ed25519.h

   1 /* Edwards curve operations
   2  * Daniel Beer <dlbeer@gmail.com>, 9 Jan 2014
   3  *
   4  * This file is in the public domain.
   5  */
   6
   7 #ifndef ED25519_H_
   8 #define ED25519_H_
   9
  10 #include "f25519.h"
  11
  12 /* This is not the Ed25519 signature system. Rather, we're implementing
  13  * basic operations on the twisted Edwards curve over (Z mod 2^255-19):
  14  *
  15  *     -x^2 + y^2 = 1 - (121665/121666)x^2y^2
  16  *
  17  * With the positive-x base point y = 4/5.
  18  *
  19  * These functions will not leak secret data through timing.
  20  *
  21  * For more information, see:
  22  *
  23  *     Bernstein, D.J. & Lange, T. (2007) "Faster addition and doubling on
  24  *     elliptic curves". Document ID: 95616567a6ba20f575c5f25e7cebaf83.
  25  *
  26  *     Hisil, H. & Wong, K K. & Carter, G. & Dawson, E. (2008) "Twisted
  27  *     Edwards curves revisited". Advances in Cryptology, ASIACRYPT 2008,
  28  *     Vol. 5350, pp. 326-343.
  29  */
  30
  31 /* Projective coordinates */
  32 struct ed25519_pt {
  33         uint8_t         x[F25519_SIZE];
  34         uint8_t         y[F25519_SIZE];
  35         uint8_t         t[F25519_SIZE];
  36         uint8_t         z[F25519_SIZE];
  37 };
  38
  39 extern const struct ed25519_pt ed25519_base;
  40
  41 /* Convert between projective and affine coordinates (x/y in F25519) */
  42 void ed25519_project(struct ed25519_pt *p,
  43                      const uint8_t *x, const uint8_t *y);
  44
  45 void ed25519_unproject(uint8_t *x, uint8_t *y,
  46                        const struct ed25519_pt *p);
  47
  48 /* Compress/uncompress points. try_unpack() will check that the
  49  * compressed point is on the curve, returning 1 if the unpacked point
  50  * is valid, and 0 otherwise.
  51  */
  52 #define ED25519_PACK_SIZE       F25519_SIZE
  53
  54 void ed25519_pack(uint8_t *c, const uint8_t *x, const uint8_t *y);
  55 uint8_t ed25519_try_unpack(uint8_t *x, uint8_t *y, const uint8_t *c);
  56
  57 /* Add, double and scalar multiply */
  58 #define ED25519_EXPONENT_SIZE   32
  59
  60 /* Prepare an exponent by clamping appropriate bits */
  61 static inline void ed25519_prepare(uint8_t *e)
  62 {
  63         e[0] &= 0xf8;
  64         e[31] &= 0x7f;
  65         e[31] |= 0x40;
  66 }
  67
  68 /* Order of the group generated by the base point */
  69 static inline void ed25519_copy(struct ed25519_pt *dst,
  70                                 const struct ed25519_pt *src)
  71 {
  72         memcpy(dst, src, sizeof(*dst));
  73 }
  74
  75 void ed25519_add(struct ed25519_pt *r,
  76                  const struct ed25519_pt *a, const struct ed25519_pt *b);
  77 void ed25519_smult(struct ed25519_pt *r, const struct ed25519_pt *a,
  78                    const uint8_t *e);
  79
  80 #endif