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- /*
- * File: dclxvi-20130329/fp6e.c
- * Author: Ruben Niederhagen, Peter Schwabe
- * Public Domain
- */
- #include <stdio.h>
- #include <assert.h>
- #include "fp6e.h"
- extern const fp2e_t bn_ypminus1;
- extern const fp2e_t bn_ypminus1_squ;
- extern const fpe_t bn_zeta;
- extern const fpe_t bn_zeta2;
- void fp6e_short_coeffred(fp6e_t rop)
- {
- fp2e_short_coeffred(rop->m_a);
- fp2e_short_coeffred(rop->m_b);
- fp2e_short_coeffred(rop->m_c);
- }
- // Set fp6e_t rop to given value:
- void fp6e_set(fp6e_t rop, const fp6e_t op)
- {
- fp2e_set(rop->m_a, op->m_a);
- fp2e_set(rop->m_b, op->m_b);
- fp2e_set(rop->m_c, op->m_c);
- }
- // Initialize an fp6e, set to value given in three fp2es
- void fp6e_set_fp2e(fp6e_t rop, const fp2e_t a, const fp2e_t b, const fp2e_t c)
- {
- fp2e_set(rop->m_a, a);
- fp2e_set(rop->m_b, b);
- fp2e_set(rop->m_c, c);
- }
- // Set rop to one:
- void fp6e_setone(fp6e_t rop)
- {
- fp2e_setzero(rop->m_a);
- fp2e_setzero(rop->m_b);
- fp2e_setone(rop->m_c);
- }
- // Set rop to zero:
- void fp6e_setzero(fp6e_t rop)
- {
- fp2e_setzero(rop->m_a);
- fp2e_setzero(rop->m_b);
- fp2e_setzero(rop->m_c);
- }
- // Compare for equality:
- int fp6e_iseq(const fp6e_t op1, const fp6e_t op2)
- {
- int ret = fp2e_iseq(op1->m_a, op2->m_a);
- ret = ret && fp2e_iseq(op1->m_b, op2->m_b);
- ret = ret && fp2e_iseq(op1->m_c, op2->m_c);
- return ret;
- }
- int fp6e_isone(const fp6e_t op)
- {
- int ret = fp2e_iszero(op->m_a);
- ret = ret && fp2e_iszero(op->m_b);
- ret = ret && fp2e_isone(op->m_c);
- return ret;
- }
- int fp6e_iszero(const fp6e_t op)
- {
- int ret = fp2e_iszero(op->m_a);
- ret = ret && fp2e_iszero(op->m_b);
- ret = ret && fp2e_iszero(op->m_c);
- return ret;
- }
- void fp6e_cmov(fp6e_t rop, const fp6e_t op, int c)
- {
- fp2e_cmov(rop->m_a, op->m_a, c);
- fp2e_cmov(rop->m_b, op->m_b, c);
- fp2e_cmov(rop->m_c, op->m_c, c);
- }
- // Add two fp6e, store result in rop:
- void fp6e_add(fp6e_t rop, const fp6e_t op1, const fp6e_t op2)
- {
- fp2e_add(rop->m_a, op1->m_a, op2->m_a);
- fp2e_add(rop->m_b, op1->m_b, op2->m_b);
- fp2e_add(rop->m_c, op1->m_c, op2->m_c);
- }
- // Subtract op2 from op1, store result in rop:
- void fp6e_sub(fp6e_t rop, const fp6e_t op1, const fp6e_t op2)
- {
- fp2e_sub(rop->m_a, op1->m_a, op2->m_a);
- fp2e_sub(rop->m_b, op1->m_b, op2->m_b);
- fp2e_sub(rop->m_c, op1->m_c, op2->m_c);
- }
- // Subtract op2 from op1, store result in rop:
- void fp6e_neg(fp6e_t rop, const fp6e_t op)
- {
- fp2e_neg(rop->m_a, op->m_a);
- fp2e_neg(rop->m_b, op->m_b);
- fp2e_neg(rop->m_c, op->m_c);
- }
- // Multiply two fp6e, store result in rop:
- void fp6e_mul(fp6e_t rop, const fp6e_t op1, const fp6e_t op2)
- {
- fp2e_t tmp1, tmp2, tmp3, tmp4, tmp5, tmp6; // Needed for intermediary values
- // See "Multiplication and Squaring in Pairing-Friendly Fields", section 4, Karatsuba method
- fp2e_mul(tmp3, op1->m_a, op2->m_a);
- fp2e_mul(tmp2, op1->m_b, op2->m_b);
- fp2e_mul(tmp1, op1->m_c, op2->m_c);
- fp2e_add(tmp4, op1->m_a, op1->m_b);
- //fp2e_short_coeffred(tmp4);
- fp2e_add(tmp5, op2->m_a, op2->m_b);
- //fp2e_short_coeffred(tmp5);
- fp2e_mul(tmp6, tmp4, tmp5);
- fp2e_sub2(tmp6, tmp2);
- //fp2e_short_coeffred(tmp6);
- fp2e_sub2(tmp6, tmp3);
- //fp2e_short_coeffred(tmp6);
- fp2e_mulxi(tmp6, tmp6);
- fp2e_add2(tmp6, tmp1);
- fp2e_add(tmp4, op1->m_b, op1->m_c);
- //fp2e_short_coeffred(tmp4);
- fp2e_add(tmp5, op2->m_b, op2->m_c);
- //fp2e_short_coeffred(tmp5);
- fp2e_mul(rop->m_b, tmp4, tmp5);
- fp2e_sub2(rop->m_b, tmp1);
- fp2e_sub2(rop->m_b, tmp2);
- //fp2e_short_coeffred(rop->m_b);
- fp2e_mulxi(tmp4, tmp3);
- fp2e_add2(rop->m_b, tmp4);
- fp2e_short_coeffred(rop->m_b);
- fp2e_add(tmp4, op1->m_a, op1->m_c);
- //fp2e_short_coeffred(tmp4);
- fp2e_add(tmp5, op2->m_a, op2->m_c);
- //fp2e_short_coeffred(tmp5);
- fp2e_set(rop->m_c, tmp6);
- fp2e_short_coeffred(rop->m_c);
- fp2e_mul(rop->m_a, tmp4, tmp5);
- fp2e_sub2(rop->m_a, tmp1);
- fp2e_add2(rop->m_a, tmp2);
- fp2e_sub2(rop->m_a, tmp3);
- fp2e_short_coeffred(rop->m_a);
- }
- // Compute the double of the Square of an fp6e, store result in rop, uses Chung-Hasan (CH-SQR3x in pairing-friendly fields)
- void fp6e_squaredouble(fp6e_t rop, const fp6e_t op)
- {
- //fp6e_mul(rop, op, op); //XXX make faster!
- fp2e_t s0, s1, s2, s3, s4, t;
- fp2e_square(s0,op->m_c);
- fp2e_add(t, op->m_a, op->m_c);
- fp2e_add(s1, t, op->m_b);
- fp2e_short_coeffred(s1);
- fp2e_square(s1, s1);
- fp2e_sub(s2, t, op->m_b);
- fp2e_short_coeffred(s2);
- fp2e_square(s2, s2);
- fp2e_mul(s3, op->m_a, op->m_b);
- fp2e_double(s3, s3);
- fp2e_square(s4, op->m_a);
- fp2e_mulxi(rop->m_c, s3);
- fp2e_add(rop->m_c, rop->m_c, s0);
- fp2e_double(rop->m_c, rop->m_c);
- fp2e_short_coeffred(rop->m_c);
- fp2e_mulxi(rop->m_b, s4);
- fp2e_sub(rop->m_b, s3, rop->m_b);
- fp2e_double(rop->m_b, rop->m_b);
- fp2e_sub(rop->m_b, s1, rop->m_b);
- fp2e_sub(rop->m_b, rop->m_b, s2);
- fp2e_short_coeffred(rop->m_b);
- fp2e_add(rop->m_a, s0, s4);
- fp2e_double(rop->m_a, rop->m_a);
- fp2e_sub(rop->m_a, s1, rop->m_a);
- fp2e_add(rop->m_a, rop->m_a, s2);
- fp2e_short_coeffred(rop->m_a);
- }
- // Multiply with tau:
- void fp6e_multau(fp6e_t rop, const fp6e_t op)
- {
- fp2e_t tmp1;
- fp2e_set(tmp1, op->m_b);
- fp2e_set(rop->m_b, op->m_c);
- fp2e_mulxi(rop->m_c, op->m_a);
- fp2e_set(rop->m_a, tmp1);
- }
- void fp6e_mul_fpe(fp6e_t rop, const fp6e_t op1, const fpe_t op2)
- {
- fp2e_mul_fpe(rop->m_a, op1->m_a, op2);
- fp2e_mul_fpe(rop->m_b, op1->m_b, op2);
- fp2e_mul_fpe(rop->m_c, op1->m_c, op2);
- }
- void fp6e_mul_fp2e(fp6e_t rop, const fp6e_t op1, const fp2e_t op2)
- {
- fp2e_mul(rop->m_a, op1->m_a, op2);
- fp2e_mul(rop->m_b, op1->m_b, op2);
- fp2e_mul(rop->m_c, op1->m_c, op2);
- }
- // Multiply an fp6e by a short fp6e, store result in rop:
- // the short fp6e op2 has a2 = 0, i.e. op2 = b2*tau + c2.
- void fp6e_mul_shortfp6e(fp6e_t rop, const fp6e_t op1, const fp6e_t op2)
- {
- fp2e_t tmp1, tmp2, tmp3, tmp4, tmp5; // Needed for intermediary values
- fp2e_mul(tmp2, op1->m_b, op2->m_b); // tmp2 = b1*b2
- fp2e_mul(tmp1, op1->m_c, op2->m_c); // tmp1 = c1*c2
- fp2e_mul(tmp3, op1->m_a, op2->m_b); // tmp3 = a1*b2
- fp2e_mulxi(tmp3, tmp3); // tmp3 = a1*b2*xi
- fp2e_add(tmp5, tmp3, tmp1); // tmp5 = c1*c2 + a1*b2*xi
- fp2e_add(tmp4, op1->m_b, op1->m_c); // tmp4 = b1+c1
- //fp2e_short_coeffred(tmp4);
- fp2e_add(tmp3, op2->m_b, op2->m_c); // tmp3 = b2+c2
- //fp2e_short_coeffred(tmp3);
- fp2e_mul(rop->m_b, tmp4, tmp3); // b3 = (b1+c1)*(b2+c2)
- fp2e_sub2(rop->m_b, tmp1);
- fp2e_sub2(rop->m_b, tmp2); // b3 = b1*c2 + b2*c1
- fp2e_short_coeffred(rop->m_b);
- fp2e_mul(rop->m_a, op1->m_a, op2->m_c); // a3 = a1*c2
- fp2e_add2(rop->m_a, tmp2); // a3 = a1*c2 + b1*b2
-
- fp2e_set(rop->m_c, tmp5); // c3 = c1*c2 + a1*b2*xi
- }
- void fp6e_invert(fp6e_t rop, const fp6e_t op)
- {
- fp2e_t tmp1, tmp2, tmp3, tmp4, tmp5; // Needed to store intermediary results
- // See "Implementing cryptographic pairings"
- fp2e_square(tmp1, op->m_c);
- fp2e_mul(tmp5, op->m_a, op->m_b);
- fp2e_mulxi(tmp5, tmp5);
- fp2e_sub2(tmp1, tmp5); // A
- fp2e_short_coeffred(tmp1);
-
- fp2e_square(tmp2, op->m_a);
- fp2e_mulxi(tmp2, tmp2);
- fp2e_mul(tmp5, op->m_b, op->m_c);
- fp2e_sub2(tmp2, tmp5); // B
- fp2e_short_coeffred(tmp2);
- fp2e_square(tmp3, op->m_b);
- fp2e_mul(tmp5, op->m_a, op->m_c);
- fp2e_sub2(tmp3, tmp5); // C
- //fp2e_short_coeffred(tmp3);
- fp2e_mul(tmp4, tmp3, op->m_b);
- fp2e_mulxi(tmp4, tmp4);
- fp2e_mul(tmp5, tmp1, op->m_c);
- fp2e_add2(tmp4, tmp5);
- fp2e_mul(tmp5, tmp2, op->m_a);
- fp2e_mulxi(tmp5, tmp5);
- fp2e_add2(tmp4, tmp5); // F
- fp2e_short_coeffred(tmp4);
-
- fp2e_invert(tmp4, tmp4);
- fp2e_mul(rop->m_a, tmp3, tmp4);
- fp2e_mul(rop->m_b, tmp2, tmp4);
- fp2e_mul(rop->m_c, tmp1, tmp4);
- }
- void fp6e_frobenius_p(fp6e_t rop, const fp6e_t op)
- {
- fp6e_set(rop, op);
- fp2e_conjugate(rop->m_a, rop->m_a);
- fp2e_conjugate(rop->m_b, rop->m_b);
- fp2e_conjugate(rop->m_c, rop->m_c);
- fp2e_mul(rop->m_b, rop->m_b, bn_ypminus1);
- fp2e_mul(rop->m_a, rop->m_a, bn_ypminus1_squ);
- }
- void fp6e_frobenius_p2(fp6e_t rop, const fp6e_t op)
- {
- fp2e_set(rop->m_c, op->m_c);
- fp2e_mul_fpe(rop->m_b, op->m_b, bn_zeta2);
- fp2e_mul_fpe(rop->m_a, op->m_a, bn_zeta);
- }
- // Print the fp6e:
- void fp6e_print(FILE * outfile, const fp6e_t op)
- {
- fprintf(outfile, "[");
- fp2e_print(outfile, op->m_a);
- fprintf(outfile, " * Y^2 + ");
- fp2e_print(outfile, op->m_b);
- fprintf(outfile, " * Y + ");
- fp2e_print(outfile, op->m_c);
- fprintf(outfile, "]");
- }
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