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authorlloyd <lloyd@randombit.net>2011-04-04 17:00:17 +0000
committerlloyd <lloyd@randombit.net>2011-04-04 17:00:17 +0000
commitc84143c2cb2554213399aee6d31e09d26aece6c8 (patch)
treeb7a2ee1dce0c111d666a2b68af6b5e128b88b144
parentac8ef535a24bd9418f52c27499e143b00844042d (diff)
A bit more BigInt documentation
-rw-r--r--doc/bigint.txt89
1 files changed, 64 insertions, 25 deletions
diff --git a/doc/bigint.txt b/doc/bigint.txt
index 1cdc685d3..cf42726cc 100644
--- a/doc/bigint.txt
+++ b/doc/bigint.txt
@@ -2,14 +2,24 @@ 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``.
+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``.
-Probably the most important are the encoding/decoding functions, which
-transform the normal representation of a ``BigInt`` into some other
-form, such as a decimal string.
+.. 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:: SecureVector<byte> BigInt::encode(const BigInt& n, Encoding enc = Binary)
@@ -42,23 +52,52 @@ you want such things, you'll have to do them yourself.
unsigned integer or a string. You can also decode an array (a ``byte``
pointer plus a length) into a ``BigInt`` using a constructor.
-Efficiency Hints
+Number Theory
----------------------------------------
-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.
-
-If you're doing repeated modular exponentiations with the same modulus, create
-a ``BarrettReducer`` ahead of time. If the exponent or base is a constant,
-use the classes in ``mod_exp.h``. This stuff is all handled for you by
-the normal high-level interfaces, of course.
-
-Never use the low-level MPI functions (those that begin with
-``bigint_``). These are completely internal to the library, and
-may make arbitrarily strange and undocumented assumptions about their
-inputs, and don't check to see if they are true, on the assumption
-that only the library itself calls them, and that the library knows
-what the assumptions are. The interfaces for these functions can
-change completely without notice.
+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``.
+