src/bls.c.in [31:95]:
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    BIG_XXX r;
    BIG_XXX_rcopy(r,CURVE_Order_ZZZ);

    BIG_XXX x2[k];

    for(int i=0; i<k; i++)
    {
        BIG_XXX_fromBytes(x2[i],X[i].val);
    }

    // Compute numerators in place using partial products
    // to achieve it in O(n)
    // c_i = x_0 * ... * x_(i-1) * x_(i+1) * ... * x_(k-1)

    // Compute partial left products
    // leave c_0 alone since it only has a right partial product
    BIG_XXX_copy(coefs[1], x2[0]);

    for(int i=2; i < k; i++)
    {
        // lp_i = x_0 * ... * x_(i-1) = lp_(i-1) * x_(i-1)
        BIG_XXX_modmul(coefs[i], coefs[i-1], x2[i-1], r);
    }

    // Compute partial right products and combine

    // Store partial right products in c_0 so at the end
    // of the procedure c_0 = x_1 * ... x_(k-1)
    BIG_XXX_copy(coefs[0], x2[k-1]);

    for(int i=k-2; i > 0; i--)
    {
        // c_i = lp_i * rp_i
        BIG_XXX_modmul(coefs[i], coefs[i], coefs[0], r);

        // rp_(i-1) = x_i * ... * x_k = x_i * rp_i
        BIG_XXX_modmul(coefs[0], coefs[0], x2[i], r);
    }

    BIG_XXX cneg;
    BIG_XXX denominator;
    BIG_XXX s;

    for(int i=0; i<k; i++)
    {
        BIG_XXX_one(denominator);

        // cneg = -x_i mod r
        BIG_XXX_sub(cneg, r, x2[i]);

        for(int j=0; j<k; j++)
        {
            if (i != j)
            {
                // denominator = denominator * (x_j - x_i)
                BIG_XXX_add(s,x2[j],cneg);
                BIG_XXX_modmul(denominator,denominator,s,r);
            }
        }

        BIG_XXX_moddiv(coefs[i], coefs[i], denominator, r);
    }
}

/* hash a message, M, to an ECP point, using SHA3 */
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -



src/bls256.c.in [31:95]:
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    BIG_XXX r;
    BIG_XXX_rcopy(r,CURVE_Order_ZZZ);

    BIG_XXX x2[k];

    for(int i=0; i<k; i++)
    {
        BIG_XXX_fromBytes(x2[i],X[i].val);
    }

    // Compute numerators in place using partial products
    // to achieve it in O(n)
    // c_i = x_0 * ... * x_(i-1) * x_(i+1) * ... * x_(k-1)

    // Compute partial left products
    // leave c_0 alone since it only has a right partial product
    BIG_XXX_copy(coefs[1], x2[0]);

    for(int i=2; i < k; i++)
    {
        // lp_i = x_0 * ... * x_(i-1) = lp_(i-1) * x_(i-1)
        BIG_XXX_modmul(coefs[i], coefs[i-1], x2[i-1], r);
    }

    // Compute partial right products and combine

    // Store partial right products in c_0 so at the end
    // of the procedure c_0 = x_1 * ... x_(k-1)
    BIG_XXX_copy(coefs[0], x2[k-1]);

    for(int i=k-2; i > 0; i--)
    {
        // c_i = lp_i * rp_i
        BIG_XXX_modmul(coefs[i], coefs[i], coefs[0], r);

        // rp_(i-1) = x_i * ... * x_k = x_i * rp_i
        BIG_XXX_modmul(coefs[0], coefs[0], x2[i], r);
    }

    BIG_XXX cneg;
    BIG_XXX denominator;
    BIG_XXX s;

    for(int i=0; i<k; i++)
    {
        BIG_XXX_one(denominator);

        // cneg = -x_i mod r
        BIG_XXX_sub(cneg, r, x2[i]);

        for(int j=0; j<k; j++)
        {
            if (i != j)
            {
                // denominator = denominator * (x_j - x_i)
                BIG_XXX_add(s,x2[j],cneg);
                BIG_XXX_modmul(denominator,denominator,s,r);
            }
        }

        BIG_XXX_moddiv(coefs[i], coefs[i], denominator, r);
    }
}

/* hash a message, M, to an ECP point, using SHA3 */
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -