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author | lloyd <[email protected]> | 2014-01-10 23:07:16 +0000 |
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committer | lloyd <[email protected]> | 2014-01-10 23:07:16 +0000 |
commit | ad6555f522ae16f6284e8dafa02f630b88bcf289 (patch) | |
tree | bd63c51dbeab75eb0f90c72589bc922141237056 /doc/manual/bigint.rst | |
parent | 6894dca64c04936d07048c0e8cbf7e25858548c3 (diff) |
Split up docs into the reference manual, the website, and everything else.
Add `website` target to makefile.
Some progress towards fixing minimized builds.
TLS now hard requires ECDSA and GCM since otherwise a minimized build
has only insecure options.
Remove boost_thread dependency in command line tool
Diffstat (limited to 'doc/manual/bigint.rst')
-rw-r--r-- | doc/manual/bigint.rst | 96 |
1 files changed, 96 insertions, 0 deletions
diff --git a/doc/manual/bigint.rst b/doc/manual/bigint.rst new file mode 100644 index 000000000..66a055eb7 --- /dev/null +++ b/doc/manual/bigint.rst @@ -0,0 +1,96 @@ +BigInt +======================================== + +``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 ``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: + +.. cpp:function:: secure_vector<byte> BigInt::encode(const BigInt& n, Encoding enc = Binary) + + This function encodes the BigInt n into a memory + vector. ``Encoding`` is an enum that has values ``Binary``, + ``Decimal``, and ``Hexadecimal``. + +.. cpp:function:: BigInt BigInt::decode(const std::vector<byte>& 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<byte> 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: + +.. cpp:function:: BigInt gcd(BigInt x, BigInt y) + + Returns the greatest common divisor of x and y + +.. cpp:function:: BigInt lcm(BigInt x, BigInt y) + + Returns an integer z which is the smallest integer such that z % x + == 0 and z % y == 0 + +.. cpp:function:: 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. + +.. cpp:function:: 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. + +.. cpp:function:: 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. + +.. cpp:function:: bool quick_check_prime(BigInt n, RandomNumberGenerator& rng) + +.. cpp:function:: bool check_prime(BigInt n, RandomNumberGenerator& rng) + +.. cpp:function:: bool verify_prime(BigInt n, RandomNumberGenerator& rng) + + Three variations on primality testing. All take an integer to test along with + a random number generator, and return true if the integer seems like it might + be prime; there is a chance that this function will return true even with + a composite number. The probability decreases with the amount of work performed, + so it is much less likely that ``verify_prime`` will return a false positive + than ``check_prime`` will. + +.. cpp:function 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 to ``coprime``, and equivalent to ``equiv`` modulo + ``equiv_mod``. + |