/* Return R = a*P where P is curve25519 base point */
void x25519_BasePointMultiply(OUT U8 *r, IN const U8 *sk)
{
Ext_POINT S;
U_WORD t[K_WORDS];
ecp_BytesToWords(t, sk);
edp_BasePointMult(&S, t, edp_custom_blinding.zr);
/* Convert ed25519 point to x25519 point */
/* u = (1 + y)/(1 - y) = (Z + Y)/(Z - Y) */
ecp_AddReduce(S.t, S.z, S.y);
ecp_SubReduce(S.z, S.z, S.y);
ecp_Inverse(S.z, S.z);
ecp_MulMod(S.t, S.t, S.z);
ecp_WordsToBytes(r, S.t);
}
void edp_BasePointMultiply(
OUT Affine_POINT *R,
IN const U_WORD *sk,
IN const void *blinding)
{
Ext_POINT S;
U_WORD t[K_WORDS];
if (blinding)
{
eco_AddReduce(t, sk, ((EDP_BLINDING_CTX*)blinding)->bl);
edp_BasePointMult(&S, t, ((EDP_BLINDING_CTX*)blinding)->zr);
edp_AddPoint(&S, &S, &((EDP_BLINDING_CTX*)blinding)->BP);
}
else
{
edp_BasePointMult(&S, sk, edp_custom_blinding.zr);
}
ecp_Inverse(S.z, S.z);
ecp_MulMod(R->x, S.x, S.z);
ecp_MulMod(R->y, S.y, S.z);
}
int curve25519_SelfTest(int level)
{
int rc = 0;
U64 A[4], B[4], C[4];
U8 a[32], b[32], c[32], d[32];
ecp_AddReduce(A, _w_I, _w_P);
ECP_MOD(A);
if (ecp_Cmp(A, _w_I) != 0)
{
rc++;
printf("assert I+p == I mod p FAILED!!\n");
ecp_PrintHexWords("A_1", A, 4);
}
if (ecp_Cmp(_w_I, _w_P) >= 0)
{
rc++;
printf("assert I < P FAILED!!\n");
}
if (ecp_Cmp(_w_P, _w_I) <= 0)
{
rc++;
printf("assert P > I FAILED!!\n");
}
ecp_MulReduce(B, _w_I, _w_D);
ECP_MOD(B);
if (ecp_Cmp(B, _w_IxD) != 0)
{
rc++;
printf("assert I*D FAILED!!\n");
ecp_PrintHexWords("A_2", B, 4);
}
// assert I*I == p-1
ecp_MulMod(A, _w_I, _w_I);
if (ecp_Cmp(A, _w_Pm1) != 0)
{
rc++;
printf("assert mul(I,I) == p-1 FAILED!!\n");
ecp_PrintHexWords("A_3", A, 4);
}
// assert I**2 == p-1
ecp_SqrReduce(B, _w_I);
ECP_MOD(B);
if (ecp_Cmp(B, _w_Pm1) != 0)
{
rc++;
printf("assert square(I) == p-1 FAILED!!\n");
ecp_PrintHexWords("B_4", B, 4);
}
// assert (-I)*(-I) == p-1
ecp_Sub(B, _w_P, _w_I);
ecp_MulMod(A, B, B);
if (ecp_Cmp(A, _w_Pm1) != 0)
{
rc++;
printf("assert mul(-I,-I) == p-1 FAILED!!\n");
ecp_PrintHexWords("A_5", A, 4);
ecp_PrintHexWords("B_5", B, 4);
}
ecp_SetValue(A, 50153);
ecp_Inverse(B, A);
ecp_MulMod(A, A, B);
if (ecp_Cmp(A, _w_One) != 0)
{
rc++;
printf("invmod FAILED!!\n");
ecp_PrintHexWords("inv_50153", B, 4);
ecp_PrintHexWords("expected_1", A, 4);
}
// assert expmod(d,(p-1)/2,p) == p-1
ecp_ExpMod(A, _w_D, _b_Pm1d2, 32);
if (ecp_Cmp(A, _w_Pm1) != 0)
{
rc++;
printf("assert expmod(d,(p-1)/2,p) == p-1 FAILED!!\n");
ecp_PrintHexWords("A_3", A, 4);
}
ecp_CalculateY(a, ecp_BasePoint);
ecp_BytesToWords(A, a);
if (ecp_Cmp(A, _w_Gy) != 0)
{
rc++;
printf("assert clacY(Base) == Base.y FAILED!!\n");
ecp_PrintHexBytes("Calculated_Base.y", a, 32);
}
ecp_PointMultiply(a, ecp_BasePoint, _b_Om1, 32);
if (memcmp(a, ecp_BasePoint, 32) != 0)
{
rc++;
printf("assert (l-1).Base == Base FAILED!!\n");
ecp_PrintHexBytes("A_5", a, 32);
}
ecp_PointMultiply(a, ecp_BasePoint, _b_O, 32);
ecp_BytesToWords(A, a);
if (!ecp_IsZero(A))
{
rc++;
printf("assert l.Base == 0 FAILED!!\n");
ecp_PrintHexBytes("A_6", a, 32);
}
// Key generation
ecp_PointMultiply(a, ecp_BasePoint, pk1, 32);
ecp_PrintHexBytes("PublicKey1", a, 32);
ecp_PointMultiply(b, ecp_BasePoint, pk2, 32);
ecp_PrintHexBytes("PublicKey2", b, 32);
// ECDH - key exchange
ecp_PointMultiply(c, b, pk1, 32);
ecp_PrintHexBytes("SharedKey1", c, 32);
ecp_PointMultiply(d, a, pk2, 32);
ecp_PrintHexBytes("SharedKey2", d, 32);
if (memcmp(c, d, 32) != 0)
{
rc++;
printf("ECDH key exchange FAILED!!\n");
}
memset(a, 0x44, 32); // our secret key
ecp_PointMultiply(b, ecp_BasePoint, a, 32); // public key
ecp_PointMultiply(c, b, _b_k1, 32);
ecp_PointMultiply(d, c, _b_k2, 32);
if (memcmp(d, b, 32) != 0)
{
rc++;
printf("assert k1.k2.D == D FAILED!!\n");
ecp_PrintHexBytes("D", d, 4);
ecp_PrintHexBytes("C", c, 4);
ecp_PrintHexBytes("A", a, 4);
}
ecp_BytesToWords(A, _b_k1);
ecp_BytesToWords(B, _b_k2);
eco_InvModBPO(C, A);
if (ecp_Cmp(C, B) != 0)
{
rc++;
printf("assert 1/k1 == k2 mod BPO FAILED!!\n");
ecp_PrintHexWords("Calc", C, 4);
ecp_PrintHexWords("Expt", B, 4);
}
eco_MulMod(C, A, B);
if (ecp_Cmp(C, _w_One) != 0)
{
rc++;
printf("assert k1*k2 == 1 mod BPO FAILED!!\n");
ecp_PrintHexWords("Calc", C, 4);
}
return rc;
}
/* K in a little-endian byte array */
void ecp_PointMultiply(
OUT U8 *PublicKey,
IN const U8 *BasePoint,
IN const U8 *SecretKey,
IN int len)
{
int i, j, k;
U_WORD X[K_WORDS];
XZ_POINT P, Q, *PP[2], *QP[2];
ecp_BytesToWords(X, BasePoint);
/* 1: P = (2k+1)G, Q = (2k+2)G */
/* 0: Q = (2k+1)G, P = (2k)G */
/* Find first non-zero bit */
while (len-- > 0)
{
k = SecretKey[len];
for (i = 0; i < 8; i++, k <<= 1)
{
/* P = kG, Q = (k+1)G */
if (k & 0x80)
{
/* We have first non-zero bit
// This is always bit 254 for keys created according to the spec.
// Start with randomized base point
*/
ecp_Add(P.Z, X, edp_custom_blinding.zr); /* P.Z = random */
ecp_MulReduce(P.X, X, P.Z);
ecp_MontDouble(&Q, &P);
PP[1] = &P; PP[0] = &Q;
QP[1] = &Q; QP[0] = &P;
/* Everything we reference in the below loop are on the stack
// and already touched (cached)
*/
while (++i < 8) { k <<= 1; ECP_MONT(7); }
while (len > 0)
{
k = SecretKey[--len];
ECP_MONT(7);
ECP_MONT(6);
ECP_MONT(5);
ECP_MONT(4);
ECP_MONT(3);
ECP_MONT(2);
ECP_MONT(1);
ECP_MONT(0);
}
ecp_Inverse(Q.Z, P.Z);
ecp_MulMod(X, P.X, Q.Z);
ecp_WordsToBytes(PublicKey, X);
return;
}
}
}
/* K is 0 */
mem_fill(PublicKey, 0, 32);
}
