diff options
author | Ulf Möller <ulf@openssl.org> | 2000-01-23 22:06:24 +0000 |
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committer | Ulf Möller <ulf@openssl.org> | 2000-01-23 22:06:24 +0000 |
commit | dd8dec69b825c9fdafc26a200961702d850496b5 (patch) | |
tree | b7d7ca7365271c822226e1ddc6a4fd68c72273ad /doc/crypto/bn.pod | |
parent | ce052b6c3b18d4ab5f74990d82d09827a6014823 (diff) |
Document the BN library.
Diffstat (limited to 'doc/crypto/bn.pod')
-rw-r--r-- | doc/crypto/bn.pod | 267 |
1 files changed, 152 insertions, 115 deletions
diff --git a/doc/crypto/bn.pod b/doc/crypto/bn.pod index fbd674dd5e..1a0e38b24c 100644 --- a/doc/crypto/bn.pod +++ b/doc/crypto/bn.pod @@ -8,131 +8,168 @@ bn - Multiprecision integer arithmetics #include <openssl/bn.h> - #define BN_prime_checks(b) - #define BN_num_bytes(a) - #define BN_is_word(a,w) - #define BN_is_zero(a) - #define BN_is_one(a) - #define BN_is_odd(a) - #define BN_one(a) - #define BN_zero(a) - - #define bn_expand(n,b) - #define bn_wexpand(n,b) - - #define bn_fix_top(a) - - BIGNUM *BN_value_one(void); - char * BN_options(void); - BN_CTX *BN_CTX_new(void); - 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_num_bits(const BIGNUM *a); - int BN_num_bits_word(BN_ULONG); BIGNUM *BN_new(void); - void BN_init(BIGNUM *); - void BN_clear_free(BIGNUM *a); + void BN_free(BIGNUM *a); + void BN_init(BIGNUM *); + void BN_clear(BIGNUM *a); + void BN_clear_free(BIGNUM *a); + + BN_CTX *BN_CTX_new(void); + void BN_CTX_init(BN_CTX *c); + void BN_CTX_free(BN_CTX *c); + BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b); - BIGNUM *BN_bin2bn(const unsigned char *s,int len,BIGNUM *ret); - int BN_bn2bin(const BIGNUM *a, unsigned char *to); - BIGNUM *BN_mpi2bn(unsigned char *s,int len,BIGNUM *ret); - int BN_bn2mpi(const BIGNUM *a, unsigned char *to); - int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); - int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); - int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); - int BN_add(BIGNUM *r, BIGNUM *a, BIGNUM *b); - int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx); - int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, - 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_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); - int BN_sub_word(BIGNUM *a, BN_ULONG w); - int BN_set_word(BIGNUM *a, BN_ULONG w); - BN_ULONG BN_get_word(BIGNUM *a); - int BN_cmp(const BIGNUM *a, const BIGNUM *b); - void BN_free(BIGNUM *a); - int BN_is_bit_set(const BIGNUM *a, int n); - int BN_lshift(BIGNUM *r, const BIGNUM *a, int n); - int BN_lshift1(BIGNUM *r, BIGNUM *a); - int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p,BN_CTX *ctx); - int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, - const BIGNUM *m,BN_CTX *ctx); - int BN_mod_exp_mont(BIGNUM *r, BIGNUM *a, const BIGNUM *p, - const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx); - int BN_mod_exp2_mont(BIGNUM *r, BIGNUM *a1, BIGNUM *p1,BIGNUM *a2, - BIGNUM *p2,BIGNUM *m,BN_CTX *ctx,BN_MONT_CTX *m_ctx); - int BN_mod_exp_simple(BIGNUM *r, BIGNUM *a, BIGNUM *p, - BIGNUM *m,BN_CTX *ctx); - int BN_mask_bits(BIGNUM *a,int n); - int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx); - int BN_print_fp(FILE *fp, BIGNUM *a); - int BN_print(BIO *fp, const BIGNUM *a); - int BN_reciprocal(BIGNUM *r, BIGNUM *m, int len, BN_CTX *ctx); - int BN_rshift(BIGNUM *r, BIGNUM *a, int n); - int BN_rshift1(BIGNUM *r, BIGNUM *a); - void BN_clear(BIGNUM *a); - BIGNUM *bn_expand2(BIGNUM *b, int bits); BIGNUM *BN_dup(const BIGNUM *a); - int BN_ucmp(const BIGNUM *a, const BIGNUM *b); - int BN_set_bit(BIGNUM *a, int n); - int BN_clear_bit(BIGNUM *a, int n); - char * BN_bn2hex(const BIGNUM *a); - char * BN_bn2dec(const BIGNUM *a); - int BN_hex2bn(BIGNUM **a, const char *str); - int BN_dec2bn(BIGNUM **a, const char *str); - int BN_gcd(BIGNUM *r,BIGNUM *in_a,BIGNUM *in_b,BN_CTX *ctx); - BIGNUM *BN_mod_inverse(BIGNUM *ret,BIGNUM *a, const BIGNUM *n,BN_CTX *ctx); + + int BN_num_bytes(const BIGNUM *a); + int BN_num_bits(const BIGNUM *a); + int BN_num_bits_word(BN_ULONG w); + + int BN_add(BIGNUM *r, BIGNUM *a, BIGNUM *b); + int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); + int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); + int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d, + BN_CTX *ctx); + int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx); + int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); + int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, + BN_CTX *ctx); + int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx); + int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, + const BIGNUM *m, BN_CTX *ctx); + int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); + + int BN_add_word(BIGNUM *a, BN_ULONG w); + int BN_sub_word(BIGNUM *a, BN_ULONG w); + int BN_mul_word(BIGNUM *a, BN_ULONG w); + BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w); + BN_ULONG BN_mod_word(BIGNUM *a, BN_ULONG w); + + int BN_cmp(BIGNUM *a, BIGNUM *b); + int BN_ucmp(BIGNUM *a, BIGNUM *b); + int BN_is_zero(BIGNUM *a); + int BN_is_one(BIGNUM *a); + int BN_is_word(BIGNUM *a, BN_ULONG w); + int BN_is_odd(BIGNUM *a); + + int BN_zero(BIGNUM *a); + int BN_one(BIGNUM *a); + BIGNUM *BN_value_one(void); + int BN_set_word(BIGNUM *a, unsigned long w); + unsigned long BN_get_word(BIGNUM *a); + + int BN_rand(BIGNUM *rnd, int bits, int top,int bottom); + 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 *), - BN_CTX *ctx,void *cb_arg); - void ERR_load_BN_strings(void ); - - BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w); - BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w); - void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num); - BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d); - BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,int num); - BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,int num); - - BN_MONT_CTX *BN_MONT_CTX_new(void ); + BIGNUM *rem,void (*callback)(int,int,void *),void *cb_arg); + int BN_is_prime(BIGNUM *p,int nchecks,void (*callback)(int,int,void *), + BN_CTX *ctx,void *cb_arg); + + int BN_set_bit(BIGNUM *a, int n); + int BN_clear_bit(BIGNUM *a, int n); + int BN_is_bit_set(const BIGNUM *a, int n); + int BN_mask_bits(BIGNUM *a, int n); + int BN_lshift(BIGNUM *r, const BIGNUM *a, int n); + int BN_lshift1(BIGNUM *r, BIGNUM *a); + int BN_rshift(BIGNUM *r, BIGNUM *a, int n); + int BN_rshift1(BIGNUM *r, BIGNUM *a); + + int BN_bn2bin(const BIGNUM *a, unsigned char *to); + BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret); + char *BN_bn2hex(const BIGNUM *a); + char *BN_bn2dec(const BIGNUM *a); + int BN_hex2bn(BIGNUM **a, const char *str); + int BN_dec2bn(BIGNUM **a, const char *str); + int BN_print_fp(FILE *fp, BIGNUM *a); + int BN_print(BIO *fp, const BIGNUM *a); + int BN_bn2mpi(const BIGNUM *a, unsigned char *to); + BIGNUM *BN_mpi2bn(unsigned char *s, int len, BIGNUM *ret); + + BIGNUM *BN_mod_inverse(BIGNUM *r, BIGNUM *a, const BIGNUM *n, + BN_CTX *ctx); + + BN_RECP_CTX *BN_RECP_CTX_new(void); + void BN_RECP_CTX_init(BN_RECP_CTX *recp); + void BN_RECP_CTX_free(BN_RECP_CTX *recp); + int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *m, BN_CTX *ctx); + int BN_mod_mul_reciprocal(BIGNUM *r, BIGNUM *a, BIGNUM *b, + BN_RECP_CTX *recp, BN_CTX *ctx); + + BN_MONT_CTX *BN_MONT_CTX_new(void); void BN_MONT_CTX_init(BN_MONT_CTX *ctx); - int BN_mod_mul_montgomery(BIGNUM *r,BIGNUM *a,BIGNUM *b,BN_MONT_CTX *mont, - BN_CTX *ctx); - int BN_from_montgomery(BIGNUM *r,BIGNUM *a,BN_MONT_CTX *mont,BN_CTX *ctx); void BN_MONT_CTX_free(BN_MONT_CTX *mont); - int BN_MONT_CTX_set(BN_MONT_CTX *mont,const BIGNUM *modulus,BN_CTX *ctx); - BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,BN_MONT_CTX *from); - - BN_BLINDING *BN_BLINDING_new(BIGNUM *A,BIGNUM *Ai,BIGNUM *mod); - void BN_BLINDING_free(BN_BLINDING *b); - int BN_BLINDING_update(BN_BLINDING *b,BN_CTX *ctx); - int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *r, BN_CTX *ctx); - int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx); - - void BN_set_params(int mul,int high,int low,int mont); - int BN_get_params(int which); - - void BN_RECP_CTX_init(BN_RECP_CTX *recp); - BN_RECP_CTX *BN_RECP_CTX_new(void); - void BN_RECP_CTX_free(BN_RECP_CTX *recp); - int BN_RECP_CTX_set(BN_RECP_CTX *recp,const BIGNUM *rdiv,BN_CTX *ctx); - int BN_mod_mul_reciprocal(BIGNUM *r, BIGNUM *x, BIGNUM *y, - BN_RECP_CTX *recp,BN_CTX *ctx); - int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, - const BIGNUM *m, BN_CTX *ctx); - int BN_div_recp(BIGNUM *dv, BIGNUM *rem, BIGNUM *m, - BN_RECP_CTX *recp, BN_CTX *ctx); + int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx); + BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from); + int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b, + BN_MONT_CTX *mont, BN_CTX *ctx); + int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont, + BN_CTX *ctx); + int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont, + BN_CTX *ctx); + =head1 DESCRIPTION +This library performs arithmetic operations on integers of arbitrary +size. It was written for use in public key cryptography, such as RSA +and Diffie-Hellman. + +It uses dynamic memory allocation for storing its data structures. +That means that there is no limit on the size of the numbers +manipulated by these functions, but return values must always be +checked in case a memory allocation error has occurred. + +The basic object in this library is a B<BIGNUM>. It is used to hold a +single large integer. This type should be considered opaque and fields +should not be modified or accessed directly. + +The creation of B<BIGNUM> objects is described in L<BN_new(3)>; +L<BN_add(3)> describes most of the arithmetic operations. +Comparision is described in L<BN_cmp(3)>; L<BN_zero(3)> describes +certain assignments, L<BN_rand(3)> the generation of random numbers, +L<BN_generate_prime(3)> deals with prime numbers and L<BN_set_bit(3)> +with bit operations. The conversion of B<BIGNUM>s to external +formats is described in L<BN_bn2bin(3)>. + +=head1 INTERNALS + +The following description is based on the SSLeay documentation: + + typedef struct bignum_st + { + int top; /* Index of last used d. */ + BN_ULONG *d; /* Pointer to an array of 'BITS2' bit chunks. */ + int max; /* Size of the d array. */ + int neg; + } BIGNUM; + +The big number is stored in B<d>, a malloc()ed array of B<BN_ULONG>s. +A B<BN_ULONG> can be either 16, 32 or 64 bits in size, depending on +the 'number of bits' specified in bn.h. + +B<max> is the size of the B<d> array that has been allocated. B<top> +is the 'last' entry being used, so for a value of 4, bn.d[0]=4 and +bn.top=1. B<neg> is 1 if the number is negative. When a BIGNUM is +'0', the B<d> field can be NULL and B<top> == 0. Various routines in +this library require the use of temporary B<BIGNUM> variables during +their execution. Since dynamic memory allocation to create B<BIGNUM>s +is rather expensive when used in conjunction with repeated subroutine +calls, the B<BN_CTX> structure is used. This structure contains +B<BN_CTX_NUM> B<BIGNUM>s. B<BN_CTX_NUM> is the maximum number of +temporary B<BIGNUM>s any publicly exported function will use. + + #define BN_CTX_NUM 12 + typedef struct bignum_ctx + { + int tos; /* top of stack */ + BIGNUM *bn[BN_CTX_NUM]; /* The variables */ + } BN_CTX; + =head1 SEE ALSO -err(3), rand(3) +dh(3), err(3), rand(3), rsa(3), BN_new(3), BN_CTX_new(3), BN_copy(3), +BN_num_bytes(3), BN_add(3), BN_add_word(3), BN_cmp(3), BN_zero(3), +BN_rand(3), BN_generate_prime(3), BN_set_bit(3), BN_bn2bin(3), +BN_mod_inverse(3), BN_mod_mul_reciprocal(3), BN_mod_mul_montgomery(3) =cut |