Problem - Kevin Tafuro

Table 7-2. Math operations supported by OpenSSL’s BIGNUM library (continued)
Function Description Limitations Comments
r = a×2 Fastest way to multiply by 2.
int BN_lshift1(BIGNUM *r,
BIGNUM *a);
int BN_lshift(BIGNUM *r,
BIGNUM *a, int n);
int BN_rshift1(BIGNUM *r,
BIGNUM *a);
int BN_rshift(BIGNUM *r,
BIGNUM *a, int n);
int BN_sqr(BIGNUM *r, BIGNUM
*a, BN_CTX *ctx);
int BN_exp(BIGNUM *r, BIGNUM
*a, BIGNUM *p, BN_CTX *ctx);
int BN_div(BIGNUM *d, BIGNUM
*r, BIGNUM *a, BIGNUM *b, BN_
CTX *ctx);
int BN_mod(BIGNUM *r, BIGNUM
*a, BIGNUM *b, BN_CTX *ctx);
int BN_nnmod(BIGNUM *r,
BIGNUM *a, BIGNUM *b, BN_CTX
*ctx);
int BN_mod_add(BIGNUM *r,
BIGNUM *a, BIGNUM *b, BIGNUM
*m, BN_CTX *ctx);
int BN_mod_sub(BIGNUM *r,
BIGNUM *a, BIGNUM *b, BIGNUM
*m, BN_CTX *ctx);
int BN_mod_mul(BIGNUM *r,
BIGNUM *a, BIGNUM *b, BIGNUM
*m, BN_CTX *ctx);
int BN_mod_sqr(BIGNUM *r,
BIGNUM *a, BIGNUM *b, BIGNUM
*m, BN_CTX *ctx);
int BN_mod_exp(BIGNUM *r,
BIGNUM *a, BIGNUM *p, BIGNUM
*m, BN_CTX *ctx);
BIGNUM *BN_mod_
inverse(BIGNUM *r, BIGNUM
*a, 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 *a);
322 | Chapter 7: Public Key Cryptography
r = a×2n Fastest way to multiply by a
power of 2 where n>1.
r = a÷2 Fastest way to divide by 2.
r=a÷2n Fastest way to divide by a
power of 2 where n>1.
r = a×a Faster than BN_mul.
r = a p r≠a, r≠p Values may be the same, but
the objects may not be.
d = a÷b
r = a mod b
d≠a, d≠b, r≠a, r≠b Values may be the same, but
the objects may not be;
either d or r may be NULL.
r = a mod b r≠a, r≠b Values may be the same, but
the objects may not be.
r = |a mod b| r≠a, r≠b Values may be the same, but
the objects may not be.
r = |a+b mod m| r≠a, r≠b, r≠m Values may be the same, but
the objects may not be.
r = |a-b mod m| r≠a, r≠b, r≠m Values may be the same, but
the objects may not be.
r = |a×b mod m| r≠a, r≠b, r≠m Values may be the same, but
the objects may not be.
r = |a×a mod m| r≠a, r≠m Values may be the same, but
the objects may not be.
Faster than BN_mod_mul.
r = |ap mod m| r≠a, r≠p, r≠m Values may be the same, but
the objects may not be.
Returns NULL on error, such
as when no modular inverse
exists.
r = GCD(a,b) Greatest common divisor.
a = a+w
a = a-w
a = a×w
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