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- /*
- * File: dclxvi-20130329/fp12e.c
- * Author: Ruben Niederhagen, Peter Schwabe
- * Public Domain
- */
- #include <stdio.h>
- #include <assert.h>
- #include "fp6e.h"
- #include "fp12e.h"
- extern const fp2e_t bn_zpminus1;
- extern const fpe_t bn_zeta;
- // Set fp12e_t rop to given value:
- void fp12e_set(fp12e_t rop, const fp12e_t op)
- {
- fp6e_set(rop->m_a, op->m_a);
- fp6e_set(rop->m_b, op->m_b);
- }
- // Initialize an fp12e, set to value given in two fp6es
- void fp12e_set_fp6e(fp12e_t rop, const fp6e_t a, const fp6e_t b)
- {
- fp6e_set(rop->m_a, a);
- fp6e_set(rop->m_b, b);
- }
- // Set rop to one:
- void fp12e_setone(fp12e_t rop)
- {
- fp6e_setzero(rop->m_a);
- fp6e_setone(rop->m_b);
- }
- // Set rop to zero:
- void fp12e_setzero(fp12e_t rop)
- {
- fp6e_setzero(rop->m_a);
- fp6e_setzero(rop->m_b);
- }
- // Compare for equality:
- int fp12e_iseq(const fp12e_t op1, const fp12e_t op2)
- {
- int ret = fp6e_iseq(op1->m_a, op2->m_a);
- ret = ret && fp6e_iseq(op1->m_b, op2->m_b);
- return ret;
- }
- int fp12e_isone(const fp12e_t op)
- {
- int ret = fp6e_iszero(op->m_a);
- ret = ret && fp6e_isone(op->m_b);
- return ret;
- }
- int fp12e_iszero(const fp12e_t op)
- {
- int ret = fp6e_iszero(op->m_a);
- ret = ret && fp6e_iszero(op->m_b);
- return ret;
- }
- void fp12e_cmov(fp12e_t rop, const fp12e_t op, int c)
- {
- fp6e_cmov(rop->m_a, op->m_a, c);
- fp6e_cmov(rop->m_b, op->m_b, c);
- }
- // Compute conjugate over Fp6:
- void fp12e_conjugate(fp12e_t rop, const fp12e_t op2)
- {
- fp6e_neg(rop->m_a, op2->m_a);
- fp6e_set(rop->m_b, op2->m_b);
- }
- // Add two fp12e, store result in rop:
- void fp12e_add(fp12e_t rop, const fp12e_t op1, const fp12e_t op2)
- {
- fp6e_add(rop->m_a, op1->m_a, op2->m_a);
- fp6e_add(rop->m_b, op1->m_b, op2->m_b);
- }
- // Subtract op2 from op1, store result in rop:
- void fp12e_sub(fp12e_t rop, const fp12e_t op1, const fp12e_t op2)
- {
- fp6e_sub(rop->m_a, op1->m_a, op2->m_a);
- fp6e_sub(rop->m_b, op1->m_b, op2->m_b);
- }
- // Multiply two fp12e, store result in rop:
- void fp12e_mul(fp12e_t rop, const fp12e_t op1, const fp12e_t op2)
- {
- #ifdef BENCH
- nummultp12 ++;
- multp12cycles -= cpucycles();
- #endif
- fp6e_t tmp1, tmp2, tmp3; // Needed to store intermediary results
- fp6e_mul(tmp1, op1->m_a, op2->m_a);
- fp6e_mul(tmp3, op1->m_b, op2->m_b);
- fp6e_add(tmp2, op2->m_a, op2->m_b);
- fp6e_short_coeffred(tmp2);
- fp6e_add(rop->m_a, op1->m_a, op1->m_b);
- fp6e_short_coeffred(rop->m_a);
- fp6e_set(rop->m_b, tmp3);
- fp6e_mul(rop->m_a, rop->m_a, tmp2);
- fp6e_sub(rop->m_a, rop->m_a, tmp1);
- fp6e_sub(rop->m_a, rop->m_a, rop->m_b);
- fp6e_short_coeffred(rop->m_a);
- fp6e_multau(tmp1, tmp1);
- fp6e_add(rop->m_b, rop->m_b, tmp1);
- fp6e_short_coeffred(rop->m_b);
- #ifdef BENCH
- multp12cycles += cpucycles();
- #endif
- }
- void fp12e_mul_fp6e(fp12e_t rop, const fp12e_t op1, const fp6e_t op2)
- {
- fp6e_mul(rop->m_a, op1->m_a, op2);
- fp6e_mul(rop->m_b, op1->m_b, op2);
- }
- // Square an fp12e, store result in rop:
- void fp12e_square(fp12e_t rop, const fp12e_t op)
- {
- #ifdef BENCH
- numsqp12 ++;
- sqp12cycles -= cpucycles();
- #endif
- fp6e_t tmp1, tmp2, tmp3; // Needed to store intermediary results
- fp6e_mul(tmp1, op->m_a, op->m_b);
- fp6e_add(tmp2, op->m_a, op->m_b);
- fp6e_short_coeffred(tmp2);
- fp6e_multau(tmp3, op->m_a);
- fp6e_add(rop->m_b, tmp3, op->m_b);
- fp6e_short_coeffred(rop->m_b);
- fp6e_mul(rop->m_b, rop->m_b, tmp2);
- fp6e_sub(rop->m_b, rop->m_b, tmp1);
- fp6e_multau(tmp2, tmp1);
- fp6e_sub(rop->m_b, rop->m_b, tmp2);
- fp6e_short_coeffred(rop->m_b);
- fp6e_add(rop->m_a, tmp1, tmp1);
- fp6e_short_coeffred(rop->m_a);
- #ifdef BENCH
- sqp12cycles += cpucycles();
- #endif
- }
- // Multiply an fp12e by a line function value, store result in rop:
- // The line function is given by 3 fp2e elements op2, op3, op4 as
- // line = (op2*tau + op3)*z + op4 = a2*z + b2.
- void fp12e_mul_line(fp12e_t rop, const fp12e_t op1, const fp2e_t op2, const fp2e_t op3, const fp2e_t op4)
- {
- #ifdef BENCH
- nummultp12 ++;
- multp12cycles -= cpucycles();
- #endif
- fp2e_t fp2_0, tmp;
- fp6e_t tmp1, tmp2, tmp3; // Needed to store intermediary results
- fp2e_setzero(fp2_0); // fp2_0 = 0
- fp6e_set_fp2e(tmp1, fp2_0, op2, op3); // tmp1 = a2 = op2*tau + op3
- fp6e_mul_shortfp6e(tmp1, op1->m_a, tmp1); // tmp1 = a1*a2
- fp6e_mul_fp2e(tmp3, op1->m_b, op4); // tmp3 = b1*op4 = b1*b2
- fp2e_add(tmp, op3, op4);
- fp2e_short_coeffred(tmp);
- fp6e_set_fp2e(tmp2, fp2_0, op2, tmp); // tmp2 = a2 + b2
- fp6e_add(rop->m_a, op1->m_a, op1->m_b); // a3 = a1 + b1
- fp6e_short_coeffred(rop->m_a);
- fp6e_set(rop->m_b, tmp3); // b3 = b1*b2
- fp6e_mul_shortfp6e(rop->m_a, rop->m_a, tmp2);// a3 = (a1+b1)*(a2+b2)
- fp6e_sub(rop->m_a, rop->m_a, tmp1);
- fp6e_sub(rop->m_a, rop->m_a, rop->m_b); // a3 = a1*b2 + a2*b1
- fp6e_short_coeffred(rop->m_a);
- fp6e_multau(tmp1, tmp1); // tmp1 = a1*a2*tau
- fp6e_add(rop->m_b, rop->m_b, tmp1); // b3 = b1*b2 + a1*a2*tau
- fp6e_short_coeffred(rop->m_b);
- #ifdef BENCH
- multp12cycles += cpucycles();
- #endif
- }
- void fp12e_pow_vartime(fp12e_t rop, const fp12e_t op, const scalar_t exp)
- {
- fp12e_t dummy;
- unsigned int startbit;
- startbit = scalar_scanb(exp);
- fp12e_set(dummy, op);
- fp12e_set(rop,op);
- int i;
- for(i = startbit; i > 0; i--)
- {
- fp12e_square(rop, rop);
- if(scalar_getbit(exp, i - 1))
- fp12e_mul(rop, rop, dummy);
- }
- }
- // Implicit fp4 squaring for Granger/Scott special squaring in final expo
- // fp4e_square takes two fp2e op1, op2 representing the fp4 element
- // op1*z^3 + op2, writes the square to rop1, rop2 representing rop1*z^3 + rop2.
- // (op1*z^3 + op2)^2 = (2*op1*op2)*z^3 + (op1^2*xi + op2^2).
- void fp4e_square(fp2e_t rop1, fp2e_t rop2, const fp2e_t op1, const fp2e_t op2)
- {
- fp2e_t t1, t2;
- fp2e_square(t1, op1); // t1 = op1^2
- fp2e_square(t2, op2); // t2 = op2^2
- //fp2e_mul(rop1, op1, op2); // rop1 = op1*op2
- //fp2e_add(rop1, rop1, rop1); // rop1 = 2*op1*op2
- fp2e_add(rop1, op1, op2);
- fp2e_short_coeffred(rop1);
- fp2e_square(rop1, rop1);
- fp2e_sub2(rop1, t1);
- fp2e_sub2(rop1, t2); // rop1 = 2*op1*op2
- fp2e_mulxi(rop2, t1); // rop2 = op1^2*xi
- fp2e_add2(rop2, t2); // rop2 = op1^2*xi + op2^2
- }
- // Special squaring for use on elements in T_6(fp2) (after the
- // easy part of the final exponentiation. Used in the hard part
- // of the final exponentiation. Function uses formulas in
- // Granger/Scott (PKC2010).
- void fp12e_special_square_finexp(fp12e_t rop, const fp12e_t op)
- {
- fp2e_t f00, f01, f02, f10, f11, f12;
- fp2e_t t00, t01, t02, t10, t11, t12, t;
- fp6e_t f0, f1;
- fp4e_square(t11, t00, op->m_a->m_b, op->m_b->m_c);
- fp4e_square(t12, t01, op->m_b->m_a, op->m_a->m_c);
- fp4e_square(t02, t10, op->m_a->m_a, op->m_b->m_b);
- fp2e_mulxi(t, t02);
- fp2e_set(t02, t10);
- fp2e_set(t10, t);
- fp2e_mul_scalar(f00, op->m_b->m_c, -2);
- fp2e_mul_scalar(f01, op->m_b->m_b, -2);
- fp2e_mul_scalar(f02, op->m_b->m_a, -2);
- fp2e_double(f10, op->m_a->m_c);
- fp2e_double(f11, op->m_a->m_b);
- fp2e_double(f12, op->m_a->m_a);
- fp2e_triple2(t00);
- fp2e_triple2(t01);
- fp2e_triple2(t02);
- fp2e_triple2(t10);
- fp2e_triple2(t11);
- fp2e_triple2(t12);
- fp2e_add2(f00, t00);
- fp2e_add2(f01, t01);
- fp2e_add2(f02, t02);
- fp2e_add2(f10, t10);
- fp2e_add2(f11, t11);
- fp2e_add2(f12, t12);
- fp6e_set_fp2e(f0, f02, f01, f00);
- fp6e_short_coeffred(f0);
- fp6e_set_fp2e(f1, f12, f11, f10);
- fp6e_short_coeffred(f1);
- fp12e_set_fp6e(rop,f1,f0);
- }
- void fp12e_invert(fp12e_t rop, const fp12e_t op)
- {
- #ifdef BENCH
- numinvp12 ++;
- invp12cycles -= cpucycles();
- #endif
- fp6e_t tmp1, tmp2; // Needed to store intermediary results
- fp6e_squaredouble(tmp1, op->m_a);
- fp6e_squaredouble(tmp2, op->m_b);
- fp6e_multau(tmp1, tmp1);
- fp6e_sub(tmp1, tmp2, tmp1);
- fp6e_short_coeffred(tmp1);
- fp6e_invert(tmp1, tmp1);
- fp6e_add(tmp1,tmp1,tmp1);
- fp6e_short_coeffred(tmp1);
- fp12e_set(rop, op);
- fp6e_neg(rop->m_a, rop->m_a);
- fp12e_mul_fp6e(rop, rop, tmp1);
- #ifdef BENCH
- invp12cycles += cpucycles();
- #endif
- }
- void fp12e_frobenius_p(fp12e_t rop, const fp12e_t op)
- {
- fp6e_frobenius_p(rop->m_a, op->m_a);
- fp6e_frobenius_p(rop->m_b, op->m_b);
- fp6e_mul_fp2e(rop->m_a, rop->m_a, bn_zpminus1);
- }
- void fp12e_frobenius_p2(fp12e_t rop, const fp12e_t op)
- {
- fp6e_t t;
- fp6e_frobenius_p2(rop->m_a, op->m_a);
- fp6e_frobenius_p2(rop->m_b, op->m_b);
- fp6e_mul_fpe(t, rop->m_a, bn_zeta);
- fp6e_neg(rop->m_a, t);
- }
- // Print the element to stdout:
- void fp12e_print(FILE *outfile, const fp12e_t op)
- {
- fp6e_print(outfile, op->m_a);
- fprintf(outfile, " * Z + ");
- fp6e_print(outfile, op->m_b);
- }
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