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Added point compression and decompression functions (for issue #2).

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This commit is contained in:
Ken MacKay
2013-07-08 23:31:59 -07:00
parent ac0d7a3fab
commit 37fe7a2e08
2 changed files with 72 additions and 5 deletions
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ecc.c
+50 -5
View File
@@ -1260,9 +1260,19 @@ int ecc_make_key(EccPoint *p_publicKey, uint32_t p_privateKey[NUM_ECC_DIGITS], u
return 1;
}
/* Compute p_result = x^3 - 3x + b */
static void curve_x_side(uint32_t p_result[NUM_ECC_DIGITS], uint32_t x[NUM_ECC_DIGITS])
{
uint32_t _3[NUM_ECC_DIGITS] = {3}; /* -a = 3 */
vli_modSquare_fast(p_result, x); /* r = x^2 */
vli_modSub(p_result, p_result, _3, curve_p); /* r = x^2 - 3 */
vli_modMult_fast(p_result, p_result, x); /* r = x^3 - 3x */
vli_modAdd(p_result, p_result, curve_b, curve_p); /* r = x^3 - 3x + b */
}
int ecc_valid_public_key(EccPoint *p_publicKey)
{
uint32_t na[NUM_ECC_DIGITS] = {3}; /* -a = 3 */
uint32_t l_tmp1[NUM_ECC_DIGITS];
uint32_t l_tmp2[NUM_ECC_DIGITS];
@@ -1278,10 +1288,7 @@ int ecc_valid_public_key(EccPoint *p_publicKey)
vli_modSquare_fast(l_tmp1, p_publicKey->y); /* tmp1 = y^2 */
vli_modSquare_fast(l_tmp2, p_publicKey->x); /* tmp2 = x^2 */
vli_modSub(l_tmp2, l_tmp2, na, curve_p); /* tmp2 = x^2 + a = x^2 - 3 */
vli_modMult_fast(l_tmp2, l_tmp2, p_publicKey->x); /* tmp2 = x^3 + ax */
vli_modAdd(l_tmp2, l_tmp2, curve_b, curve_p); /* tmp2 = x^3 + ax + b */
curve_x_side(l_tmp2, p_publicKey->x); /* tmp2 = x^3 - 3x + b */
/* Make sure that y^2 == x^3 + ax + b */
if(vli_cmp(l_tmp1, l_tmp2) != 0)
@@ -1517,3 +1524,41 @@ void ecc_native2bytes(uint8_t p_bytes[NUM_ECC_DIGITS*4], uint32_t p_native[NUM_E
p_digit[3] = p_native[i];
}
}
/* Compute a = sqrt(a) (mod curve_p). */
static void mod_sqrt(uint32_t a[NUM_ECC_DIGITS])
{
unsigned i;
uint32_t p1[NUM_ECC_DIGITS] = {1};
uint32_t l_result[NUM_ECC_DIGITS] = {1};
/* Since curve_p == 3 (mod 4) for all supported curves, we can
compute sqrt(a) = a^((curve_p + 1) / 4) (mod curve_p). */
vli_add(p1, curve_p, p1); /* p1 = curve_p + 1 */
for(i = vli_numBits(p1) - 1; i > 1; --i)
{
vli_modSquare_fast(l_result, l_result);
if(vli_testBit(p1, i))
{
vli_modMult_fast(l_result, l_result, a);
}
}
vli_set(a, l_result);
}
void ecc_point_compress(uint8_t p_compressed[NUM_ECC_DIGITS*4 + 1], EccPoint *p_point)
{
p_compressed[0] = 2 + (p_point->y[0] & 0x01);
ecc_native2bytes(p_compressed + 1, p_point->x);
}
void ecc_point_decompress(EccPoint *p_point, uint8_t p_compressed[NUM_ECC_DIGITS*4 + 1])
{
ecc_bytes2native(p_point->x, p_compressed + 1);
curve_x_side(p_point->y, p_point->x);
mod_sqrt(p_point->y);
if((p_point->y[0] & 0x01) != (p_compressed[0] & 0x01))
{
vli_sub(p_point->y, curve_p, p_point->y);
}
}
ecc.h
+22
View File
@@ -152,4 +152,26 @@ Inputs:
*/
void ecc_native2bytes(uint8_t p_bytes[NUM_ECC_DIGITS*4], uint32_t p_native[NUM_ECC_DIGITS]);
/* ecc_point_compress() function.
Compress a point from native format into the standard compressed octet representation.
Outputs:
p_compressed - Will be filled in with the compressed point representation.
Inputs:
p_point - The point to compress.
*/
void ecc_point_compress(uint8_t p_compressed[NUM_ECC_DIGITS*4 + 1], EccPoint *p_point);
/* ecc_point_compress() function.
Decompress a point from the standard compressed octet representation to native format.
Outputs:
p_point - Will be filled in with the native point representation.
Inputs:
p_compressed - The standard compressed octet representation of the point.
*/
void ecc_point_decompress(EccPoint *p_point, uint8_t p_compressed[NUM_ECC_DIGITS*4 + 1]);
#endif /* _MICRO_ECC_H_ */