[thirdparty/openssl.git] / doc / crypto / bn.pod

=pod

=head1 NAME

bn - multiprecision integer arithmetics

=head1 SYNOPSIS

 #include <openssl/bn.h>

 BIGNUM *BN_new(void);
 void BN_free(BIGNUM *a);
 void BN_clear(BIGNUM *a);
 void BN_clear_free(BIGNUM *a);

 BN_CTX *BN_CTX_new(void);
 BN_CTX *BN_CTX_secure_new(void);
 void BN_CTX_free(BN_CTX *c);

 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
 BIGNUM *BN_dup(const BIGNUM *a);

 BIGNUM *BN_swap(BIGNUM *a, BIGNUM *b);

 int BN_num_bytes(const BIGNUM *a);
 int BN_num_bits(const BIGNUM *a);
 int BN_num_bits_word(BN_ULONG w);

 void BN_set_negative(BIGNUM *a, int n);
 int  BN_is_negative(const BIGNUM *a);

 int BN_add(BIGNUM *r, const BIGNUM *a, const 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_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
         BN_CTX *ctx);
 int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
 int BN_nnmod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
 int BN_mod_add(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
         BN_CTX *ctx);
 int BN_mod_sub(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
         BN_CTX *ctx);
 int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
         BN_CTX *ctx);
 int BN_mod_sqr(BIGNUM *ret, BIGNUM *a, 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(const 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);
 const 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);
 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
 int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
 int BN_pseudo_rand_range(BIGNUM *rnd, BIGNUM *range);

 int BN_generate_prime_ex(BIGNUM *ret,int bits,int safe, const BIGNUM *add,
     const BIGNUM *rem, BN_GENCB *cb);

 int BN_is_prime_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx, BN_GENCB *cb);

 int BN_is_prime_fasttest_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx,
     int do_trial_division, BN_GENCB *cb);

 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
 BN_GENCB *BN_GENCB_new(void);
 void BN_GENCB_free(BN_GENCB *cb);
 void BN_GENCB_set_old(BN_GENCB *gencb, void (*callback)(int, int, void *), void *cb_arg);
 void BN_GENCB_set(BN_GENCB *gencb, int (*callback)(int, int, BN_GENCB *), void *cb_arg);
 void *BN_GENCB_get_arg(BN_GENCB *cb);

 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(BIO *fp, const BIGNUM *a);
 int BN_print_fp(FILE *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_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_free(BN_MONT_CTX *mont);
 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);

 BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const 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 *b, BN_CTX *ctx);
 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
 int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b,
	BN_CTX *ctx);
 int BN_BLINDING_invert_ex(BIGNUM *n,const BIGNUM *r,BN_BLINDING *b,
	BN_CTX *ctx);
 unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *);
 void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long);
 unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
 void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
 BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
	const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
	int (*bn_mod_exp)(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
			  const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx),
	BN_MONT_CTX *m_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)|BN_new(3)>;
L<BN_add(3)|BN_add(3)> describes most of the arithmetic operations.
Comparison is described in L<BN_cmp(3)|BN_cmp(3)>; L<BN_zero(3)|BN_zero(3)>
describes certain assignments, L<BN_rand(3)|BN_rand(3)> the generation of
random numbers, L<BN_generate_prime(3)|BN_generate_prime(3)> deals with prime
numbers and L<BN_set_bit(3)|BN_set_bit(3)> with bit operations. The conversion
of B<BIGNUM>s to external formats is described in L<BN_bn2bin(3)|BN_bn2bin(3)>.

=head1 SEE ALSO

L<bn_internal(3)|bn_internal(3)>,
L<dh(3)|dh(3)>, L<err(3)|err(3)>, L<rand(3)|rand(3)>, L<rsa(3)|rsa(3)>,
L<BN_new(3)|BN_new(3)>, L<BN_CTX_new(3)|BN_CTX_new(3)>,
L<BN_copy(3)|BN_copy(3)>, L<BN_swap(3)|BN_swap(3)>, L<BN_num_bytes(3)|BN_num_bytes(3)>,
L<BN_add(3)|BN_add(3)>, L<BN_add_word(3)|BN_add_word(3)>,
L<BN_cmp(3)|BN_cmp(3)>, L<BN_zero(3)|BN_zero(3)>, L<BN_rand(3)|BN_rand(3)>,
L<BN_generate_prime(3)|BN_generate_prime(3)>, L<BN_set_bit(3)|BN_set_bit(3)>,
L<BN_bn2bin(3)|BN_bn2bin(3)>, L<BN_mod_inverse(3)|BN_mod_inverse(3)>,
L<BN_mod_mul_reciprocal(3)|BN_mod_mul_reciprocal(3)>,
L<BN_mod_mul_montgomery(3)|BN_mod_mul_montgomery(3)>,
L<BN_BLINDING_new(3)|BN_BLINDING_new(3)>

=cut
Commit	Line	Data
4486d0cd UM	1	=pod
	2
	3	=head1 NAME
	4
4d524e10	5	bn - multiprecision integer arithmetics
4486d0cd UM	6
	7	=head1 SYNOPSIS
	8
	9	#include <openssl/bn.h>
	10
4486d0cd	11	BIGNUM *BN_new(void);
dd8dec69	12	void BN_free(BIGNUM *a);
dd8dec69 UM	13	void BN_clear(BIGNUM *a);
	14	void BN_clear_free(BIGNUM *a);
	15
	16	BN_CTX *BN_CTX_new(void);
74924dcb	17	BN_CTX *BN_CTX_secure_new(void);
dd8dec69 UM	18	void BN_CTX_free(BN_CTX *c);
dd8dec69 UM	19
4486d0cd	20	BIGNUM BN_copy(BIGNUM a, const BIGNUM *b);
4486d0cd	21	BIGNUM BN_dup(const BIGNUM a);
dd8dec69	22
78a0c1f1 BM	23	BIGNUM BN_swap(BIGNUM a, BIGNUM *b);
78a0c1f1 BM	24
dd8dec69 UM	25	int BN_num_bytes(const BIGNUM *a);
	26	int BN_num_bits(const BIGNUM *a);
	27	int BN_num_bits_word(BN_ULONG w);
	28
ff22e913 NL	29	void BN_set_negative(BIGNUM *a, int n);
	30	int BN_is_negative(const BIGNUM *a);
	31
78a0c1f1	32	int BN_add(BIGNUM r, const BIGNUM a, const BIGNUM *b);
dd8dec69 UM	33	int BN_sub(BIGNUM r, const BIGNUM a, const BIGNUM *b);
dd8dec69 UM	34	int BN_mul(BIGNUM r, BIGNUM a, BIGNUM b, BN_CTX ctx);
78a0c1f1	35	int BN_sqr(BIGNUM r, BIGNUM a, BN_CTX *ctx);
dd8dec69 UM	36	int BN_div(BIGNUM dv, BIGNUM rem, const BIGNUM a, const BIGNUM d,
dd8dec69 UM	37	BN_CTX *ctx);
dd8dec69	38	int BN_mod(BIGNUM rem, const BIGNUM a, const BIGNUM m, BN_CTX ctx);
78a0c1f1 BM	39	int BN_nnmod(BIGNUM rem, const BIGNUM a, const BIGNUM m, BN_CTX ctx);
	40	int BN_mod_add(BIGNUM ret, BIGNUM a, BIGNUM b, const BIGNUM m,
	41	BN_CTX *ctx);
	42	int BN_mod_sub(BIGNUM ret, BIGNUM a, BIGNUM b, const BIGNUM m,
	43	BN_CTX *ctx);
dd8dec69 UM	44	int BN_mod_mul(BIGNUM ret, BIGNUM a, BIGNUM b, const BIGNUM m,
dd8dec69 UM	45	BN_CTX *ctx);
78a0c1f1	46	int BN_mod_sqr(BIGNUM ret, BIGNUM a, const BIGNUM m, BN_CTX ctx);
dd8dec69 UM	47	int BN_exp(BIGNUM r, BIGNUM a, BIGNUM p, BN_CTX ctx);
	48	int BN_mod_exp(BIGNUM r, BIGNUM a, const BIGNUM *p,
	49	const BIGNUM m, BN_CTX ctx);
	50	int BN_gcd(BIGNUM r, BIGNUM a, BIGNUM b, BN_CTX ctx);
	51
	52	int BN_add_word(BIGNUM *a, BN_ULONG w);
	53	int BN_sub_word(BIGNUM *a, BN_ULONG w);
	54	int BN_mul_word(BIGNUM *a, BN_ULONG w);
	55	BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
7999c65c	56	BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
dd8dec69 UM	57
	58	int BN_cmp(BIGNUM a, BIGNUM b);
	59	int BN_ucmp(BIGNUM a, BIGNUM b);
	60	int BN_is_zero(BIGNUM *a);
	61	int BN_is_one(BIGNUM *a);
	62	int BN_is_word(BIGNUM *a, BN_ULONG w);
	63	int BN_is_odd(BIGNUM *a);
	64
	65	int BN_zero(BIGNUM *a);
	66	int BN_one(BIGNUM *a);
98499135	67	const BIGNUM *BN_value_one(void);
dd8dec69 UM	68	int BN_set_word(BIGNUM *a, unsigned long w);
	69	unsigned long BN_get_word(BIGNUM *a);
	70
4d524e10 UM	71	int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
4d524e10 UM	72	int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
e3068929	73	int BN_rand_range(BIGNUM rnd, BIGNUM range);
983495c4	74	int BN_pseudo_rand_range(BIGNUM rnd, BIGNUM range);
dd8dec69	75
e35af275 MC	76	int BN_generate_prime_ex(BIGNUM ret,int bits,int safe, const BIGNUM add,
	77	const BIGNUM rem, BN_GENCB cb);
	78
	79	int BN_is_prime_ex(const BIGNUM p,int nchecks, BN_CTX ctx, BN_GENCB *cb);
	80
	81	int BN_is_prime_fasttest_ex(const BIGNUM p,int nchecks, BN_CTX ctx,
	82	int do_trial_division, BN_GENCB *cb);
	83
	84	int BN_GENCB_call(BN_GENCB *cb, int a, int b);
	85	BN_GENCB *BN_GENCB_new(void);
	86	void BN_GENCB_free(BN_GENCB *cb);
	87	void BN_GENCB_set_old(BN_GENCB gencb, void (callback)(int, int, void ), void cb_arg);
	88	void BN_GENCB_set(BN_GENCB gencb, int (callback)(int, int, BN_GENCB ), void cb_arg);
	89	void BN_GENCB_get_arg(BN_GENCB cb);
dd8dec69 UM	90
	91	int BN_set_bit(BIGNUM *a, int n);
	92	int BN_clear_bit(BIGNUM *a, int n);
	93	int BN_is_bit_set(const BIGNUM *a, int n);
	94	int BN_mask_bits(BIGNUM *a, int n);
	95	int BN_lshift(BIGNUM r, const BIGNUM a, int n);
	96	int BN_lshift1(BIGNUM r, BIGNUM a);
	97	int BN_rshift(BIGNUM r, BIGNUM a, int n);
	98	int BN_rshift1(BIGNUM r, BIGNUM a);
	99
	100	int BN_bn2bin(const BIGNUM a, unsigned char to);
	101	BIGNUM BN_bin2bn(const unsigned char s, int len, BIGNUM *ret);
	102	char BN_bn2hex(const BIGNUM a);
	103	char BN_bn2dec(const BIGNUM a);
	104	int BN_hex2bn(BIGNUM *a, const char str);
	105	int BN_dec2bn(BIGNUM *a, const char str);
dd8dec69	106	int BN_print(BIO fp, const BIGNUM a);
e93f9a32	107	int BN_print_fp(FILE fp, const BIGNUM a);
dd8dec69 UM	108	int BN_bn2mpi(const BIGNUM a, unsigned char to);
	109	BIGNUM BN_mpi2bn(unsigned char s, int len, BIGNUM *ret);
	110
	111	BIGNUM BN_mod_inverse(BIGNUM r, BIGNUM a, const BIGNUM n,
	112	BN_CTX *ctx);
	113
	114	BN_RECP_CTX *BN_RECP_CTX_new(void);
dd8dec69 UM	115	void BN_RECP_CTX_free(BN_RECP_CTX *recp);
	116	int BN_RECP_CTX_set(BN_RECP_CTX recp, const BIGNUM m, BN_CTX *ctx);
	117	int BN_mod_mul_reciprocal(BIGNUM r, BIGNUM a, BIGNUM *b,
	118	BN_RECP_CTX recp, BN_CTX ctx);
	119
	120	BN_MONT_CTX *BN_MONT_CTX_new(void);
4486d0cd	121	void BN_MONT_CTX_free(BN_MONT_CTX *mont);
dd8dec69 UM	122	int BN_MONT_CTX_set(BN_MONT_CTX mont, const BIGNUM m, BN_CTX *ctx);
	123	BN_MONT_CTX BN_MONT_CTX_copy(BN_MONT_CTX to, BN_MONT_CTX *from);
	124	int BN_mod_mul_montgomery(BIGNUM r, BIGNUM a, BIGNUM *b,
	125	BN_MONT_CTX mont, BN_CTX ctx);
	126	int BN_from_montgomery(BIGNUM r, BIGNUM a, BN_MONT_CTX *mont,
	127	BN_CTX *ctx);
	128	int BN_to_montgomery(BIGNUM r, BIGNUM a, BN_MONT_CTX *mont,
	129	BN_CTX *ctx);
	130
9ca46ff6 NL	131	BN_BLINDING BN_BLINDING_new(const BIGNUM A, const BIGNUM *Ai,
	132	BIGNUM *mod);
	133	void BN_BLINDING_free(BN_BLINDING *b);
	134	int BN_BLINDING_update(BN_BLINDING b,BN_CTX ctx);
	135	int BN_BLINDING_convert(BIGNUM n, BN_BLINDING b, BN_CTX *ctx);
	136	int BN_BLINDING_invert(BIGNUM n, BN_BLINDING b, BN_CTX *ctx);
	137	int BN_BLINDING_convert_ex(BIGNUM n, BIGNUM r, BN_BLINDING *b,
	138	BN_CTX *ctx);
	139	int BN_BLINDING_invert_ex(BIGNUM n,const BIGNUM r,BN_BLINDING *b,
	140	BN_CTX *ctx);
5f834ab1 GT	141	unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *);
5f834ab1 GT	142	void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long);
9ca46ff6 NL	143	unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
	144	void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
	145	BN_BLINDING BN_BLINDING_create_param(BN_BLINDING b,
	146	const BIGNUM e, BIGNUM m, BN_CTX *ctx,
	147	int (bn_mod_exp)(BIGNUM r, const BIGNUM a, const BIGNUM p,
	148	const BIGNUM m, BN_CTX ctx, BN_MONT_CTX *m_ctx),
	149	BN_MONT_CTX *m_ctx);
4486d0cd UM	150
	151	=head1 DESCRIPTION
	152
dd8dec69 UM	153	This library performs arithmetic operations on integers of arbitrary
	154	size. It was written for use in public key cryptography, such as RSA
	155	and Diffie-Hellman.
	156
	157	It uses dynamic memory allocation for storing its data structures.
	158	That means that there is no limit on the size of the numbers
	159	manipulated by these functions, but return values must always be
	160	checked in case a memory allocation error has occurred.
	161
	162	The basic object in this library is a B<BIGNUM>. It is used to hold a
	163	single large integer. This type should be considered opaque and fields
	164	should not be modified or accessed directly.
	165
bb075f88 RL	166	The creation of B<BIGNUM> objects is described in L<BN_new(3)\|BN_new(3)>;
bb075f88 RL	167	L<BN_add(3)\|BN_add(3)> describes most of the arithmetic operations.
e93f9a32	168	Comparison is described in L<BN_cmp(3)\|BN_cmp(3)>; L<BN_zero(3)\|BN_zero(3)>
bb075f88 RL	169	describes certain assignments, L<BN_rand(3)\|BN_rand(3)> the generation of
	170	random numbers, L<BN_generate_prime(3)\|BN_generate_prime(3)> deals with prime
	171	numbers and L<BN_set_bit(3)\|BN_set_bit(3)> with bit operations. The conversion
	172	of B<BIGNUM>s to external formats is described in L<BN_bn2bin(3)\|BN_bn2bin(3)>.
dd8dec69	173
4486d0cd UM	174	=head1 SEE ALSO
4486d0cd UM	175
775c63fc	176	L<bn_internal(3)\|bn_internal(3)>,
bb075f88 RL	177	L<dh(3)\|dh(3)>, L<err(3)\|err(3)>, L<rand(3)\|rand(3)>, L<rsa(3)\|rsa(3)>,
bb075f88 RL	178	L<BN_new(3)\|BN_new(3)>, L<BN_CTX_new(3)\|BN_CTX_new(3)>,
78a0c1f1	179	L<BN_copy(3)\|BN_copy(3)>, L<BN_swap(3)\|BN_swap(3)>, L<BN_num_bytes(3)\|BN_num_bytes(3)>,
bb075f88 RL	180	L<BN_add(3)\|BN_add(3)>, L<BN_add_word(3)\|BN_add_word(3)>,
	181	L<BN_cmp(3)\|BN_cmp(3)>, L<BN_zero(3)\|BN_zero(3)>, L<BN_rand(3)\|BN_rand(3)>,
	182	L<BN_generate_prime(3)\|BN_generate_prime(3)>, L<BN_set_bit(3)\|BN_set_bit(3)>,
	183	L<BN_bn2bin(3)\|BN_bn2bin(3)>, L<BN_mod_inverse(3)\|BN_mod_inverse(3)>,
	184	L<BN_mod_mul_reciprocal(3)\|BN_mod_mul_reciprocal(3)>,
d753c3f5 NL	185	L<BN_mod_mul_montgomery(3)\|BN_mod_mul_montgomery(3)>,
d753c3f5 NL	186	L<BN_BLINDING_new(3)\|BN_BLINDING_new(3)>
4486d0cd UM	187
4486d0cd UM	188	=cut