BigInt¶
BigInt
is Botan’s implementation of a multipleprecision
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 botan/bigint.h
and botan/numthry.h
.
Encoding Functions¶
These transform the normal representation of a BigInt
into some
other form, such as a decimal string:

secure_vector<uint8_t> BigInt
::
encode
(const BigInt &n, Encoding enc = Binary)¶ This function encodes the BigInt n into a memory vector.
Encoding
is an enum that has valuesBinary
,Decimal
, andHexadecimal
.

BigInt BigInt
::
decode
(const std::vector<uint8_t> &vec, Encoding enc)¶ Decode the integer from
vec
using 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
yourself.
BigInt
has constructors that can create a BigInt
from an
unsigned integer or a string. You can also decode an array (a byte
pointer plus a length) into a BigInt
using a constructor.
Number Theory¶
Number theoretic functions available include:

BigInt
gcd
(BigInt x, BigInt y)¶ Returns the greatest common divisor of x and y

BigInt
lcm
(BigInt x, BigInt y)¶ Returns an integer z which is the smallest integer such that z % x == 0 and z % y == 0

BigInt
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.

BigInt
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
Power_Mod
implementation.

BigInt
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.

bool
is_prime
(BigInt n, RandomNumberGenerator &rng, size_t prob = 56, double is_random = false)¶ Test n for primality using a probablistic algorithm (MillerRabin). With this algorithm, there is some nonzero 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 2^{prob}. 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.

bool
quick_check_prime
(BigInt n, RandomNumberGenerator &rng)¶

bool
check_prime
(BigInt n, RandomNumberGenerator &rng)¶

bool
verify_prime
(BigInt n, RandomNumberGenerator &rng)¶ Three variations on is_prime, with probabilities set to 32, 56, and 80 respectively.

BigInt
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
bits
bits long that is relatively prime tocoprime
, and equivalent toequiv
moduloequiv_mod
.