int EphemeralKeyGeneration_A()

in src/sidh.c [40:120]

• 62 lines of code
• 4 McCabe index (conditional complexity)

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;
    digit_t SecretKeyA[NWORDS_ORDER] = {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: A24plus = A+2C, C24 = 4C, where A=6, C=1
    fpcopy((digit_t*)&Montgomery_one, A24plus[0]);
    mp2_add(A24plus, A24plus, A24plus);
    mp2_add(A24plus, A24plus, C24);
    mp2_add(A24plus, C24, A);
    mp2_add(C24, C24, A24plus);

    // Retrieve kernel point
    decode_to_digits(PrivateKeyA, SecretKeyA, SECRETKEY_A_BYTES, NWORDS_ORDER);
    LADDER3PT(XPA, XQA, XRA, SecretKeyA, ALICE, R, A);       

#if (OALICE_BITS % 2 == 1)
    point_proj_t S;

    xDBLe(R, S, A24plus, C24, (int)(OALICE_BITS-1));
    get_2_isog(S, A24plus, C24); 
    eval_2_isog(phiP, S); 
    eval_2_isog(phiQ, S); 
    eval_2_isog(phiR, S);
    eval_2_isog(R, S);
#endif

    // 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;
}