r->z, &c);
  89   fe25519_sub(&r->y, &d, &b);
  90 }
  91
  92 static void add_p1p1(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_p3 *q)
  93 {
  94   fe25519 a, b, c, d, t, fd;
  95   fe25519_unpack(&fd, ecd);
  96
  97   fe25519_sub(&a, &p->y, &p->x); // A = (Y1-X1)*(Y2-X2)
  98   fe25519_sub(&t, &q->y, &q->x);
  99   fe25519_mul(&a, &a, &t);
 100   fe25519_add(&b, &p->x, &p->y); // B = (Y1+X1)*(Y2+X2)
 101   fe25519_add(&t, &q->x, &q->y);
 102   fe25519_mul(&b, &b, &t);
 103   fe25519_mul(&c, &p->t, &q->t); //C = T1*k*T2
 104   fe25519_mul(&c, &c, &fd);
 105   fe25519_add(&c, &c, &c);       //XXX: Can save this addition by precomputing 2*ecd
 106   fe25519_mul(&d, &p->z, &q->z); //D = Z1*2*Z2
 107   fe25519_add(&d, &d, &d);
 108   fe25519_sub(&r->x, &b, &a); // E = B-A
 109   fe25519_sub(&r->t, &d, &c); // F = D-C
 110   fe25519_add(&r->z, &d, &c); // G = D+C
 111   fe25519_add(&r->y, &b, &a); // H = B+A
 112 }
 113
 114 /* ********************************************************************
 115  *                    EXPORTED FUNCTIONS
 116  ******************************************************************** */
 117
 118 /* return 0 on success, -1 otherwise */
 119 int ge25519_unpack_vartime(ge25519_p3 *r, const unsigned char p[32])
 120 {
 121   int ret;
 122   fe25519 t, fd;
 123   fe25519_setone(&r->z);
 124   fe25519_unpack(&fd, ecd);
 125   unsigned char par = p[31] >> 7;
 126   fe25519_unpack(&r->y, p);
 127   fe25519_square(&r->x, &r->y);
 128   fe25519_mul(&t, &r->x, &fd);
 129   fe25519_sub(&r->x, &r->x, &r->z);
 130   fe25519_add(&t, &r->z, &t);
 131   fe25519_invert(&t, &t);
 132   fe25519_mul(&r->x, &r->x, &t);
 133   ret = fe25519_sqrt_vartime(&r->x, &r->x, par);
 134   fe25519_mul(&r->t, &r->x, &r->y);
 135   return ret;
 136 }
 137
 138 void ge25519_pack(unsigned char r[32], const ge25519_p3 *p)
 139 {
 140   fe25519 tx, ty, zi;
 141   fe25519_invert(&zi, &p->z);
 142   fe25519_mul(&tx, &p->x, &zi);
 143   fe25519_mul(&ty, &p->y, &zi);
 144   fe25519_pack(r, &ty);
 145   r[31] ^= fe25519_getparity(&tx) << 7;
 146 }
 147
 148 void ge25519_add(ge25519_p3 *r, const ge25519_p3 *p, const ge25519_p3 *q)
 149 {
 150   ge25519_p1p1 grp1p1;
 151   add_p1p1(&grp1p1, p, q);
 152   p1p1_to_p3(r, &grp1p1);
 153 }
 154
 155 void ge25519_double(ge25519_p3 *r, const ge25519_p3 *p)
 156 {
 157   ge25519_p1p1 grp1p1;
 158   dbl_p1p1(&grp1p1, (ge25519_p2 *)p);
 159   p1p1_to_p3(r, &grp1p1);
 160 }
 161
 162 void ge25519_scalarmult(ge25519_p3 *r, const ge25519_p3 *p, const sc25519 *s)
 163 {
 164   int i,j,k;
 165   ge25519_p3 g;
 166   fe25519_unpack(&g.x, ge25519_neutral_x);
 167   fe25519_unpack(&g.y, ge25519_neutral_y);
 168   fe25519_unpack(&g.z, ge25519_neutral_z);
 169   fe25519_unpack(&g.t, ge25519_neutral_t);
 170
 171   ge25519_p3 pre[(1 << WINDOWSIZE)];
 172   ge25519_p3 t;
 173   ge25519_p1p1 tp1p1;
 174   unsigned char w;
 175   unsigned char sb[32];
 176   sc25519_to32bytes(sb, s);
 177
 178   // Precomputation
 179   pre[0] = g;
 180   pre[1] = *p;
 181   for(i=2;i<(1<<WINDOWSIZE);i+=2)
 182   {
 183     dbl_p1p1(&tp1p1, (ge25519_p2 *)(pre+i/2));
 184     p1p1_to_p3(pre+i, &tp1p1);
 185     add_p1p1(&tp1p1, pre+i, pre+1);
 186     p1p1_to_p3(pre+i+1, &tp1p1);
 187   }
 188
 189   // Fixed-window scalar multiplication
 190   for(i=32;i>0;i--)
 191   {
 192     for(j=8-WINDOWSIZE;j>=0;j-=WINDOWSIZE)
 193     {
 194       for(k=0;k<WINDOWSIZE-1;k++)
 195       {
 196         dbl_p1p1(&tp1p1, (ge25519_p2 *)&g);
 197         p1p1_to_p2((ge25519_p2 *)&g, &tp1p1);
 198       }
 199       dbl_p1p1(&tp1p1, (ge25519_p2 *)&g);
 200       p1p1_to_p3(&g, &tp1p1);
 201       // Cache-timing resistant loading of precomputed value:
 202       w = (sb[i-1]>>j) & WINDOWMASK;
 203       t = pre[0];
 204       for(k=1;k<(1<<WINDOWSIZE);k++)
 205         cmov_p3(&t, &pre[k], k==w);
 206
 207       add_p1p1(&tp1p1, &g, &t);
 208       if(j != 0) p1p1_to_p2((ge25519_p2 *)&g, &tp1p1);
 209       else p1p1_to_p3(&g, &tp1p1); /* convert to p3 representation at the end */
 210     }
 211   }
 212   r->x = g.x;
 213   r->y = g.y;
 214   r->z = g.z;
 215   r->t = g.t;
 216 }
 217
 218 void ge25519_scalarmult_base(ge25519_p3 *r, const sc25519 *s)
 219 {
 220   /* XXX: Better algorithm for known-base-point scalar multiplication */
 221   ge25519_p3 t;
 222   fe25519_unpack(&t.x, ge25519_base_x);
 223   fe25519_unpack(&t.y, ge25519_base_y);
 224   fe25519_unpack(&t.z, ge25519_base_z);
 225   fe25519_unpack(&t.t, ge25519_base_t);
 226   ge25519_scalarmult(r, &t, s);
 227 }