int ri; /* number of bits in R */
BIGNUM RR; /* used to convert to montgomery form */
BIGNUM N; /* The modulus */
- BIGNUM Ni; /* The inverse of N (bignum form) */
- BN_ULONG n0; /* The inverse of N in word form */
+ BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
+ * (Ni is only stored for bignum algorithm) */
+ BN_ULONG n0; /* least significant word of Ni */
int flags;
} BN_MONT_CTX;
#define BN_prime_checks 0 /* default: select number of iterations
based on the size of the number */
+
+/* number of Miller-Rabin iterations for an error rate of less than 2^-80
+ * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
+ * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
+ * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
+ * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
+#define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
+ (b) >= 850 ? 3 : \
+ (b) >= 650 ? 4 : \
+ (b) >= 550 ? 5 : \
+ (b) >= 450 ? 6 : \
+ (b) >= 400 ? 7 : \
+ (b) >= 350 ? 8 : \
+ (b) >= 300 ? 9 : \
+ (b) >= 250 ? 12 : \
+ (b) >= 200 ? 15 : \
+ (b) >= 150 ? 18 : \
+ /* b >= 100 */ 27)
+
#define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
#define BN_is_word(a,w) (((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w)))
#define BN_is_zero(a) (((a)->top == 0) || BN_is_word(a,0))
void BN_CTX_init(BN_CTX *c);
void BN_CTX_free(BN_CTX *c);
int BN_rand(BIGNUM *rnd, int bits, int top,int bottom);
+int BN_pseudo_rand(BIGNUM *rnd, int bits, int top,int bottom);
int BN_num_bits(const BIGNUM *a);
int BN_num_bits_word(BN_ULONG);
BIGNUM *BN_new(void);
BN_CTX *ctx);
int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
int BN_sqr(BIGNUM *r, BIGNUM *a,BN_CTX *ctx);
-BN_ULONG BN_mod_word(BIGNUM *a, BN_ULONG w);
+BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
int BN_mul_word(BIGNUM *a, BN_ULONG w);
int BN_add_word(BIGNUM *a, BN_ULONG w);
BIGNUM *BN_mod_inverse(BIGNUM *ret,BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int safe,BIGNUM *add,
BIGNUM *rem,void (*callback)(int,int,void *),void *cb_arg);
-int BN_is_prime(BIGNUM *p,int nchecks,void (*callback)(int,int,void *),
+int BN_is_prime(const BIGNUM *p,int nchecks,
+ void (*callback)(int,int,void *),
BN_CTX *ctx,void *cb_arg);
+int BN_is_prime_fasttest(const BIGNUM *p,int nchecks,
+ void (*callback)(int,int,void *),BN_CTX *ctx,void *cb_arg,
+ int do_trial_division);
void ERR_load_BN_strings(void );
BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w);