17209789316

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Merge 3014a1a0c into 0852a2a74

Pull Request Pull Request #5047: X.509 Path: Option for Non-Self-Signed Trust Anchors

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/src/lib/math/numbertheory/numthry.cpp

/*
* Number Theory Functions
* (C) 1999-2011,2016,2018,2019 Jack Lloyd
* (C) 2007,2008 Falko Strenzke, FlexSecure GmbH
*
* Botan is released under the Simplified BSD License (see license.txt)
*/

#include <botan/numthry.h>

#include <botan/rng.h>
#include <botan/internal/barrett.h>
#include <botan/internal/ct_utils.h>
#include <botan/internal/divide.h>
#include <botan/internal/monty.h>
#include <botan/internal/monty_exp.h>
#include <botan/internal/mp_core.h>
#include <botan/internal/primality.h>
#include <algorithm>

namespace Botan {

/*
* Tonelli-Shanks algorithm
*/
BigInt sqrt_modulo_prime(const BigInt& a, const BigInt& p) {
   BOTAN_ARG_CHECK(p > 1, "invalid prime");
   BOTAN_ARG_CHECK(a < p, "value to solve for must be less than p");
   BOTAN_ARG_CHECK(a >= 0, "value to solve for must not be negative");

   // some very easy cases
   if(p == 2 || a <= 1) {
      return a;
   }

   BOTAN_ARG_CHECK(p.is_odd(), "invalid prime");

   if(jacobi(a, p) != 1) {  // not a quadratic residue
      return BigInt::from_s32(-1);
   }

   auto mod_p = Barrett_Reduction::for_public_modulus(p);
   const Montgomery_Params monty_p(p, mod_p);

   // If p == 3 (mod 4) there is a simple solution
   if(p % 4 == 3) {
      return monty_exp_vartime(monty_p, a, ((p + 1) >> 2)).value();
   }

   // Otherwise we have to use Shanks-Tonelli
   size_t s = low_zero_bits(p - 1);
   BigInt q = p >> s;

   q -= 1;
   q >>= 1;

   BigInt r = monty_exp_vartime(monty_p, a, q).value();
   BigInt n = mod_p.multiply(a, mod_p.square(r));
   r = mod_p.multiply(r, a);

   if(n == 1) {
      return r;
   }

   // find random quadratic nonresidue z
   word z = 2;
   for(;;) {
      if(jacobi(BigInt::from_word(z), p) == -1) {  // found one
         break;
      }

      z += 1;  // try next z

      /*
      * The expected number of tests to find a non-residue modulo a
      * prime is 2. If we have not found one after 256 then almost
      * certainly we have been given a non-prime p.
      */
      if(z >= 256) {
         return BigInt::from_s32(-1);
      }
   }

   BigInt c = monty_exp_vartime(monty_p, BigInt::from_word(z), (q << 1) + 1).value();

   while(n > 1) {
      q = n;

      size_t i = 0;
      while(q != 1) {
         q = mod_p.square(q);
         ++i;

         if(i >= s) {
            return BigInt::from_s32(-1);
         }
      }

      BOTAN_ASSERT_NOMSG(s >= (i + 1));  // No underflow!
      c = monty_exp_vartime(monty_p, c, BigInt::power_of_2(s - i - 1)).value();
      r = mod_p.multiply(r, c);
      c = mod_p.square(c);
      n = mod_p.multiply(n, c);

      // s decreases as the algorithm proceeds
      BOTAN_ASSERT_NOMSG(s >= i);
      s = i;
   }

   return r;
}

/*
* Calculate the Jacobi symbol
*
* See Algorithm 2.149 in Handbook of Applied Cryptography
*/
int32_t jacobi(BigInt a, BigInt n) {
   BOTAN_ARG_CHECK(n.is_odd() && n >= 3, "Argument n must be an odd integer >= 3");

   if(a < 0 || a >= n) {
      a %= n;
   }

   if(a == 0) {
      return 0;
   }
   if(a == 1) {
      return 1;
   }

   int32_t s = 1;

   for(;;) {
      const size_t e = low_zero_bits(a);
      a >>= e;
      const word n_mod_8 = n.word_at(0) % 8;
      const word n_mod_4 = n_mod_8 % 4;

      if(e % 2 == 1 && (n_mod_8 == 3 || n_mod_8 == 5)) {
         s = -s;
      }

      if(n_mod_4 == 3 && a % 4 == 3) {
         s = -s;
      }

      /*
      * The HAC presentation of the algorithm uses recursion, which is not
      * desirable or necessary.
      *
      * Instead we loop accumulating the product of the various jacobi()
      * subcomputations into s, until we reach algorithm termination, which
      * occurs in one of two ways.
      *
      * If a == 1 then the recursion has completed; we can return the value of s.
      *
      * Otherwise, after swapping and reducing, check for a == 0 [this value is
      * called `n1` in HAC's presentation]. This would imply that jacobi(n1,a1)
      * would have the value 0, due to Line 1 in HAC 2.149, in which case the
      * entire product is zero, and we can immediately return that result.
      */

      if(a == 1) {
         return s;
      }

      std::swap(a, n);

      BOTAN_ASSERT_NOMSG(n.is_odd());

      a %= n;

      if(a == 0) {
         return 0;
      }
   }
}

/*
* Square a BigInt
*/
BigInt square(const BigInt& x) {
   BigInt z = x;
   secure_vector<word> ws;
   z.square(ws);
   return z;
}

/*
* Return the number of 0 bits at the end of n
*/
size_t low_zero_bits(const BigInt& n) {
   size_t low_zero = 0;

   auto seen_nonempty_word = CT::Mask<word>::cleared();

   for(size_t i = 0; i != n.size(); ++i) {
      const word x = n.word_at(i);

      // ctz(0) will return sizeof(word)
      const size_t tz_x = ctz(x);

      // if x > 0 we want to count tz_x in total but not any
      // further words, so set the mask after the addition
      low_zero += seen_nonempty_word.if_not_set_return(tz_x);

      seen_nonempty_word |= CT::Mask<word>::expand(x);
   }

   // if we saw no words with x > 0 then n == 0 and the value we have
   // computed is meaningless. Instead return BigInt::zero() in that case.
   return static_cast<size_t>(seen_nonempty_word.if_set_return(low_zero));
}

/*
* Calculate the GCD in constant time
*/
BigInt gcd(const BigInt& a, const BigInt& b) {
   if(a.is_zero()) {
      return abs(b);
   }
   if(b.is_zero()) {
      return abs(a);
   }

   const size_t sz = std::max(a.sig_words(), b.sig_words());
   auto u = BigInt::with_capacity(sz);
   auto v = BigInt::with_capacity(sz);
   u += a;
   v += b;

   CT::poison_all(u, v);

   u.set_sign(BigInt::Positive);
   v.set_sign(BigInt::Positive);

   // In the worst case we have two fully populated big ints. After right
   // shifting so many times, we'll have reached the result for sure.
   const size_t loop_cnt = u.bits() + v.bits();

   // This temporary is big enough to hold all intermediate results of the
   // algorithm. No reallocation will happen during the loop.
   // Note however, that `ct_cond_assign()` will invalidate the 'sig_words'
   // cache, which _does not_ shrink the capacity of the underlying buffer.
   auto tmp = BigInt::with_capacity(sz);
   secure_vector<word> ws(sz * 2);
   size_t factors_of_two = 0;
   for(size_t i = 0; i != loop_cnt; ++i) {
      auto both_odd = CT::Mask<word>::expand_bool(u.is_odd()) & CT::Mask<word>::expand_bool(v.is_odd());

      // Subtract the smaller from the larger if both are odd
      auto u_gt_v = CT::Mask<word>::expand_bool(bigint_cmp(u._data(), u.size(), v._data(), v.size()) > 0);
      bigint_sub_abs(tmp.mutable_data(), u._data(), v._data(), sz, ws.data());
      u.ct_cond_assign((u_gt_v & both_odd).as_bool(), tmp);
      v.ct_cond_assign((~u_gt_v & both_odd).as_bool(), tmp);

      const auto u_is_even = CT::Mask<word>::expand_bool(u.is_even());
      const auto v_is_even = CT::Mask<word>::expand_bool(v.is_even());
      BOTAN_DEBUG_ASSERT((u_is_even | v_is_even).as_bool());

      // When both are even, we're going to eliminate a factor of 2.
      // We have to reapply this factor to the final result.
      factors_of_two += (u_is_even & v_is_even).if_set_return(1);

      // remove one factor of 2, if u is even
      bigint_shr2(tmp.mutable_data(), u._data(), sz, 1);
      u.ct_cond_assign(u_is_even.as_bool(), tmp);

      // remove one factor of 2, if v is even
      bigint_shr2(tmp.mutable_data(), v._data(), sz, 1);
      v.ct_cond_assign(v_is_even.as_bool(), tmp);
   }

   // The GCD (without factors of two) is either in u or v, the other one is
   // zero. The non-zero variable _must_ be odd, because all factors of two were
   // removed in the loop iterations above.
   BOTAN_DEBUG_ASSERT(u.is_zero() || v.is_zero());
   BOTAN_DEBUG_ASSERT(u.is_odd() || v.is_odd());

   // make sure that the GCD (without factors of two) is in u
   u.ct_cond_assign(u.is_even() /* .is_zero() would not be constant time */, v);

   // re-apply the factors of two
   u.ct_shift_left(factors_of_two);

   CT::unpoison_all(u, v);

   return u;
}

/*
* Calculate the LCM
*/
BigInt lcm(const BigInt& a, const BigInt& b) {
   if(a == b) {
      return a;
   }

   auto ab = a * b;
   ab.set_sign(BigInt::Positive);  // ignore the signs of a & b
   const auto g = gcd(a, b);
   return ct_divide(ab, g);
}

/*
* Modular Exponentiation
*/
BigInt power_mod(const BigInt& base, const BigInt& exp, const BigInt& mod) {
   if(mod.is_negative() || mod == 1) {
      return BigInt::zero();
   }

   if(base.is_zero() || mod.is_zero()) {
      if(exp.is_zero()) {
         return BigInt::one();
      }
      return BigInt::zero();
   }

   auto reduce_mod = Barrett_Reduction::for_secret_modulus(mod);

   const size_t exp_bits = exp.bits();

   if(mod.is_odd()) {
      const Montgomery_Params monty_params(mod, reduce_mod);
      return monty_exp(monty_params, ct_modulo(base, mod), exp, exp_bits).value();
   }

   /*
   Support for even modulus is just a convenience and not considered
   cryptographically important, so this implementation is slow ...
   */
   BigInt accum = BigInt::one();
   BigInt g = ct_modulo(base, mod);
   BigInt t;

   for(size_t i = 0; i != exp_bits; ++i) {
      t = reduce_mod.multiply(g, accum);
      g = reduce_mod.square(g);
      accum.ct_cond_assign(exp.get_bit(i), t);
   }
   return accum;
}

BigInt is_perfect_square(const BigInt& C) {
   if(C < 1) {
      throw Invalid_Argument("is_perfect_square requires C >= 1");
   }
   if(C == 1) {
      return BigInt::one();
   }

   const size_t n = C.bits();
   const size_t m = (n + 1) / 2;
   const BigInt B = C + BigInt::power_of_2(m);

   BigInt X = BigInt::power_of_2(m) - 1;
   BigInt X2 = (X * X);

   for(;;) {
      X = (X2 + C) / (2 * X);
      X2 = (X * X);

      if(X2 < B) {
         break;
      }
   }

   if(X2 == C) {
      return X;
   } else {
      return BigInt::zero();
   }
}

/*
* Test for primality using Miller-Rabin
*/
bool is_prime(const BigInt& n, RandomNumberGenerator& rng, size_t prob, bool is_random) {
   if(n == 2) {
      return true;
   }
   if(n <= 1 || n.is_even()) {
      return false;
   }

   const size_t n_bits = n.bits();

   // Fast path testing for small numbers (<= 65521)
   if(n_bits <= 16) {
      const uint16_t num = static_cast<uint16_t>(n.word_at(0));

      return std::binary_search(PRIMES, PRIMES + PRIME_TABLE_SIZE, num);
   }

   auto mod_n = Barrett_Reduction::for_secret_modulus(n);

   if(rng.is_seeded()) {
      const size_t t = miller_rabin_test_iterations(n_bits, prob, is_random);

      if(!is_miller_rabin_probable_prime(n, mod_n, rng, t)) {
         return false;
      }

      if(is_random) {
         return true;
      } else {
         return is_lucas_probable_prime(n, mod_n);
      }
   } else {
      return is_bailie_psw_probable_prime(n, mod_n);
   }
}

}  // namespace Botan

1	/*
2	* Number Theory Functions
3	* (C) 1999-2011,2016,2018,2019 Jack Lloyd
4	* (C) 2007,2008 Falko Strenzke, FlexSecure GmbH
5	*
6	* Botan is released under the Simplified BSD License (see license.txt)
7	*/
8
9	#include <botan/numthry.h>
10
11	#include <botan/rng.h>
12	#include <botan/internal/barrett.h>
13	#include <botan/internal/ct_utils.h>
14	#include <botan/internal/divide.h>
15	#include <botan/internal/monty.h>
16	#include <botan/internal/monty_exp.h>
17	#include <botan/internal/mp_core.h>
18	#include <botan/internal/primality.h>
19	#include <algorithm>
20
21	namespace Botan {
22
23	/*
24	* Tonelli-Shanks algorithm
25	*/
26	BigInt sqrt_modulo_prime(const BigInt& a, const BigInt& p) {	1,474✔
27	BOTAN_ARG_CHECK(p > 1, "invalid prime");	1,474✔
28	BOTAN_ARG_CHECK(a < p, "value to solve for must be less than p");	1,474✔
29	BOTAN_ARG_CHECK(a >= 0, "value to solve for must not be negative");	1,474✔
30
31	// some very easy cases
32	if(p == 2 \|\| a <= 1) {	2,946✔
33	return a;	3✔
34	}
35
36	BOTAN_ARG_CHECK(p.is_odd(), "invalid prime");	2,942✔
37
38	if(jacobi(a, p) != 1) { // not a quadratic residue	1,471✔
39	return BigInt::from_s32(-1);	133✔
40	}
41
42	auto mod_p = Barrett_Reduction::for_public_modulus(p);	1,338✔
43	const Montgomery_Params monty_p(p, mod_p);	1,338✔
44
45	// If p == 3 (mod 4) there is a simple solution
46	if(p % 4 == 3) {	1,338✔
47	return monty_exp_vartime(monty_p, a, ((p + 1) >> 2)).value();	984✔
48	}
49
50	// Otherwise we have to use Shanks-Tonelli
51	size_t s = low_zero_bits(p - 1);	354✔
52	BigInt q = p >> s;	354✔
53
54	q -= 1;	354✔
55	q >>= 1;	354✔
56
57	BigInt r = monty_exp_vartime(monty_p, a, q).value();	354✔
58	BigInt n = mod_p.multiply(a, mod_p.square(r));	354✔
59	r = mod_p.multiply(r, a);	354✔
60
61	if(n == 1) {	354✔
62	return r;	169✔
63	}
64
65	// find random quadratic nonresidue z
66	word z = 2;
67	for(;;) {	501✔
68	if(jacobi(BigInt::from_word(z), p) == -1) { // found one	501✔
69	break;
70	}
71
72	z += 1; // try next z	317✔
73
74	/*
75	* The expected number of tests to find a non-residue modulo a
76	* prime is 2. If we have not found one after 256 then almost
77	* certainly we have been given a non-prime p.
78	*/
79	if(z >= 256) {	317✔
80	return BigInt::from_s32(-1);	1✔
81	}
82	}
83
84	BigInt c = monty_exp_vartime(monty_p, BigInt::from_word(z), (q << 1) + 1).value();	368✔
85
86	while(n > 1) {	567✔
87	q = n;	389✔
88
89	size_t i = 0;	389✔
90	while(q != 1) {	10,766✔
91	q = mod_p.square(q);	10,383✔
92	++i;	10,383✔
93
94	if(i >= s) {	10,383✔
95	return BigInt::from_s32(-1);	6✔
96	}
97	}
98
99	BOTAN_ASSERT_NOMSG(s >= (i + 1)); // No underflow!	383✔
100	c = monty_exp_vartime(monty_p, c, BigInt::power_of_2(s - i - 1)).value();	383✔
101	r = mod_p.multiply(r, c);	383✔
102	c = mod_p.square(c);	383✔
103	n = mod_p.multiply(n, c);	383✔
104
105	// s decreases as the algorithm proceeds
106	BOTAN_ASSERT_NOMSG(s >= i);	383✔
107	s = i;
108	}
109
110	return r;	178✔
111	}	3,030✔
112
113	/*
114	* Calculate the Jacobi symbol
115	*
116	* See Algorithm 2.149 in Handbook of Applied Cryptography
117	*/
118	int32_t jacobi(BigInt a, BigInt n) {	101,833✔
119	BOTAN_ARG_CHECK(n.is_odd() && n >= 3, "Argument n must be an odd integer >= 3");	305,499✔
120
121	if(a < 0 \|\| a >= n) {	172,487✔
122	a %= n;	31,451✔
123	}
124
125	if(a == 0) {	101,833✔
126	return 0;
127	}
128	if(a == 1) {	101,810✔
129	return 1;
130	}
131
132	int32_t s = 1;
133
134	for(;;) {	389,966✔
135	const size_t e = low_zero_bits(a);	389,966✔
136	a >>= e;	389,966✔
137	const word n_mod_8 = n.word_at(0) % 8;	389,966✔
138	const word n_mod_4 = n_mod_8 % 4;	389,966✔
139
140	if(e % 2 == 1 && (n_mod_8 == 3 \|\| n_mod_8 == 5)) {	389,966✔
141	s = -s;	66,997✔
142	}
143
144	if(n_mod_4 == 3 && a % 4 == 3) {	389,966✔
145	s = -s;	68,310✔
146	}
147
148	/*
149	* The HAC presentation of the algorithm uses recursion, which is not
150	* desirable or necessary.
151	*
152	* Instead we loop accumulating the product of the various jacobi()
153	* subcomputations into s, until we reach algorithm termination, which
154	* occurs in one of two ways.
155	*
156	* If a == 1 then the recursion has completed; we can return the value of s.
157	*
158	* Otherwise, after swapping and reducing, check for a == 0 [this value is
159	* called `n1` in HAC's presentation]. This would imply that jacobi(n1,a1)
160	* would have the value 0, due to Line 1 in HAC 2.149, in which case the
161	* entire product is zero, and we can immediately return that result.
162	*/
163
164	if(a == 1) {	389,966✔
165	return s;	85,184✔
166	}
167
168	std::swap(a, n);	304,782✔
169
170	BOTAN_ASSERT_NOMSG(n.is_odd());	609,564✔
171
172	a %= n;	304,782✔
173
174	if(a == 0) {	304,782✔
175	return 0;
176	}
177	}
178	}
179
180	/*
181	* Square a BigInt
182	*/
183	BigInt square(const BigInt& x) {	1,021✔
184	BigInt z = x;	1,021✔
185	secure_vector<word> ws;	1,021✔
186	z.square(ws);	1,021✔
187	return z;	1,021✔
188	}	1,021✔
189
190	/*
191	* Return the number of 0 bits at the end of n
192	*/
193	size_t low_zero_bits(const BigInt& n) {	628,912✔
194	size_t low_zero = 0;	628,912✔
195
196	auto seen_nonempty_word = CT::Mask<word>::cleared();	628,912✔
197
198	for(size_t i = 0; i != n.size(); ++i) {	6,630,666✔
199	const word x = n.word_at(i);	6,001,754✔
200
201	// ctz(0) will return sizeof(word)
202	const size_t tz_x = ctz(x);	6,001,754✔
203
204	// if x > 0 we want to count tz_x in total but not any
205	// further words, so set the mask after the addition
206	low_zero += seen_nonempty_word.if_not_set_return(tz_x);	6,001,754✔
207
208	seen_nonempty_word \|= CT::Mask<word>::expand(x);	6,001,754✔
209	}
210
211	// if we saw no words with x > 0 then n == 0 and the value we have
212	// computed is meaningless. Instead return BigInt::zero() in that case.
213	return static_cast<size_t>(seen_nonempty_word.if_set_return(low_zero));	628,912✔
214	}
215
216	/*
217	* Calculate the GCD in constant time
218	*/
219	BigInt gcd(const BigInt& a, const BigInt& b) {	26,639✔
220	if(a.is_zero()) {	28,800✔
221	return abs(b);	3✔
222	}
223	if(b.is_zero()) {	27,076✔
224	return abs(a);	26,639✔
225	}
226
227	const size_t sz = std::max(a.sig_words(), b.sig_words());	26,634✔
228	auto u = BigInt::with_capacity(sz);	26,634✔
229	auto v = BigInt::with_capacity(sz);	26,634✔
230	u += a;	26,634✔
231	v += b;	26,634✔
232
233	CT::poison_all(u, v);	26,634✔
234
235	u.set_sign(BigInt::Positive);	26,634✔
236	v.set_sign(BigInt::Positive);	26,634✔
237
238	// In the worst case we have two fully populated big ints. After right
239	// shifting so many times, we'll have reached the result for sure.
240	const size_t loop_cnt = u.bits() + v.bits();	26,634✔
241
242	// This temporary is big enough to hold all intermediate results of the
243	// algorithm. No reallocation will happen during the loop.
244	// Note however, that `ct_cond_assign()` will invalidate the 'sig_words'
245	// cache, which _does not_ shrink the capacity of the underlying buffer.
246	auto tmp = BigInt::with_capacity(sz);	26,634✔
247	secure_vector<word> ws(sz * 2);	26,634✔
248	size_t factors_of_two = 0;	26,634✔
249	for(size_t i = 0; i != loop_cnt; ++i) {	5,735,716✔
250	auto both_odd = CT::Mask<word>::expand_bool(u.is_odd()) & CT::Mask<word>::expand_bool(v.is_odd());	17,127,246✔
251
252	// Subtract the smaller from the larger if both are odd
253	auto u_gt_v = CT::Mask<word>::expand_bool(bigint_cmp(u._data(), u.size(), v._data(), v.size()) > 0);	5,709,082✔
254	bigint_sub_abs(tmp.mutable_data(), u._data(), v._data(), sz, ws.data());	5,709,082✔
255	u.ct_cond_assign((u_gt_v & both_odd).as_bool(), tmp);	5,709,082✔
256	v.ct_cond_assign((~u_gt_v & both_odd).as_bool(), tmp);	5,709,082✔
257
258	const auto u_is_even = CT::Mask<word>::expand_bool(u.is_even());	11,418,164✔
259	const auto v_is_even = CT::Mask<word>::expand_bool(v.is_even());	11,418,164✔
260	BOTAN_DEBUG_ASSERT((u_is_even \| v_is_even).as_bool());	5,709,082✔
261
262	// When both are even, we're going to eliminate a factor of 2.
263	// We have to reapply this factor to the final result.
264	factors_of_two += (u_is_even & v_is_even).if_set_return(1);	5,709,082✔
265
266	// remove one factor of 2, if u is even
267	bigint_shr2(tmp.mutable_data(), u._data(), sz, 1);	5,709,082✔
268	u.ct_cond_assign(u_is_even.as_bool(), tmp);	5,709,082✔
269
270	// remove one factor of 2, if v is even
271	bigint_shr2(tmp.mutable_data(), v._data(), sz, 1);	5,709,082✔
272	v.ct_cond_assign(v_is_even.as_bool(), tmp);	5,709,082✔
273	}
274
275	// The GCD (without factors of two) is either in u or v, the other one is
276	// zero. The non-zero variable _must_ be odd, because all factors of two were
277	// removed in the loop iterations above.
278	BOTAN_DEBUG_ASSERT(u.is_zero() \|\| v.is_zero());	26,634✔
279	BOTAN_DEBUG_ASSERT(u.is_odd() \|\| v.is_odd());	26,634✔
280
281	// make sure that the GCD (without factors of two) is in u
282	u.ct_cond_assign(u.is_even() /* .is_zero() would not be constant time */, v);	53,268✔
283
284	// re-apply the factors of two
285	u.ct_shift_left(factors_of_two);	26,634✔
286
287	CT::unpoison_all(u, v);	26,634✔
288
289	return u;	26,634✔
290	}	26,634✔
291
292	/*
293	* Calculate the LCM
294	*/
295	BigInt lcm(const BigInt& a, const BigInt& b) {	4,636✔
296	if(a == b) {	4,636✔
297	return a;	×
298	}
299
300	auto ab = a * b;	4,636✔
301	ab.set_sign(BigInt::Positive); // ignore the signs of a & b	4,636✔
302	const auto g = gcd(a, b);	4,636✔
303	return ct_divide(ab, g);	4,636✔
304	}	4,636✔
305
306	/*
307	* Modular Exponentiation
308	*/
309	BigInt power_mod(const BigInt& base, const BigInt& exp, const BigInt& mod) {	71✔
310	if(mod.is_negative() \|\| mod == 1) {	142✔
311	return BigInt::zero();	×
312	}
313
314	if(base.is_zero() \|\| mod.is_zero()) {	206✔
315	if(exp.is_zero()) {	2✔
316	return BigInt::one();	1✔
317	}
318	return BigInt::zero();	×
319	}
320
321	auto reduce_mod = Barrett_Reduction::for_secret_modulus(mod);	70✔
322
323	const size_t exp_bits = exp.bits();	70✔
324
325	if(mod.is_odd()) {	70✔
326	const Montgomery_Params monty_params(mod, reduce_mod);	54✔
327	return monty_exp(monty_params, ct_modulo(base, mod), exp, exp_bits).value();	54✔
328	}	54✔
329
330	/*
331	Support for even modulus is just a convenience and not considered
332	cryptographically important, so this implementation is slow ...
333	*/
334	BigInt accum = BigInt::one();	16✔
335	BigInt g = ct_modulo(base, mod);	16✔
336	BigInt t;	16✔
337
338	for(size_t i = 0; i != exp_bits; ++i) {	3,907✔
339	t = reduce_mod.multiply(g, accum);	3,891✔
340	g = reduce_mod.square(g);	3,891✔
341	accum.ct_cond_assign(exp.get_bit(i), t);	7,782✔
342	}
343	return accum;	16✔
344	}	86✔
345
346	BigInt is_perfect_square(const BigInt& C) {	705✔
347	if(C < 1) {	705✔
348	throw Invalid_Argument("is_perfect_square requires C >= 1");	×
349	}
350	if(C == 1) {	705✔
351	return BigInt::one();	×
352	}
353
354	const size_t n = C.bits();	705✔
355	const size_t m = (n + 1) / 2;	705✔
356	const BigInt B = C + BigInt::power_of_2(m);	705✔
357
358	BigInt X = BigInt::power_of_2(m) - 1;	1,410✔
359	BigInt X2 = (X * X);	705✔
360
361	for(;;) {	1,659✔
362	X = (X2 + C) / (2 * X);	1,659✔
363	X2 = (X * X);	1,659✔
364
365	if(X2 < B) {	1,659✔
366	break;
367	}
368	}
369
370	if(X2 == C) {	705✔
371	return X;	63✔
372	} else {
373	return BigInt::zero();	642✔
374	}
375	}	705✔
376
377	/*
378	* Test for primality using Miller-Rabin
379	*/
380	bool is_prime(const BigInt& n, RandomNumberGenerator& rng, size_t prob, bool is_random) {	51,766✔
381	if(n == 2) {	51,766✔
382	return true;
383	}
384	if(n <= 1 \|\| n.is_even()) {	103,526✔
385	return false;
386	}
387
388	const size_t n_bits = n.bits();	51,695✔
389
390	// Fast path testing for small numbers (<= 65521)
391	if(n_bits <= 16) {	51,695✔
392	const uint16_t num = static_cast<uint16_t>(n.word_at(0));	32,802✔
393
394	return std::binary_search(PRIMES, PRIMES + PRIME_TABLE_SIZE, num);	32,802✔
395	}
396
397	auto mod_n = Barrett_Reduction::for_secret_modulus(n);	18,893✔
398
399	if(rng.is_seeded()) {	18,893✔
400	const size_t t = miller_rabin_test_iterations(n_bits, prob, is_random);	18,893✔
401
402	if(!is_miller_rabin_probable_prime(n, mod_n, rng, t)) {	18,893✔
403	return false;
404	}
405
406	if(is_random) {	3,357✔
407	return true;
408	} else {
409	return is_lucas_probable_prime(n, mod_n);	3,162✔
410	}
411	} else {
412	return is_bailie_psw_probable_prime(n, mod_n);	×
413	}
414	}	18,893✔
415
416	} // namespace Botan

randombit / botan / 17209789316

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