BigInt is Botan’s implementation of a multiple-precision
integer. Thanks to C++’s operator overloading features, using
BigInt is often quite similar to using a native integer type. The
number of functions related to
BigInt is quite large. You can find
most of them in
These transform the normal representation of a
BigInt into some
other form, such as a decimal string:
encode(const BigInt &n, Encoding enc = Binary)¶
This function encodes the BigInt n into a memory vector.
Encodingis an enum that has values
decode(const std::vector<uint8_t> &vec, Encoding enc)¶
Decode the integer from
vecusing the encoding specified.
These functions are static member functions, so they would be called like this:
BigInt n1 = ...; // some number secure_vector<uint8_t> n1_encoded = BigInt::encode(n1); BigInt n2 = BigInt::decode(n1_encoded); assert(n1 == n2);
There are also C++-style I/O operators defined for use with
BigInt. The input operator understands negative numbers and
hexadecimal numbers (marked with a leading “0x”). The ‘-‘ must come
before the “0x” marker. The output operator will never adorn the
output; for example, when printing a hexadecimal number, there will
not be a leading “0x” (though a leading ‘-‘ will be printed if the
number is negative). If you want such things, you’ll have to do them
BigInt has constructors that can create a
BigInt from an
unsigned integer or a string. You can also decode an array (a
pointer plus a length) into a
BigInt using a constructor.
Number theoretic functions available include:
gcd(BigInt x, BigInt y)¶
Returns the greatest common divisor of x and y
lcm(BigInt x, BigInt y)¶
Returns an integer z which is the smallest integer such that z % x == 0 and z % y == 0
inverse_mod(BigInt x, BigInt m)¶
Returns the modular inverse of x modulo m, that is, an integer y such that (x*y) % m == 1. If no such y exists, returns zero.
power_mod(BigInt b, BigInt x, BigInt m)¶
Returns b to the xth power modulo m. If you are doing many exponentiations with a single fixed modulus, it is faster to use a
ressol(BigInt x, BigInt p)¶
Returns the square root modulo a prime, that is, returns a number y such that (y*y) % p == x. Returns -1 if no such integer exists.
is_prime(BigInt n, RandomNumberGenerator &rng, size_t prob = 56, double is_random = false)¶
Test n for primality using a probablistic algorithm (Miller-Rabin). With this algorithm, there is some non-zero probability that true will be returned even if n is actually composite. Modifying prob allows you to decrease the chance of such a false positive, at the cost of increased runtime. Sufficient tests will be run such that the chance n is composite is no more than 1 in 2prob. Set is_random to true if (and only if) n was randomly chosen (ie, there is no danger it was chosen maliciously) as far fewer tests are needed in that case.
quick_check_prime(BigInt n, RandomNumberGenerator &rng)¶
check_prime(BigInt n, RandomNumberGenerator &rng)¶
verify_prime(BigInt n, RandomNumberGenerator &rng)¶
Three variations on is_prime, with probabilities set to 32, 56, and 80 respectively.
random_prime(RandomNumberGenerator &rng, size_t bits, BigInt coprime = 1, size_t equiv = 1, size_t equiv_mod = 2)¶
Return a random prime number of
bitsbits long that is relatively prime to
coprime, and equivalent to