Пример #1
0
        /* p=q0^u0.q1^u1.q2^u2.q3^u3 */
        // Bos & Costello https://eprint.iacr.org/2013/458.pdf
        // Faz-Hernandez & Longa & Sanchez  https://eprint.iacr.org/2013/158.pdf
        // Side channel attack secure

        public static FP12 Pow4(FP12[] q, BIG[] u)
        {
            int i, j, nb, pb;

            FP12[] g = new FP12[8];
            FP12   r = new FP12(1);
            FP12   p = new FP12(0);

            BIG[] t  = new BIG[4];
            BIG   mt = new BIG(0);

            sbyte[] w = new sbyte[BIG.NLEN * BIG.BASEBITS + 1];
            sbyte[] s = new sbyte[BIG.NLEN * BIG.BASEBITS + 1];

            for (i = 0; i < 4; i++)
            {
                t[i] = new BIG(u[i]);
                t[i].Norm();
            }
            g[0] = new FP12(q[0]);      // q[0]
            g[1] = new FP12(g[0]);
            g[1].mul(q[1]);             // q[0].q[1]
            g[2] = new FP12(g[0]);
            g[2].mul(q[2]);             // q[0].q[2]
            g[3] = new FP12(g[1]);
            g[3].mul(q[2]);             // q[0].q[1].q[2]
            g[4] = new FP12(q[0]);
            g[4].mul(q[3]);             // q[0].q[3]
            g[5] = new FP12(g[1]);
            g[5].mul(q[3]);             // q[0].q[1].q[3]
            g[6] = new FP12(g[2]);
            g[6].mul(q[3]);             // q[0].q[2].q[3]
            g[7] = new FP12(g[3]);
            g[7].mul(q[3]);             // q[0].q[1].q[2].q[3]

            // Make it odd
            pb = 1 - t[0].Parity();
            t[0].Inc(pb);
            t[0].Norm();

            // Number of bits
            mt.Zero();
            for (i = 0; i < 4; i++)
            {
                mt.Or(t[i]);
            }
            nb = 1 + mt.NBits();

            // Sign pivot
            s[nb - 1] = 1;
            for (i = 0; i < nb - 1; i++)
            {
                t[0].FShr(1);
                s[i] = (sbyte)(2 * t[0].Parity() - 1);
            }

            // Recoded exponent
            for (i = 0; i < nb; i++)
            {
                w[i] = 0;
                int k = 1;
                for (j = 1; j < 4; j++)
                {
                    sbyte bt = (sbyte)(s[i] * t[j].Parity());
                    t[j].FShr(1);
                    t[j].Dec((int)(bt) >> 1);
                    t[j].Norm();
                    w[i] += (sbyte)(bt * (sbyte)k);
                    k    *= 2;
                }
            }

            // Main loop
            p.Select(g, (int)(2 * w[nb - 1] + 1));
            for (i = nb - 2; i >= 0; i--)
            {
                p.USqr();
                r.Select(g, (int)(2 * w[i] + s[i]));
                p.mul(r);
            }

            // apply correction
            r.Copy(q[0]);
            r.Conj();
            r.mul(p);
            p.CMove(r, pb);

            p.Reduce();
            return(p);
        }