bn.h

RSA VC++实现

/* ---> Basic arithmetic <--- */

/* b = -a */
int mp_neg(mp_int *a, mp_int *b);

/* b = |a| */
int mp_abs(mp_int *a, mp_int *b);

/* compare a to b */
int mp_cmp(mp_int *a, mp_int *b);

/* compare |a| to |b| */
int mp_cmp_mag(mp_int *a, mp_int *b);

/* c = a + b */
int mp_add(mp_int *a, mp_int *b, mp_int *c);

/* c = a - b */
int mp_sub(mp_int *a, mp_int *b, mp_int *c);

/* c = a * b */
int mp_mul(mp_int *a, mp_int *b, mp_int *c);

/* b = a*a  */
int mp_sqr(mp_int *a, mp_int *b);

/* a/b => cb + d == a */
int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d);

/* c = a mod b, 0 <= c < b  */
int mp_mod(mp_int *a, mp_int *b, mp_int *c);

/* ---> single digit functions <--- */

/* compare against a single digit */
int mp_cmp_d(mp_int *a, mp_digit b);

/* c = a + b */
int mp_add_d(mp_int *a, mp_digit b, mp_int *c);

/* c = a - b */
int mp_sub_d(mp_int *a, mp_digit b, mp_int *c);

/* c = a * b */
int mp_mul_d(mp_int *a, mp_digit b, mp_int *c);

/* a/b => cb + d == a */
int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);

/* a/3 => 3c + d == a */
int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);

/* c = a**b */
int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);

/* c = a mod b, 0 <= c < b  */
int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);

/* ---> number theory <--- */

/* d = a + b (mod c) */
int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);

/* d = a - b (mod c) */
int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);

/* d = a * b (mod c) */
int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);

/* d = a / b (mod c) */
int mp_divmod(mp_int * a, mp_int * b, mp_int * c, mp_int * d);

/* c = a * a (mod b) */
int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c);

/* c = 1/a (mod b) */
int mp_invmod(mp_int *a, mp_int *b, mp_int *c);

/* c = (a, b) */
int mp_gcd(mp_int *a, mp_int *b, mp_int *c);

/* produces value such that U1*a + U2*b = U3 */
int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3);

/* c = [a, b] or (a*b)/(a, b) */
int mp_lcm(mp_int *a, mp_int *b, mp_int *c);

/* finds one of the b'th root of a, such that |c|**b <= |a|
 *
 * returns error if a < 0 and b is even
 */
int mp_n_root(mp_int *a, mp_digit b, mp_int *c);

/* special sqrt algo */
int mp_sqrt(mp_int *arg, mp_int *ret);

/* is number a square? */
int mp_is_square(mp_int *arg, int *ret);

/* computes the jacobi c = (a | n) (or Legendre if b is prime)  */
int mp_jacobi(mp_int *a, mp_int *n, int *c);

/* used to setup the Barrett reduction for a given modulus b */
int mp_reduce_setup(mp_int *a, mp_int *b);

/* Barrett Reduction, computes a (mod b) with a precomputed value c
 *
 * Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely
 * compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code].
 */
int mp_reduce(mp_int *a, mp_int *b, mp_int *c);

/* setups the montgomery reduction */
int mp_montgomery_setup(mp_int *a, mp_digit *mp);

/* computes a = B**n mod b without division or multiplication useful for
 * normalizing numbers in a Montgomery system.
 */
int mp_montgomery_calc_normalization(mp_int *a, mp_int *b);

/* computes x/R == x (mod N) via Montgomery Reduction */
int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);

/* returns 1 if a is a valid DR modulus */
int mp_dr_is_modulus(mp_int *a);

/* sets the value of "d" required for mp_dr_reduce */
void mp_dr_setup(mp_int *a, mp_digit *d);

/* reduces a modulo b using the Diminished Radix method */
int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp);

/* returns true if a can be reduced with mp_reduce_2k */
int mp_reduce_is_2k(mp_int *a);

/* determines k value for 2k reduction */
int mp_reduce_2k_setup(mp_int *a, mp_digit *d);

/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);

/* returns true if a can be reduced with mp_reduce_2k_l */
int mp_reduce_is_2k_l(mp_int *a);

/* determines k value for 2k reduction */
int mp_reduce_2k_setup_l(mp_int *a, mp_int *d);

/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);

/* d = a**b (mod c) */
int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);

int mp_exptmod_crt(mp_int * m, mp_int * e, mp_int * p, mp_int * q, mp_int * c);

/* ---> Primes <--- */

/* number of primes */
#ifdef MP_8BIT
   #define PRIME_SIZE      31
#else
   #define PRIME_SIZE      256
#endif

/* table of first PRIME_SIZE primes */
extern const mp_digit ltm_prime_tab[];

/* result=1 if a is divisible by one of the first PRIME_SIZE primes */
int mp_prime_is_divisible(mp_int *a, int *result);

/* performs one Fermat test of "a" using base "b".
 * Sets result to 0 if composite or 1 if probable prime
 */
int mp_prime_fermat(mp_int *a, mp_int *b, int *result);

/* performs one Miller-Rabin test of "a" using base "b".
 * Sets result to 0 if composite or 1 if probable prime
 */
int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result);

/* This gives [for a given bit size] the number of trials required
 * such that Miller-Rabin gives a prob of failure lower than 2^-96
 */
int mp_prime_rabin_miller_trials(int size);

/* performs t rounds of Miller-Rabin on "a" using the first
 * t prime bases.  Also performs an initial sieve of trial
 * division.  Determines if "a" is prime with probability
 * of error no more than (1/4)**t.
 *
 * Sets result to 1 if probably prime, 0 otherwise
 */
int mp_prime_is_prime(mp_int *a, int t, int *result);

/* finds the next prime after the number "a" using "t" trials
 * of Miller-Rabin.
 *
 * bbs_style = 1 means the prime must be congruent to 3 mod 4
 */
int mp_prime_next_prime(mp_int *a, int t, int bbs_style);

/* makes a truly random prime of a given size (bytes),
 * call with bbs = 1 if you want it to be congruent to 3 mod 4
 *
 * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
 * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
 * so it can be NULL
 *
 * The prime generated will be larger than 2^(8*size).
 */
#define mp_prime_random(a, t, size, bbs, cb, dat) mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat)

/* makes a truly random prime of a given size (bits),
 *
 * Flags are as follows:
 *
 *   LTM_PRIME_BBS      - make prime congruent to 3 mod 4
 *   LTM_PRIME_SAFE     - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
 *   LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
 *   LTM_PRIME_2MSB_ON  - make the 2nd highest bit one
 *
 * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
 * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
 * so it can be NULL
 *
 */
int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat);

int mp_generate_strong_prime_r(mp_int *r, int rsbits, ltm_prime_callback cb);

int mp_generate_strong_prime_p(mp_int *ret, int bits, ltm_prime_callback cb);

/* ---> radix conversion <--- */
int mp_count_bits(mp_int *a);
int mp_is_bit_set(mp_int * a, int b);

int mp_unsigned_bin_size(mp_int *a);
int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c);
int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);

int mp_signed_bin_size(mp_int *a);
int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c);
int mp_to_signed_bin(mp_int *a,  unsigned char *b);
int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);

int mp_read_radix(mp_int *a, const char *str, int radix);
int mp_toradix(mp_int *a, char *str, int radix);
int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
int mp_radix_size(mp_int *a, int radix, int *size);

int mp_fread(mp_int *a, int radix, FILE *stream);
int mp_fwrite(mp_int *a, int radix, FILE *stream);

#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
#define mp_raw_size(mp)           mp_signed_bin_size(mp)
#define mp_toraw(mp, str)         mp_to_signed_bin((mp), (str))
#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
#define mp_mag_size(mp)           mp_unsigned_bin_size(mp)
#define mp_tomag(mp, str)         mp_to_unsigned_bin((mp), (str))

#define mp_tobinary(M, S)  mp_toradix((M), (S), 2)
#define mp_tooctal(M, S)   mp_toradix((M), (S), 8)
#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
#define mp_tohex(M, S)     mp_toradix((M), (S), 16)

/* lowlevel functions, do not call! */
int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
int s_mp_sub(mp_int *a, mp_int *b, mp_int *c);
#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
int fast_s_mp_sqr(mp_int *a, mp_int *b);
int s_mp_sqr(mp_int *a, mp_int *b);
int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c);
int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);
int mp_karatsuba_sqr(mp_int *a, mp_int *b);
int mp_toom_sqr(mp_int *a, mp_int *b);
int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode);
int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode);
void bn_reverse(unsigned char *s, int len);
void mp_int_struct_dump(char *pref, mp_int *b);
void mp_int_word_dump(mp_int *b, int max);
void dump_mp_int_to_char (mp_int * b, int max, char * c);

extern const char *mp_s_rmap;

#ifdef __cplusplus
   }
#endif

#endif