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+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``.
+
+.. note::
+
+  If you can, always use expressions of the form ``a += b`` over ``a =
+  a + b``. The difference can be *very* substantial, because the first
+  form prevents at least one needless memory allocation, and possibly
+  as many as three. This will be less of an issue once the library
+  adopts use of C++0x's rvalue references.
+
+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``,
+  ``Octal``, ``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,
+hexadecimal numbers (marked with a leading "0x"), and octal numbers
+(marked with a leading '0'). The '-' must come before the "0x" or '0'
+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``.
+