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/********************************************************************************************
* SIDH: an efficient supersingular isogeny cryptography library
*
* Abstract: ephemeral supersingular isogeny Diffie-Hellman key exchange (SIDH)
*********************************************************************************************/
#include "../s2n_pq_random.h"
#include "utils/s2n_safety.h"
static void init_basis(const digit_t *gen, f2elm_t *XP, f2elm_t *XQ, f2elm_t *XR) { // Initialization of basis points
fpcopy(gen, XP->e[0]);
fpcopy(gen + NWORDS_FIELD, XP->e[1]);
fpcopy(gen + 2 * NWORDS_FIELD, XQ->e[0]);
fpcopy(gen + 3 * NWORDS_FIELD, XQ->e[1]);
fpcopy(gen + 4 * NWORDS_FIELD, XR->e[0]);
fpcopy(gen + 5 * NWORDS_FIELD, XR->e[1]);
}
int random_mod_order_A(unsigned char *random_digits) { // Generation of Alice's secret key
// Outputs random value in [0, 2^eA - 1]
GUARD_AS_POSIX(s2n_get_random_bytes(random_digits, SECRETKEY_A_BYTES));
random_digits[SECRETKEY_A_BYTES - 1] &= MASK_ALICE; // Masking last byte
return S2N_SUCCESS;
}
int random_mod_order_B(unsigned char *random_digits) { // Generation of Bob's secret key
// Outputs random value in [0, 2^Floor(Log(2, oB)) - 1]
GUARD_AS_POSIX(s2n_get_random_bytes(random_digits, SECRETKEY_B_BYTES));
random_digits[SECRETKEY_B_BYTES - 1] &= MASK_BOB; // Masking last byte
return S2N_SUCCESS;
}
int EphemeralKeyGeneration_A(const digit_t *PrivateKeyA, unsigned char *PublicKeyA) { // Alice's ephemeral public key generation
// Input: a private key PrivateKeyA in the range [0, 2^eA - 1].
// Output: the public key PublicKeyA consisting of 3 elements in GF(p^2) which are encoded by removing leading 0 bytes.
point_proj_t R, phiP = {0}, phiQ = {0}, phiR = {0}, pts[MAX_INT_POINTS_ALICE];
f2elm_t _XPA, _XQA, _XRA, coeff[3], _A24plus = {0}, _C24 = {0}, _A = {0};
f2elm_t *XPA=&_XPA, *XQA=&_XQA, *XRA=&_XRA, *A24plus=&_A24plus, *C24=&_C24, *A=&_A;
unsigned int i, row, m, index = 0, pts_index[MAX_INT_POINTS_ALICE], npts = 0, ii = 0;
// Initialize basis points
init_basis((const digit_t *) A_gen, XPA, XQA, XRA);
init_basis((const digit_t *) B_gen, &phiP->X, &phiQ->X, &phiR->X);
fpcopy((const digit_t *) &Montgomery_one, (phiP->Z.e)[0]);
fpcopy((const digit_t *) &Montgomery_one, (phiQ->Z.e)[0]);
fpcopy((const digit_t *) &Montgomery_one, (phiR->Z.e)[0]);
// Initialize constants: A24plus = A+2C, C24 = 4C, where A=6, C=1
fpcopy((const digit_t *) &Montgomery_one, A24plus->e[0]);
fp2add(A24plus, A24plus, A24plus);
fp2add(A24plus, A24plus, C24);
fp2add(A24plus, C24, A);
fp2add(C24, C24, A24plus);
// Retrieve kernel point
LADDER3PT(XPA, XQA, XRA, PrivateKeyA, ALICE, R, A);
// Traverse tree
index = 0;
for (row = 1; row < MAX_Alice; row++) {
while (index < MAX_Alice - row) {
fp2copy(&R->X, &pts[npts]->X);
fp2copy(&R->Z, &pts[npts]->Z);
pts_index[npts++] = index;
m = strat_Alice[ii++];
xDBLe(R, R, A24plus, C24, (int) (2 * m));
index += m;
}
get_4_isog(R, A24plus, C24, coeff);
for (i = 0; i < npts; i++) {
eval_4_isog(pts[i], coeff);
}
eval_4_isog(phiP, coeff);
eval_4_isog(phiQ, coeff);
eval_4_isog(phiR, coeff);
fp2copy(&pts[npts - 1]->X, &R->X);
fp2copy(&pts[npts - 1]->Z, &R->Z);
index = pts_index[npts - 1];
npts -= 1;
}
get_4_isog(R, A24plus, C24, coeff);
eval_4_isog(phiP, coeff);
eval_4_isog(phiQ, coeff);
eval_4_isog(phiR, coeff);
inv_3_way(&phiP->Z, &phiQ->Z, &phiR->Z);
fp2mul_mont(&phiP->X, &phiP->Z, &phiP->X);
fp2mul_mont(&phiQ->X, &phiQ->Z, &phiQ->X);
fp2mul_mont(&phiR->X, &phiR->Z, &phiR->X);
// Format public key
fp2_encode(&phiP->X, PublicKeyA);
fp2_encode(&phiQ->X, PublicKeyA + FP2_ENCODED_BYTES);
fp2_encode(&phiR->X, PublicKeyA + 2 * FP2_ENCODED_BYTES);
return 0;
}
int EphemeralKeyGeneration_B(const digit_t *PrivateKeyB, unsigned char *PublicKeyB) { // Bob's ephemeral public key generation
// Input: a private key PrivateKeyB in the range [0, 2^Floor(Log(2,oB)) - 1].
// Output: the public key PublicKeyB consisting of 3 elements in GF(p^2) which are encoded by removing leading 0 bytes.
point_proj_t R, phiP = {0}, phiQ = {0}, phiR = {0}, pts[MAX_INT_POINTS_BOB];
f2elm_t _XPB, _XQB, _XRB, coeff[3], _A24plus = {0}, _A24minus = {0}, _A = {0};
f2elm_t *XPB=&_XPB, *XQB=&_XQB, *XRB=&_XRB, *A24plus=&_A24plus, *A24minus=&_A24minus, *A=&_A;
unsigned int i, row, m, index = 0, pts_index[MAX_INT_POINTS_BOB], npts = 0, ii = 0;
// Initialize basis points
init_basis((const digit_t *) B_gen, XPB, XQB, XRB);
init_basis((const digit_t *) A_gen, &phiP->X, &phiQ->X, &phiR->X);
fpcopy((const digit_t *) &Montgomery_one, (phiP->Z.e)[0]);
fpcopy((const digit_t *) &Montgomery_one, (phiQ->Z.e)[0]);
fpcopy((const digit_t *) &Montgomery_one, (phiR->Z.e)[0]);
// Initialize constants: A24minus = A-2C, A24plus = A+2C, where A=6, C=1
fpcopy((const digit_t *) &Montgomery_one, A24plus->e[0]);
fp2add(A24plus, A24plus, A24plus);
fp2add(A24plus, A24plus, A24minus);
fp2add(A24plus, A24minus, A);
fp2add(A24minus, A24minus, A24plus);
// Retrieve kernel point
LADDER3PT(XPB, XQB, XRB, PrivateKeyB, BOB, R, A);
// Traverse tree
index = 0;
for (row = 1; row < MAX_Bob; row++) {
while (index < MAX_Bob - row) {
fp2copy(&R->X, &pts[npts]->X);
fp2copy(&R->Z, &pts[npts]->Z);
pts_index[npts++] = index;
m = strat_Bob[ii++];
xTPLe(R, R, A24minus, A24plus, (int) m);
index += m;
}
get_3_isog(R, A24minus, A24plus, coeff);
for (i = 0; i < npts; i++) {
eval_3_isog(pts[i], coeff);
}
eval_3_isog(phiP, coeff);
eval_3_isog(phiQ, coeff);
eval_3_isog(phiR, coeff);
fp2copy(&pts[npts - 1]->X, &R->X);
fp2copy(&pts[npts - 1]->Z, &R->Z);
index = pts_index[npts - 1];
npts -= 1;
}
get_3_isog(R, A24minus, A24plus, coeff);
eval_3_isog(phiP, coeff);
eval_3_isog(phiQ, coeff);
eval_3_isog(phiR, coeff);
inv_3_way(&phiP->Z, &phiQ->Z, &phiR->Z);
fp2mul_mont(&phiP->X, &phiP->Z, &phiP->X);
fp2mul_mont(&phiQ->X, &phiQ->Z, &phiQ->X);
fp2mul_mont(&phiR->X, &phiR->Z, &phiR->X);
// Format public key
fp2_encode(&phiP->X, PublicKeyB);
fp2_encode(&phiQ->X, PublicKeyB + FP2_ENCODED_BYTES);
fp2_encode(&phiR->X, PublicKeyB + 2 * FP2_ENCODED_BYTES);
return 0;
}
int EphemeralSecretAgreement_A(const digit_t *PrivateKeyA, const unsigned char *PublicKeyB, unsigned char *SharedSecretA) { // Alice's ephemeral shared secret computation
// It produces a shared secret key SharedSecretA using her secret key PrivateKeyA and Bob's public key PublicKeyB
// Inputs: Alice's PrivateKeyA is an integer in the range [0, oA-1].
// Bob's PublicKeyB consists of 3 elements in GF(p^2) encoded by removing leading 0 bytes.
// Output: a shared secret SharedSecretA that consists of one element in GF(p^2) encoded by removing leading 0 bytes.
point_proj_t R, pts[MAX_INT_POINTS_ALICE];
f2elm_t coeff[3], PKB[3], _jinv;
f2elm_t _A24plus = {0}, _C24 = {0}, _A = {0};
f2elm_t *jinv=&_jinv, *A24plus=&_A24plus, *C24=&_C24, *A=&_A;
unsigned int i, row, m, index = 0, pts_index[MAX_INT_POINTS_ALICE], npts = 0, ii = 0;
// Initialize images of Bob's basis
fp2_decode(PublicKeyB, &PKB[0]);
fp2_decode(PublicKeyB + FP2_ENCODED_BYTES, &PKB[1]);
fp2_decode(PublicKeyB + 2 * FP2_ENCODED_BYTES, &PKB[2]);
// Initialize constants: A24plus = A+2C, C24 = 4C, where C=1
get_A(&PKB[0], &PKB[1], &PKB[2], A);
fpadd((const digit_t *) &Montgomery_one, (const digit_t *) &Montgomery_one, C24->e[0]);
fp2add(A, C24, A24plus);
fpadd(C24->e[0], C24->e[0], C24->e[0]);
// Retrieve kernel point
LADDER3PT(&PKB[0], &PKB[1], &PKB[2], PrivateKeyA, ALICE, R, A);
// Traverse tree
index = 0;
for (row = 1; row < MAX_Alice; row++) {
while (index < MAX_Alice - row) {
fp2copy(&R->X, &pts[npts]->X);
fp2copy(&R->Z, &pts[npts]->Z);
pts_index[npts++] = index;
m = strat_Alice[ii++];
xDBLe(R, R, A24plus, C24, (int) (2 * m));
index += m;
}
get_4_isog(R, A24plus, C24, coeff);
for (i = 0; i < npts; i++) {
eval_4_isog(pts[i], coeff);
}
fp2copy(&pts[npts - 1]->X, &R->X);
fp2copy(&pts[npts - 1]->Z, &R->Z);
index = pts_index[npts - 1];
npts -= 1;
}
get_4_isog(R, A24plus, C24, coeff);
fp2add(A24plus, A24plus, A24plus);
fp2sub(A24plus, C24, A24plus);
fp2add(A24plus, A24plus, A24plus);
j_inv(A24plus, C24, jinv);
fp2_encode(jinv, SharedSecretA); // Format shared secret
return 0;
}
int EphemeralSecretAgreement_B(const digit_t *PrivateKeyB, const unsigned char *PublicKeyA, unsigned char *SharedSecretB) { // Bob's ephemeral shared secret computation
// It produces a shared secret key SharedSecretB using his secret key PrivateKeyB and Alice's public key PublicKeyA
// Inputs: Bob's PrivateKeyB is an integer in the range [0, 2^Floor(Log(2,oB)) - 1].
// Alice's PublicKeyA consists of 3 elements in GF(p^2) encoded by removing leading 0 bytes.
// Output: a shared secret SharedSecretB that consists of one element in GF(p^2) encoded by removing leading 0 bytes.
point_proj_t R, pts[MAX_INT_POINTS_BOB];
f2elm_t coeff[3], PKB[3], _jinv;
f2elm_t _A24plus = {0}, _A24minus = {0}, _A = {0};
f2elm_t *jinv=&_jinv, *A24plus=&_A24plus, *A24minus=&_A24minus, *A=&_A;
unsigned int i, row, m, index = 0, pts_index[MAX_INT_POINTS_BOB], npts = 0, ii = 0;
// Initialize images of Alice's basis
fp2_decode(PublicKeyA, &PKB[0]);
fp2_decode(PublicKeyA + FP2_ENCODED_BYTES, &PKB[1]);
fp2_decode(PublicKeyA + 2 * FP2_ENCODED_BYTES, &PKB[2]);
// Initialize constants: A24plus = A+2C, A24minus = A-2C, where C=1
get_A(&PKB[0], &PKB[1], &PKB[2], A);
fpadd((const digit_t *) &Montgomery_one, (const digit_t *) &Montgomery_one, A24minus->e[0]);
fp2add(A, A24minus, A24plus);
fp2sub(A, A24minus, A24minus);
// Retrieve kernel point
LADDER3PT(&PKB[0], &PKB[1], &PKB[2], PrivateKeyB, BOB, R, A);
// Traverse tree
index = 0;
for (row = 1; row < MAX_Bob; row++) {
while (index < MAX_Bob - row) {
fp2copy(&R->X, &pts[npts]->X);
fp2copy(&R->Z, &pts[npts]->Z);
pts_index[npts++] = index;
m = strat_Bob[ii++];
xTPLe(R, R, A24minus, A24plus, (int) m);
index += m;
}
get_3_isog(R, A24minus, A24plus, coeff);
for (i = 0; i < npts; i++) {
eval_3_isog(pts[i], coeff);
}
fp2copy(&pts[npts - 1]->X, &R->X);
fp2copy(&pts[npts - 1]->Z, &R->Z);
index = pts_index[npts - 1];
npts -= 1;
}
get_3_isog(R, A24minus, A24plus, coeff);
fp2add(A24plus, A24minus, A);
fp2add(A, A, A);
fp2sub(A24plus, A24minus, A24plus);
j_inv(A, A24plus, jinv);
fp2_encode(jinv, SharedSecretB); // Format shared secret
return 0;
}
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