sike_ifma/sidh_ref/sidh.c

/********************************************************************************************
* Supersingular Isogeny Key Encapsulation Library
*
* Abstract: ephemeral supersingular isogeny Diffie-Hellman key exchange (SIDH)
*********************************************************************************************/

#include "P751_internal.h"
#include "random/random.h"

#include <stdio.h>
static void clear_words(void *mem, digit_t nwords)
{ // Clear digits from memory. "nwords" indicates the number of digits to be zeroed.
    // This function uses the volatile type qualifier to inform the compiler not to optimize out the memory clearing.
    unsigned int i;
    volatile digit_t *v = mem;

    for (i = 0; i < nwords; i++)
    {
        v[i] = 0;
    }
}

static void init_basis(digit_t *gen, f2elm_t XP, f2elm_t XQ, f2elm_t XR)
{ // Initialization of basis points

    fpcopy(gen, XP[0]);
    fpcopy(gen + NWORDS_FIELD, XP[1]);
    fpcopy(gen + 2 * NWORDS_FIELD, XQ[0]);
    fpzero(XQ[1]);
    fpcopy(gen + 3 * NWORDS_FIELD, XR[0]);
    fpcopy(gen + 4 * NWORDS_FIELD, XR[1]);
}

static void fp2_encode(const f2elm_t x, unsigned char *enc)
{ // Conversion of GF(p^2) element from Montgomery to standard representation, and encoding by removing leading 0 bytes
    unsigned int i;
    f2elm_t t;

    from_fp2mont(x, t);
    for (i = 0; i < FP2_ENCODED_BYTES / 2; i++)
    {
        enc[i] = ((unsigned char *)t)[i];
        enc[i + FP2_ENCODED_BYTES / 2] = ((unsigned char *)t)[i + MAXBITS_FIELD / 8];
    }
}

static void fp2_decode(const unsigned char *enc, f2elm_t x)
{ // Parse byte sequence back into GF(p^2) element, and conversion to Montgomery representation
    unsigned int i;

    for (i = 0; i < 2 * (MAXBITS_FIELD / 8); i++)
        ((unsigned char *)x)[i] = 0;
    for (i = 0; i < FP2_ENCODED_BYTES / 2; i++)
    {
        ((unsigned char *)x)[i] = enc[i];
        ((unsigned char *)x)[i + MAXBITS_FIELD / 8] = enc[i + FP2_ENCODED_BYTES / 2];
    }
    to_fp2mont(x, x);
}

void random_mod_order_A(unsigned char *random_digits)
{ // Generation of Alice's secret key
    // Outputs random value in [0, 2^eA - 1]
    unsigned long long nbytes = NBITS_TO_NBYTES(OALICE_BITS);

    clear_words((void *)random_digits, MAXWORDS_ORDER);
    randombytes(random_digits, nbytes);
    random_digits[nbytes - 1] &= MASK_ALICE; // Masking last byte
}

void 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]
    unsigned long long nbytes = NBITS_TO_NBYTES(OBOB_BITS - 1);

    clear_words((void *)random_digits, MAXWORDS_ORDER);
    randombytes(random_digits, nbytes);
    random_digits[nbytes - 1] &= MASK_BOB; // Masking last byte
}

int EphemeralKeyGeneration_A(const unsigned char *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};
    unsigned int i, row, m, index = 0, pts_index[MAX_INT_POINTS_ALICE], npts = 0, ii = 0;

    // Initialize basis points
    init_basis((digit_t *)A_gen, XPA, XQA, XRA);
    init_basis((digit_t *)B_gen, phiP->X, phiQ->X, phiR->X);

    fpcopy((digit_t *)&Montgomery_one, (phiP->Z)[0]);
    fpcopy((digit_t *)&Montgomery_one, (phiQ->Z)[0]);
    fpcopy((digit_t *)&Montgomery_one, (phiR->Z)[0]);

    // Initialize constants
    fpcopy((digit_t *)&Montgomery_one, A24plus[0]);
    fp2add(A24plus, A24plus, C24);

    uint64_t temp[12];
    uint64_t ifma_temp[15];

    // Retrieve kernel point
    LADDER3PT(XPA, XQA, XRA, (digit_t *)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 unsigned char *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};
    unsigned int i, row, m, index = 0, pts_index[MAX_INT_POINTS_BOB], npts = 0, ii = 0;

    // Initialize basis points
    init_basis((digit_t *)B_gen, XPB, XQB, XRB);
    init_basis((digit_t *)A_gen, phiP->X, phiQ->X, phiR->X);
    fpcopy((digit_t *)&Montgomery_one, (phiP->Z)[0]);
    fpcopy((digit_t *)&Montgomery_one, (phiQ->Z)[0]);
    fpcopy((digit_t *)&Montgomery_one, (phiR->Z)[0]);

    // Initialize constants
    fpcopy((digit_t *)&Montgomery_one, A24plus[0]);
    fp2add(A24plus, A24plus, A24plus);
    fp2copy(A24plus, A24minus);
    fp2neg(A24minus);

    // Retrieve kernel point
    LADDER3PT(XPB, XQB, XRB, (digit_t *)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 unsigned char *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};
    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
    get_A(PKB[0], PKB[1], PKB[2], A); // TODO: Can return projective A?
    fpadd((digit_t *)&Montgomery_one, (digit_t *)&Montgomery_one, C24[0]);
    fp2add(A, C24, A24plus);
    fpadd(C24[0], C24[0], C24[0]);

    // Retrieve kernel point
    LADDER3PT(PKB[0], PKB[1], PKB[2], (digit_t *)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);
    fp2div2(C24, C24);
    fp2sub(A24plus, C24, A24plus);
    fp2div2(C24, C24);
    j_inv(A24plus, C24, jinv);
    fp2_encode(jinv, SharedSecretA); // Format shared secret

    return 0;
}

int EphemeralSecretAgreement_B(const unsigned char *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};
    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
    get_A(PKB[0], PKB[1], PKB[2], A); // TODO: Can return projective A?
    fpadd((digit_t *)&Montgomery_one, (digit_t *)&Montgomery_one, A24minus[0]);
    fp2add(A, A24minus, A24plus);
    fp2sub(A, A24minus, A24minus);

    // Retrieve kernel point
    LADDER3PT(PKB[0], PKB[1], PKB[2], (digit_t *)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;
}