1 files changed, 346 insertions, 0 deletions
diff --git a/old/botan/src/math/numbertheory/numthry.cpp b/old/botan/src/math/numbertheory/numthry.cpp
new file mode 100644
index 0000000..4486813
--- /dev/null
+++ b/old/botan/src/math/numbertheory/numthry.cpp
@@ -0,0 +1,346 @@
+/*
+* Number Theory Functions
+* (C) 1999-2009 Jack Lloyd
+*
+* Distributed under the terms of the Botan license
+*/
+
+#include <botan/numthry.h>
+#include <botan/bit_ops.h>
+#include <algorithm>
+
+namespace Botan {
+
+namespace {
+
+/*
+* Miller-Rabin Iterations
+*/
+u32bit miller_rabin_test_iterations(u32bit bits, bool verify)
+   {
+   struct mapping { u32bit bits; u32bit verify_iter; u32bit check_iter; };
+
+   static const mapping tests[] = {
+      {   50, 55, 25 },
+      {  100, 38, 22 },
+      {  160, 32, 18 },
+      {  163, 31, 17 },
+      {  168, 30, 16 },
+      {  177, 29, 16 },
+      {  181, 28, 15 },
+      {  185, 27, 15 },
+      {  190, 26, 15 },
+      {  195, 25, 14 },
+      {  201, 24, 14 },
+      {  208, 23, 14 },
+      {  215, 22, 13 },
+      {  222, 21, 13 },
+      {  231, 20, 13 },
+      {  241, 19, 12 },
+      {  252, 18, 12 },
+      {  264, 17, 12 },
+      {  278, 16, 11 },
+      {  294, 15, 10 },
+      {  313, 14,  9 },
+      {  334, 13,  8 },
+      {  360, 12,  8 },
+      {  392, 11,  7 },
+      {  430, 10,  7 },
+      {  479,  9,  6 },
+      {  542,  8,  6 },
+      {  626,  7,  5 },
+      {  746,  6,  4 },
+      {  926,  5,  3 },
+      { 1232,  4,  2 },
+      { 1853,  3,  2 },
+      {    0,  0,  0 }
+   };
+
+   for(u32bit i = 0; tests[i].bits; ++i)
+      {
+      if(bits <= tests[i].bits)
+         {
+         if(verify)
+            return tests[i].verify_iter;
+         else
+            return tests[i].check_iter;
+         }
+      }
+   return 2;
+   }
+
+}
+
+/*
+* Return the number of 0 bits at the end of n
+*/
+u32bit low_zero_bits(const BigInt& n)
+   {
+   if(n.is_negative() || n.is_zero()) return 0;
+
+   u32bit low_zero = 0;
+
+   if(n.is_positive() && n.is_nonzero())
+      {
+      for(u32bit i = 0; i != n.size(); ++i)
+         {
+         word x = n[i];
+
+         if(x)
+            {
+            low_zero += ctz(x);
+            break;
+            }
+         else
+            low_zero += BOTAN_MP_WORD_BITS;
+         }
+      }
+
+   return low_zero;
+   }
+
+/*
+* Calculate the GCD
+*/
+BigInt gcd(const BigInt& a, const BigInt& b)
+   {
+   if(a.is_zero() || b.is_zero()) return 0;
+   if(a == 1 || b == 1)           return 1;
+
+   BigInt x = a, y = b;
+   x.set_sign(BigInt::Positive);
+   y.set_sign(BigInt::Positive);
+   u32bit shift = std::min(low_zero_bits(x), low_zero_bits(y));
+
+   x >>= shift;
+   y >>= shift;
+
+   while(x.is_nonzero())
+      {
+      x >>= low_zero_bits(x);
+      y >>= low_zero_bits(y);
+      if(x >= y) { x -= y; x >>= 1; }
+      else       { y -= x; y >>= 1; }
+      }
+
+   return (y << shift);
+   }
+
+/*
+* Calculate the LCM
+*/
+BigInt lcm(const BigInt& a, const BigInt& b)
+   {
+   return ((a * b) / gcd(a, b));
+   }
+
+/*
+* Find the Modular Inverse
+*/
+BigInt inverse_mod(const BigInt& n, const BigInt& mod)
+   {
+   if(mod.is_zero())
+      throw BigInt::DivideByZero();
+   if(mod.is_negative() || n.is_negative())
+      throw Invalid_Argument("inverse_mod: arguments must be non-negative");
+
+   if(n.is_zero() || (n.is_even() && mod.is_even()))
+      return 0;
+
+   BigInt x = mod, y = n, u = mod, v = n;
+   BigInt A = 1, B = 0, C = 0, D = 1;
+
+   while(u.is_nonzero())
+      {
+      u32bit zero_bits = low_zero_bits(u);
+      u >>= zero_bits;
+      for(u32bit i = 0; i != zero_bits; ++i)
+         {
+         if(A.is_odd() || B.is_odd())
+            { A += y; B -= x; }
+         A >>= 1; B >>= 1;
+         }
+
+      zero_bits = low_zero_bits(v);
+      v >>= zero_bits;
+      for(u32bit i = 0; i != zero_bits; ++i)
+         {
+         if(C.is_odd() || D.is_odd())
+            { C += y; D -= x; }
+         C >>= 1; D >>= 1;
+         }
+
+      if(u >= v) { u -= v; A -= C; B -= D; }
+      else       { v -= u; C -= A; D -= B; }
+      }
+
+   if(v != 1)
+      return 0;
+
+   while(D.is_negative()) D += mod;
+   while(D >= mod) D -= mod;
+
+   return D;
+   }
+
+/*
+* Modular Exponentiation
+*/
+BigInt power_mod(const BigInt& base, const BigInt& exp, const BigInt& mod)
+   {
+   Power_Mod pow_mod(mod);
+   pow_mod.set_base(base);
+   pow_mod.set_exponent(exp);
+   return pow_mod.execute();
+   }
+
+/*
+* Do simple tests of primality
+*/
+s32bit simple_primality_tests(const BigInt& n)
+   {
+   const s32bit NOT_PRIME = -1, UNKNOWN = 0, PRIME = 1;
+
+   if(n == 2)
+      return PRIME;
+   if(n <= 1 || n.is_even())
+      return NOT_PRIME;
+
+   if(n <= PRIMES[PRIME_TABLE_SIZE-1])
+      {
+      const word num = n.word_at(0);
+      for(u32bit i = 0; PRIMES[i]; ++i)
+         {
+         if(num == PRIMES[i]) return PRIME;
+         if(num <  PRIMES[i]) return NOT_PRIME;
+         }
+      return NOT_PRIME;
+      }
+
+   u32bit check_first = std::min(n.bits() / 32, PRIME_PRODUCTS_TABLE_SIZE);
+   for(u32bit i = 0; i != check_first; ++i)
+      if(gcd(n, PRIME_PRODUCTS[i]) != 1)
+         return NOT_PRIME;
+
+   return UNKNOWN;
+   }
+
+/*
+* Fast check of primality
+*/
+bool check_prime(const BigInt& n, RandomNumberGenerator& rng)
+   {
+   return run_primality_tests(rng, n, 0);
+   }
+
+/*
+* Test for primality
+*/
+bool is_prime(const BigInt& n, RandomNumberGenerator& rng)
+   {
+   return run_primality_tests(rng, n, 1);
+   }
+
+/*
+* Verify primality
+*/
+bool verify_prime(const BigInt& n, RandomNumberGenerator& rng)
+   {
+   return run_primality_tests(rng, n, 2);
+   }
+
+/*
+* Verify primality
+*/
+bool run_primality_tests(RandomNumberGenerator& rng,
+                         const BigInt& n, u32bit level)
+   {
+   s32bit simple_tests = simple_primality_tests(n);
+   if(simple_tests) return (simple_tests == 1) ? true : false;
+   return passes_mr_tests(rng, n, level);
+   }
+
+/*
+* Test for primaility using Miller-Rabin
+*/
+bool passes_mr_tests(RandomNumberGenerator& rng,
+                     const BigInt& n, u32bit level)
+   {
+   const u32bit PREF_NONCE_BITS = 40;
+
+   if(level > 2)
+      level = 2;
+
+   MillerRabin_Test mr(n);
+
+   if(!mr.passes_test(2))
+      return false;
+
+   if(level == 0)
+      return true;
+
+   const u32bit NONCE_BITS = std::min(n.bits() - 1, PREF_NONCE_BITS);
+
+   const bool verify = (level == 2);
+
+   u32bit tests = miller_rabin_test_iterations(n.bits(), verify);
+
+   BigInt nonce;
+   for(u32bit i = 0; i != tests; ++i)
+      {
+      if(!verify && PRIMES[i] < (n-1))
+         nonce = PRIMES[i];
+      else
+         {
+         while(nonce < 2 || nonce >= (n-1))
+            nonce.randomize(rng, NONCE_BITS);
+         }
+
+      if(!mr.passes_test(nonce))
+         return false;
+      }
+   return true;
+   }
+
+/*
+* Miller-Rabin Test
+*/
+bool MillerRabin_Test::passes_test(const BigInt& a)
+   {
+   if(a < 2 || a >= n_minus_1)
+      throw Invalid_Argument("Bad size for nonce in Miller-Rabin test");
+
+   BigInt y = pow_mod(a);
+   if(y == 1 || y == n_minus_1)
+      return true;
+
+   for(u32bit i = 1; i != s; ++i)
+      {
+      y = reducer.square(y);
+
+      if(y == 1)
+         return false;
+      if(y == n_minus_1)
+         return true;
+      }
+   return false;
+   }
+
+/*
+* Miller-Rabin Constructor
+*/
+MillerRabin_Test::MillerRabin_Test(const BigInt& num)
+   {
+   if(num.is_even() || num < 3)
+      throw Invalid_Argument("MillerRabin_Test: Invalid number for testing");
+
+   n = num;
+   n_minus_1 = n - 1;
+   s = low_zero_bits(n_minus_1);
+   r = n_minus_1 >> s;
+
+   pow_mod = Fixed_Exponent_Power_Mod(r, n);
+   reducer = Modular_Reducer(n);
+   }
+
+}