void bn254_fp2_sqr(Element z, const Element x)
{
Element* t = field(z)->base->tmp;
if (strcmp(x->field->field_name, "bn254_fp2a") == 0)
{
bn254_fp_addn(t[0], rep1(x), rep1(x)); //
bn254_fp_muln(t[0], t[0], rep0(x)); // t0 = 2*x1*x0
bn254_fp_addp(t[1], rep0(x));
bn254_fp_subn(t[1], t[1], rep1(x)); // t1 = x0-x1
bn254_fp_addn(t[2], rep1(x), rep1(x)); //
bn254_fp_addn(t[2], t[2], t[2]); //
bn254_fp_addn(t[2], t[2], rep1(x)); //
bn254_fp_addn(t[2], t[2], rep0(x)); // t2 = 5*x1 + x0
bn254_fp_muln(t[1], t[1], t[2]); // t1 = t1 * t2
bn254_fp_mod(rep1(z), t[0]); // c1 = t0
bn254_fp_addn(t[0], t[0], t[0]); //
bn254_fp_subn(t[1], t[1], t[0]); // t1 = 2*t0*t1
bn254_fp_mod(rep0(z), t[1]); // c0 = t1
}
if (strcmp(x->field->field_name, "bn254_fp2b") == 0)
{
bn254_fp_addn(t[0], rep1(x), rep1(x)); // t0 = 2*x1
bn254_fp_muln(t[0], t[0], rep0(x)); // t0 = 2*x1*x0
bn254_fp_addn(t[1], rep0(x), rep1(x)); // t1 = x0+x1
bn254_fp_subn(t[2], rep0(x), rep1(x)); // t2 = x0-x1
bn254_fp_muln(t[1], t[1], t[2]); // t1 = t1*t2
bn254_fp_mod(rep1(z), t[0]); // c1 = t0
bn254_fp_mod(rep0(z), t[1]); // c0 = t1
}
}
void bn254_fp2_sqr(Element z, const Element x)
{
Element* t = field(z)->base->tmp;
bn254_fp_addn(t[0], rep1(x), rep1(x)); //
bn254_fp_muln(t[0], t[0], rep0(x)); // t0 = 2*x1*x0
bn254_fp_addp(t[1], rep0(x));
bn254_fp_subn(t[1], t[1], rep1(x)); // t1 = x0-x1
bn254_fp_addn(t[2], rep1(x), rep1(x)); //
bn254_fp_addn(t[2], t[2], t[2]); //
bn254_fp_addn(t[2], t[2], rep1(x)); //
bn254_fp_addn(t[2], t[2], rep0(x)); // t2 = 5*x1 + x0
bn254_fp_muln(t[1], t[1], t[2]); // t1 = t1 * t2
bn254_fp_mod(rep1(z), t[0]); // c1 = t0
bn254_fp_addn(t[0], t[0], t[0]); //
bn254_fp_subn(t[1], t[1], t[0]); // t1 = 2*t0*t1
bn254_fp_mod(rep0(z), t[1]); // c0 = t1
}
//------------------------------------------------------
// multipulication is implemented by Karatsuba method.
//------------------------------------------------------
void bn254_fp2_mul(Element z, const Element x, const Element y)
{
Element* t = field(z)->base->tmp;
bn254_fp_addn(t[1], rep0(x), rep1(x)); // t1 = x0 + x1
bn254_fp_addn(t[2], rep0(y), rep1(y)); // t2 = y0 + y1
bn254_fp_muln(t[0], t[1], t[2]); // t0 = t1 * t2
bn254_fp_muln(t[1], rep0(x), rep0(y)); // t1 = x0 * y0
bn254_fp_muln(t[2], rep1(x), rep1(y)); // t2 = x1 * y1
bn254_fp_subn(t[0], t[0], t[1]); //
bn254_fp_subn(rep1(z), t[0], t[2]); // z1 = x0*y1 + y0*x1
bn254_fp_mod(rep1(z), rep1(z)); //
bn254_fp_addn(rep0(z), t[2], t[2]); //
bn254_fp_addn(rep0(z), rep0(z), rep0(z));
bn254_fp_addn(rep0(z), rep0(z), t[2]); //
bn254_fp_subn(rep0(z), t[1], rep0(z)); //
bn254_fp_mod(rep0(z), rep0(z)); // z0 = t1 - 5*t2
}
//------------------------------------------------------
// multipulication is implemented by Karatsuba method.
//------------------------------------------------------
void bn254_fp2_mul(Element z, const Element x, const Element y)
{
Element* t = field(z)->base->tmp;
//int i;
//Element* t = (Element *)malloc(sizeof(Element)*10);
//for(i=0;i<10;i++){ element_init(t[i], field(z)->base); }
if (strcmp(x->field->field_name, "bn254_fp2a") == 0)
{
bn254_fp_addn(t[1], rep0(x), rep1(x)); // t1 = x0 + x1
bn254_fp_addn(t[2], rep0(y), rep1(y)); // t2 = y0 + y1
bn254_fp_muln(t[0], t[1], t[2]); // t0 = t1 * t2
bn254_fp_muln(t[1], rep0(x), rep0(y)); // t1 = x0 * y0
bn254_fp_muln(t[2], rep1(x), rep1(y)); // t2 = x1 * y1
bn254_fp_subn(t[0], t[0], t[1]); //
bn254_fp_subn(rep1(z), t[0], t[2]); // z1 = x0*y1 + y0*x1
bn254_fp_mod(rep1(z), rep1(z)); //
bn254_fp_addn(rep0(z), t[2], t[2]); //
bn254_fp_addn(rep0(z), rep0(z), rep0(z));
bn254_fp_addn(rep0(z), rep0(z), t[2]); //
bn254_fp_subn(rep0(z), t[1], rep0(z)); //
bn254_fp_mod(rep0(z), rep0(z)); // z0 = t1 - 5*t2
}
if (strcmp(x->field->field_name, "bn254_fp2b") == 0)
{
bn254_fp_addn(t[1], rep0(x), rep1(x)); // t1 = x0 + x1
bn254_fp_addn(t[2], rep0(y), rep1(y)); // t2 = y0 + y1
bn254_fp_muln(t[0], t[1], t[2]); // t0 = t1 * t2
bn254_fp_muln(t[1], rep0(x), rep0(y)); // t1 = x0 * y0
bn254_fp_muln(t[2], rep1(x), rep1(y)); // t2 = x1 * y1
bn254_fp_subn(t[0], t[0], t[1]); // (x0+x1)*(y0+y1)-x0*y0
bn254_fp_subn(rep1(z), t[0], t[2]); // z1 = x0*y1 + y0*x1
bn254_fp_mod(rep1(z), rep1(z)); //
bn254_fp_sub(rep0(z), t[1], t[2]); // x0*y0 - x1*y1
bn254_fp_mod(rep0(z), rep0(z)); // z0 = t1 - t2
}
//for(i=0;i<10;i++){ element_clear(t[i]);}
}
void bn254_fp2_mod(Element z, const Element x)
{
bn254_fp_mod(rep0(z), rep0(x));
bn254_fp_mod(rep1(z), rep1(x));
}
