static bool FirstPoint_dual()

in src/compression/torsion_basis.c [159:212]

• 45 lines of code
• 10 McCabe index (conditional complexity)

static bool FirstPoint_dual(const point_proj_t P, point_full_proj_t R, unsigned char *ind)
{
    point_full_proj_t R3,S3;
    f2elm_t gX[2],gZ[2];
    felm_t zero = {0};
    unsigned long long nbytes = NBITS_TO_NBYTES(NBITS_FIELD);
    unsigned char alpha,beta;

    fpcopy((digit_t*)B_gen_3_tors + 0*NWORDS_FIELD, (R3->X)[0]);
    fpcopy((digit_t*)B_gen_3_tors + 1*NWORDS_FIELD, (R3->X)[1]);
    fpcopy((digit_t*)B_gen_3_tors + 2*NWORDS_FIELD, (R3->Y)[0]);
    fpcopy((digit_t*)B_gen_3_tors + 3*NWORDS_FIELD, (R3->Y)[1]);
    fpcopy((digit_t*)B_gen_3_tors + 4*NWORDS_FIELD, (S3->X)[0]);
    fpcopy((digit_t*)B_gen_3_tors + 5*NWORDS_FIELD, (S3->X)[1]);
    fpcopy((digit_t*)B_gen_3_tors + 6*NWORDS_FIELD, (S3->Y)[0]);
    fpcopy((digit_t*)B_gen_3_tors + 7*NWORDS_FIELD, (S3->Y)[1]);

    CompletePoint(P,R);
    Tate3_proj(R3,R,gX[0],gZ[0]);
    Tate3_proj(S3,R,gX[1],gZ[1]);
    FinalExpo3_2way(gX,gZ);

    // Do small DLog with respect to g_R3_S3
    fp2correction(gX[0]);
    fp2correction(gX[1]);
    if (memcmp(gX[0][1], zero, (size_t)nbytes) == 0)    // = 1
        alpha = 0;
    else if (memcmp(gX[0][1], g_R_S_im, (size_t)nbytes) == 0)    // = g_R3_S3
        alpha = 1;
    else    // = g_R3_S3^2
        alpha = 2;

    if (memcmp(gX[1][1], zero, (size_t)nbytes) == 0)    // = 1
        beta = 0;
    else if (memcmp(gX[1][1], g_R_S_im, (size_t)nbytes) == 0)    // = g_R3_S3
        beta = 1;
    else    // = g_R3_S3^2
        beta = 2;

    if (alpha == 0 && beta == 0)   // Not full order
        return false;

    // Return the 3-torsion point that R lies above
    if (alpha == 0)                // Lies above R3
        *ind = 0;
    else if (beta == 0)            // Lies above S3
        *ind = 1;
    else if (alpha + beta == 3)    // Lies above R3+S3
        *ind = 3;
    else                           // Lies above R3-S3
        *ind = 2;

    return true;
}