Initial checkin1.5.6

1 files changed, 323 insertions, 0 deletions

diff --git a/src/numthry.cpp b/src/numthry.cpp
new file mode 100644
index 000000000..382150906
--- /dev/null
+++ b/src/numthry.cpp
@@ -0,0 +1,323 @@
+/*************************************************
+* Number Theory Source File                      *
+* (C) 1999-2006 The Botan Project                *
+*************************************************/
+
+#include <botan/numthry.h>
+#include <botan/ui.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 j = 0; tests[j].bits; ++j)
+      {
+      if(bits <= tests[j].bits)
+         if(verify)
+            return tests[j].verify_iter;
+         else
+            return tests[j].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_zero()) return 0;
+
+   u32bit bits = 0, max_bits = n.bits();
+   while((n.get_bit(bits) == 0) && bits < max_bits)
+      ++bits;
+   return bits;
+   }
+
+/*************************************************
+* 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 j = 0; j != zero_bits; ++j)
+         {
+         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 j = 0; j != zero_bits; ++j)
+         {
+         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 j = 0; PRIMES[j]; ++j)
+         {
+         if(num == PRIMES[j]) return PRIME;
+         if(num <  PRIMES[j]) return NOT_PRIME;
+         }
+      return NOT_PRIME;
+      }
+
+   u32bit check_first = std::min(n.bits() / 32, PRIME_PRODUCTS_TABLE_SIZE);
+   for(u32bit j = 0; j != check_first; ++j)
+      if(gcd(n, PRIME_PRODUCTS[j]) != 1)
+         return NOT_PRIME;
+
+   return UNKNOWN;
+   }
+
+/*************************************************
+* Fast check of primality                        *
+*************************************************/
+bool check_prime(const BigInt& n)
+   {
+   return run_primality_tests(n, 0);
+   }
+
+/*************************************************
+* Test for primality                             *
+*************************************************/
+bool is_prime(const BigInt& n)
+   {
+   return run_primality_tests(n, 1);
+   }
+
+/*************************************************
+* Verify primality                               *
+*************************************************/
+bool verify_prime(const BigInt& n)
+   {
+   return run_primality_tests(n, 2);
+   }
+
+/*************************************************
+* Verify primality                               *
+*************************************************/
+bool run_primality_tests(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(n, level);
+   }
+
+/*************************************************
+* Test for primaility using Miller-Rabin         *
+*************************************************/
+bool passes_mr_tests(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 j = 0; j != tests; ++j)
+      {
+      if(verify) nonce = random_integer(NONCE_BITS);
+      else       nonce = PRIMES[j];
+
+      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");
+
+   UI::pulse(UI::PRIME_TESTING);
+
+   BigInt y = pow_mod(a);
+   if(y == 1 || y == n_minus_1)
+      return true;
+
+   for(u32bit j = 1; j != s; ++j)
+      {
+      UI::pulse(UI::PRIME_TESTING);
+      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);
+   }
+
+}