static int bn_blinding_create_param(BN_BLINDING *b, const RSA *rsa, BN_CTX *ctx) { int retry_counter = 32; do { if (!BN_rand_range(b->A, rsa->n)) { OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR); return 0; } /* `BN_from_montgomery` + `BN_mod_inverse_no_branch` is equivalent to, but * more efficient than, `BN_mod_inverse_no_branch` + `BN_to_montgomery`. */ if (!BN_from_montgomery(b->Ai, b->A, rsa->mont_n, ctx)) { return 0; } assert(BN_get_flags(b->A, BN_FLG_CONSTTIME)); int no_inverse; if (BN_mod_inverse_no_branch(b->Ai, &no_inverse, b->Ai, rsa->n, ctx) == NULL) { /* this should almost never happen for good RSA keys */ if (no_inverse) { if (retry_counter-- == 0) { OPENSSL_PUT_ERROR(RSA, RSA_R_TOO_MANY_ITERATIONS); return 0; } ERR_clear_error(); } else { OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR); return 0; } } else { break; } } while (1); if (!BN_mod_exp_mont(b->A, b->A, rsa->e, rsa->n, ctx, rsa->mont_n)) { OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR); return 0; } if (!BN_to_montgomery(b->A, b->A, rsa->mont_n, ctx)) { OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR); return 0; } return 1; }
BIGNUM *BN_mod_inverse(BIGNUM *in, const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx) { BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL; BIGNUM *ret=NULL; int sign; if ((BN_get_flags(a, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(n, BN_FLG_CONSTTIME) != 0)) { return BN_mod_inverse_no_branch(in, a, n, ctx); } bn_check_top(a); bn_check_top(n); BN_CTX_start(ctx); A = BN_CTX_get(ctx); B = BN_CTX_get(ctx); X = BN_CTX_get(ctx); D = BN_CTX_get(ctx); M = BN_CTX_get(ctx); Y = BN_CTX_get(ctx); T = BN_CTX_get(ctx); if (T == NULL) goto err; if (in == NULL) R=BN_new(); else R=in; if (R == NULL) goto err; BN_one(X); BN_zero(Y); if (BN_copy(B,a) == NULL) goto err; if (BN_copy(A,n) == NULL) goto err; A->neg = 0; if (B->neg || (BN_ucmp(B, A) >= 0)) { if (!BN_nnmod(B, B, A, ctx)) goto err; } sign = -1; /* From B = a mod |n|, A = |n| it follows that * * 0 <= B < A, * -sign*X*a == B (mod |n|), * sign*Y*a == A (mod |n|). */ if (BN_is_odd(n) && (BN_num_bits(n) <= (BN_BITS <= 32 ? 450 : 2048))) { /* Binary inversion algorithm; requires odd modulus. * This is faster than the general algorithm if the modulus * is sufficiently small (about 400 .. 500 bits on 32-bit * sytems, but much more on 64-bit systems) */ int shift; while (!BN_is_zero(B)) { /* * 0 < B < |n|, * 0 < A <= |n|, * (1) -sign*X*a == B (mod |n|), * (2) sign*Y*a == A (mod |n|) */ /* Now divide B by the maximum possible power of two in the integers, * and divide X by the same value mod |n|. * When we're done, (1) still holds. */ shift = 0; while (!BN_is_bit_set(B, shift)) /* note that 0 < B */ { shift++; if (BN_is_odd(X)) { if (!BN_uadd(X, X, n)) goto err; } /* now X is even, so we can easily divide it by two */ if (!BN_rshift1(X, X)) goto err; } if (shift > 0) { if (!BN_rshift(B, B, shift)) goto err; } /* Same for A and Y. Afterwards, (2) still holds. */ shift = 0; while (!BN_is_bit_set(A, shift)) /* note that 0 < A */ { shift++; if (BN_is_odd(Y)) { if (!BN_uadd(Y, Y, n)) goto err; } /* now Y is even */ if (!BN_rshift1(Y, Y)) goto err; } if (shift > 0) { if (!BN_rshift(A, A, shift)) goto err; } /* We still have (1) and (2). * Both A and B are odd. * The following computations ensure that * * 0 <= B < |n|, * 0 < A < |n|, * (1) -sign*X*a == B (mod |n|), * (2) sign*Y*a == A (mod |n|), * * and that either A or B is even in the next iteration. */ if (BN_ucmp(B, A) >= 0) { /* -sign*(X + Y)*a == B - A (mod |n|) */ if (!BN_uadd(X, X, Y)) goto err; /* NB: we could use BN_mod_add_quick(X, X, Y, n), but that * actually makes the algorithm slower */ if (!BN_usub(B, B, A)) goto err; } else { /* sign*(X + Y)*a == A - B (mod |n|) */ if (!BN_uadd(Y, Y, X)) goto err; /* as above, BN_mod_add_quick(Y, Y, X, n) would slow things down */ if (!BN_usub(A, A, B)) goto err; } } } else { /* general inversion algorithm */ while (!BN_is_zero(B)) { BIGNUM *tmp; /* * 0 < B < A, * (*) -sign*X*a == B (mod |n|), * sign*Y*a == A (mod |n|) */ /* (D, M) := (A/B, A%B) ... */ if (BN_num_bits(A) == BN_num_bits(B)) { if (!BN_one(D)) goto err; if (!BN_sub(M,A,B)) goto err; } else if (BN_num_bits(A) == BN_num_bits(B) + 1) { /* A/B is 1, 2, or 3 */ if (!BN_lshift1(T,B)) goto err; if (BN_ucmp(A,T) < 0) { /* A < 2*B, so D=1 */ if (!BN_one(D)) goto err; if (!BN_sub(M,A,B)) goto err; } else { /* A >= 2*B, so D=2 or D=3 */ if (!BN_sub(M,A,T)) goto err; if (!BN_add(D,T,B)) goto err; /* use D (:= 3*B) as temp */ if (BN_ucmp(A,D) < 0) { /* A < 3*B, so D=2 */ if (!BN_set_word(D,2)) goto err; /* M (= A - 2*B) already has the correct value */ } else { /* only D=3 remains */ if (!BN_set_word(D,3)) goto err; /* currently M = A - 2*B, but we need M = A - 3*B */ if (!BN_sub(M,M,B)) goto err; } } } else { if (!BN_div(D,M,A,B,ctx)) goto err; } /* Now * A = D*B + M; * thus we have * (**) sign*Y*a == D*B + M (mod |n|). */ tmp=A; /* keep the BIGNUM object, the value does not matter */ /* (A, B) := (B, A mod B) ... */ A=B; B=M; /* ... so we have 0 <= B < A again */ /* Since the former M is now B and the former B is now A, * (**) translates into * sign*Y*a == D*A + B (mod |n|), * i.e. * sign*Y*a - D*A == B (mod |n|). * Similarly, (*) translates into * -sign*X*a == A (mod |n|). * * Thus, * sign*Y*a + D*sign*X*a == B (mod |n|), * i.e. * sign*(Y + D*X)*a == B (mod |n|). * * So if we set (X, Y, sign) := (Y + D*X, X, -sign), we arrive back at * -sign*X*a == B (mod |n|), * sign*Y*a == A (mod |n|). * Note that X and Y stay non-negative all the time. */ /* most of the time D is very small, so we can optimize tmp := D*X+Y */ if (BN_is_one(D)) { if (!BN_add(tmp,X,Y)) goto err; } else { if (BN_is_word(D,2)) { if (!BN_lshift1(tmp,X)) goto err; } else if (BN_is_word(D,4)) { if (!BN_lshift(tmp,X,2)) goto err; } else if (D->top == 1) { if (!BN_copy(tmp,X)) goto err; if (!BN_mul_word(tmp,D->d[0])) goto err; } else { if (!BN_mul(tmp,D,X,ctx)) goto err; } if (!BN_add(tmp,tmp,Y)) goto err; } M=Y; /* keep the BIGNUM object, the value does not matter */ Y=X; X=tmp; sign = -sign; } } /* * The while loop (Euclid's algorithm) ends when * A == gcd(a,n); * we have * sign*Y*a == A (mod |n|), * where Y is non-negative. */ if (sign < 0) { if (!BN_sub(Y,n,Y)) goto err; } /* Now Y*a == A (mod |n|). */ if (BN_is_one(A)) { /* Y*a == 1 (mod |n|) */ if (!Y->neg && BN_ucmp(Y,n) < 0) { if (!BN_copy(R,Y)) goto err; } else { if (!BN_nnmod(R,Y,n,ctx)) goto err; } } else { BNerr(BN_F_BN_MOD_INVERSE,BN_R_NO_INVERSE); goto err; } ret=R; err: if ((ret == NULL) && (in == NULL)) BN_free(R); BN_CTX_end(ctx); bn_check_top(ret); return(ret); }