5123321399

Committed 30 May 2023 04:06PM UTC coverage: 92.213% (+0.004%) from 92.209%

Build # 5123321399

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Pull #3558

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web-flow

Commit Message

Merge dd72f7389 into 057bcbc35

Pull Request Pull Request #3558: Add braces around all if/else statements

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92.04

/src/lib/math/numbertheory/make_prm.cpp

/*
* Prime Generation
* (C) 1999-2007,2018,2019 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/

#include <botan/internal/primality.h>

#include <botan/numthry.h>
#include <botan/reducer.h>
#include <botan/rng.h>
#include <botan/internal/bit_ops.h>
#include <botan/internal/ct_utils.h>
#include <botan/internal/loadstor.h>
#include <algorithm>

namespace Botan {

namespace {

class Prime_Sieve final {
   public:
      Prime_Sieve(const BigInt& init_value, size_t sieve_size, word step, bool check_2p1) :
            m_sieve(std::min(sieve_size, PRIME_TABLE_SIZE)), m_step(step), m_check_2p1(check_2p1) {
         for(size_t i = 0; i != m_sieve.size(); ++i) {
            m_sieve[i] = init_value % PRIMES[i];
         }
      }

      size_t sieve_size() const { return m_sieve.size(); }

      bool check_2p1() const { return m_check_2p1; }

      bool next() {
         auto passes = CT::Mask<word>::set();
         for(size_t i = 0; i != m_sieve.size(); ++i) {
            m_sieve[i] = (m_sieve[i] + m_step) % PRIMES[i];

            // If m_sieve[i] == 0 then val % p == 0 -> not prime
            passes &= CT::Mask<word>::expand(m_sieve[i]);

            if(this->check_2p1()) {
               /*
               If v % p == (p-1)/2 then 2*v+1 == 0 (mod p)

               So if potentially generating a safe prime, we want to
               avoid this value because 2*v+1 will certainly not be prime.

               See "Safe Prime Generation with a Combined Sieve" M. Wiener
               https://eprint.iacr.org/2003/186.pdf
               */
               passes &= ~CT::Mask<word>::is_equal(m_sieve[i], (PRIMES[i] - 1) / 2);
            }
         }

         return passes.is_set();
      }

   private:
      std::vector<word> m_sieve;
      const word m_step;
      const bool m_check_2p1;
};

#if defined(BOTAN_ENABLE_DEBUG_ASSERTS)

bool no_small_multiples(const BigInt& v, const Prime_Sieve& sieve) {
   const size_t sieve_size = sieve.sieve_size();
   const bool check_2p1 = sieve.check_2p1();

   if(v.is_even())
      return false;

   const BigInt v_x2_p1 = 2 * v + 1;

   for(size_t i = 0; i != sieve_size; ++i) {
      if((v % PRIMES[i]) == 0)
         return false;

      if(check_2p1) {
         if(v_x2_p1 % PRIMES[i] == 0)
            return false;
      }
   }

   return true;
}

#endif

}  // namespace

/*
* Generate a random prime
*/
BigInt random_prime(
   RandomNumberGenerator& rng, size_t bits, const BigInt& coprime, size_t equiv, size_t modulo, size_t prob) {
   if(bits <= 1) {
      throw Invalid_Argument("random_prime: Can't make a prime of " + std::to_string(bits) + " bits");
   }
   if(coprime.is_negative() || (!coprime.is_zero() && coprime.is_even()) || coprime.bits() >= bits) {
      throw Invalid_Argument("random_prime: invalid coprime");
   }
   if(modulo == 0 || modulo >= 100000) {
      throw Invalid_Argument("random_prime: Invalid modulo value");
   }

   equiv %= modulo;

   if(equiv == 0) {
      throw Invalid_Argument("random_prime Invalid value for equiv/modulo");
   }

   // Handle small values:

   if(bits <= 16) {
      if(equiv != 1 || modulo != 2 || coprime != 0) {
         throw Not_Implemented("random_prime equiv/modulo/coprime options not usable for small primes");
      }

      if(bits == 2) {
         return BigInt::from_word(((rng.next_byte() % 2) ? 2 : 3));
      } else if(bits == 3) {
         return BigInt::from_word(((rng.next_byte() % 2) ? 5 : 7));
      } else if(bits == 4) {
         return BigInt::from_word(((rng.next_byte() % 2) ? 11 : 13));
      } else {
         for(;;) {
            // This is slightly biased, but for small primes it does not seem to matter
            uint8_t b[4];
            rng.randomize(b, 4);
            const size_t idx = load_le<uint32_t>(b, 0) % PRIME_TABLE_SIZE;
            const uint16_t small_prime = PRIMES[idx];

            if(high_bit(small_prime) == bits) {
               return BigInt::from_word(small_prime);
            }
         }
      }
   }

   const size_t MAX_ATTEMPTS = 32 * 1024;

   const size_t mr_trials = miller_rabin_test_iterations(bits, prob, true);

   while(true) {
      BigInt p(rng, bits);

      // Force lowest and two top bits on
      p.set_bit(bits - 1);
      p.set_bit(bits - 2);
      p.set_bit(0);

      // Force p to be equal to equiv mod modulo
      p += (modulo - (p % modulo)) + equiv;

      Prime_Sieve sieve(p, bits, modulo, true);

      for(size_t attempt = 0; attempt <= MAX_ATTEMPTS; ++attempt) {
         p += modulo;

         if(!sieve.next()) {
            continue;
         }

         // here p can be even if modulo is odd, continue on in that case
         if(p.is_even()) {
            continue;
         }

         BOTAN_DEBUG_ASSERT(no_small_multiples(p, sieve));

         Modular_Reducer mod_p(p);

         if(coprime > 1) {
            /*
            First do a single M-R iteration to quickly elimate most non-primes,
            before doing the coprimality check which is expensive
            */
            if(is_miller_rabin_probable_prime(p, mod_p, rng, 1) == false) {
               continue;
            }

            /*
            * Check if p - 1 and coprime are relatively prime, using gcd.
            * The gcd computation is const-time
            */
            if(gcd(p - 1, coprime) > 1) {
               continue;
            }
         }

         if(p.bits() > bits) {
            break;
         }

         if(is_miller_rabin_probable_prime(p, mod_p, rng, mr_trials) == false) {
            continue;
         }

         if(prob > 32 && !is_lucas_probable_prime(p, mod_p)) {
            continue;
         }

         return p;
      }
   }
}

BigInt generate_rsa_prime(RandomNumberGenerator& keygen_rng,
                          RandomNumberGenerator& prime_test_rng,
                          size_t bits,
                          const BigInt& coprime,
                          size_t prob) {
   if(bits < 512) {
      throw Invalid_Argument("generate_rsa_prime bits too small");
   }

   /*
   * The restriction on coprime <= 64 bits is arbitrary but generally speaking
   * very large RSA public exponents are a bad idea both for performance and due
   * to attacks on small d.
   */
   if(coprime <= 1 || coprime.is_even() || coprime.bits() > 64) {
      throw Invalid_Argument("generate_rsa_prime coprime must be small odd positive integer");
   }

   const size_t MAX_ATTEMPTS = 32 * 1024;

   const size_t mr_trials = miller_rabin_test_iterations(bits, prob, true);

   while(true) {
      BigInt p(keygen_rng, bits);

      /*
      Force high two bits so multiplication always results in expected n bit integer

      Force the two low bits, and step by 4, so the generated prime is always == 3 (mod 4).
      This way when we perform the inversion modulo phi(n) it is always of the form 2*o
      with o odd, which allows a fastpath and avoids leaking any information about the
      structure of the prime.
      */
      p.set_bit(bits - 1);
      p.set_bit(bits - 2);
      p.set_bit(1);
      p.set_bit(0);

      const word step = 4;

      Prime_Sieve sieve(p, bits, step, false);

      for(size_t attempt = 0; attempt <= MAX_ATTEMPTS; ++attempt) {
         p += step;

         if(!sieve.next()) {
            continue;
         }

         BOTAN_DEBUG_ASSERT(no_small_multiples(p, sieve));

         Modular_Reducer mod_p(p);

         /*
         * Do a single primality test first before checking coprimality, since
         * currently a single Miller-Rabin test is faster than computing gcd,
         * and this eliminates almost all wasted gcd computations.
         */
         if(is_miller_rabin_probable_prime(p, mod_p, prime_test_rng, 1) == false) {
            continue;
         }

         /*
         * Check if p - 1 and coprime are relatively prime.
         */
         if(gcd(p - 1, coprime) > 1) {
            continue;
         }

         if(p.bits() > bits) {
            break;
         }

         if(is_miller_rabin_probable_prime(p, mod_p, prime_test_rng, mr_trials) == true) {
            return p;
         }
      }
   }
}

/*
* Generate a random safe prime
*/
BigInt random_safe_prime(RandomNumberGenerator& rng, size_t bits) {
   if(bits <= 64) {
      throw Invalid_Argument("random_safe_prime: Can't make a prime of " + std::to_string(bits) + " bits");
   }

   const size_t error_bound = 128;

   BigInt q, p;
   for(;;) {
      /*
      Generate q == 2 (mod 3), since otherwise [in the case of q == 1 (mod 3)],
      2*q+1 == 3 (mod 3) and so certainly not prime.
      */
      q = random_prime(rng, bits - 1, BigInt::zero(), 2, 3, error_bound);
      p = (q << 1) + 1;

      if(is_prime(p, rng, error_bound, true)) {
         return p;
      }
   }
}

}  // namespace Botan

1	/*
2	* Prime Generation
3	* (C) 1999-2007,2018,2019 Jack Lloyd
4	*
5	* Botan is released under the Simplified BSD License (see license.txt)
6	*/
7
8	#include <botan/internal/primality.h>
9
10	#include <botan/numthry.h>
11	#include <botan/reducer.h>
12	#include <botan/rng.h>
13	#include <botan/internal/bit_ops.h>
14	#include <botan/internal/ct_utils.h>
15	#include <botan/internal/loadstor.h>
16	#include <algorithm>
17
18	namespace Botan {
19
20	namespace {
21
22	class Prime_Sieve final {	365✔
23	public:
24	Prime_Sieve(const BigInt& init_value, size_t sieve_size, word step, bool check_2p1) :	365✔
25	m_sieve(std::min(sieve_size, PRIME_TABLE_SIZE)), m_step(step), m_check_2p1(check_2p1) {	365✔
26	for(size_t i = 0; i != m_sieve.size(); ++i) {	302,844✔
27	m_sieve[i] = init_value % PRIMES[i];	302,479✔
28	}
29	}	365✔
30
31	size_t sieve_size() const { return m_sieve.size(); }
32
33	bool check_2p1() const { return m_check_2p1; }	794,989,919✔
34
35	bool next() {	652,109✔
36	auto passes = CT::Mask<word>::set();	652,109✔
37	for(size_t i = 0; i != m_sieve.size(); ++i) {	795,642,028✔
38	m_sieve[i] = (m_sieve[i] + m_step) % PRIMES[i];	794,989,919✔
39
40	// If m_sieve[i] == 0 then val % p == 0 -> not prime
41	passes &= CT::Mask<word>::expand(m_sieve[i]);	794,989,919✔
42
43	if(this->check_2p1()) {	794,989,919✔
44	/*
45	If v % p == (p-1)/2 then 2*v+1 == 0 (mod p)
46
47	So if potentially generating a safe prime, we want to
48	avoid this value because 2*v+1 will certainly not be prime.
49
50	See "Safe Prime Generation with a Combined Sieve" M. Wiener
51	https://eprint.iacr.org/2003/186.pdf
52	*/
53	passes &= ~CT::Mask<word>::is_equal(m_sieve[i], (PRIMES[i] - 1) / 2);	762,065,887✔
54	}
55	}
56
57	return passes.is_set();	652,109✔
58	}
59
60	private:
61	std::vector<word> m_sieve;
62	const word m_step;
63	const bool m_check_2p1;
64	};
65
66	#if defined(BOTAN_ENABLE_DEBUG_ASSERTS)
67
68	bool no_small_multiples(const BigInt& v, const Prime_Sieve& sieve) {
69	const size_t sieve_size = sieve.sieve_size();
70	const bool check_2p1 = sieve.check_2p1();
71
72	if(v.is_even())
73	return false;
74
75	const BigInt v_x2_p1 = 2 * v + 1;
76
77	for(size_t i = 0; i != sieve_size; ++i) {
78	if((v % PRIMES[i]) == 0)
79	return false;
80
81	if(check_2p1) {
82	if(v_x2_p1 % PRIMES[i] == 0)
83	return false;
84	}
85	}
86
87	return true;
88	}
89
90	#endif
91
92	} // namespace
93
94	/*
95	* Generate a random prime
96	*/
97	BigInt random_prime(	251✔
98	RandomNumberGenerator& rng, size_t bits, const BigInt& coprime, size_t equiv, size_t modulo, size_t prob) {
99	if(bits <= 1) {	251✔
100	throw Invalid_Argument("random_prime: Can't make a prime of " + std::to_string(bits) + " bits");	4✔
101	}
102	if(coprime.is_negative() \|\| (!coprime.is_zero() && coprime.is_even()) \|\| coprime.bits() >= bits) {	505✔
103	throw Invalid_Argument("random_prime: invalid coprime");	×
104	}
105	if(modulo == 0 \|\| modulo >= 100000) {	249✔
106	throw Invalid_Argument("random_prime: Invalid modulo value");	×
107	}
108
109	equiv %= modulo;	249✔
110
111	if(equiv == 0) {	249✔
112	throw Invalid_Argument("random_prime Invalid value for equiv/modulo");	1✔
113	}
114
115	// Handle small values:
116
117	if(bits <= 16) {	248✔
118	if(equiv != 1 \|\| modulo != 2 \|\| coprime != 0) {	30✔
119	throw Not_Implemented("random_prime equiv/modulo/coprime options not usable for small primes");	×
120	}
121
122	if(bits == 2) {	15✔
123	return BigInt::from_word(((rng.next_byte() % 2) ? 2 : 3));	1✔
124	} else if(bits == 3) {	14✔
125	return BigInt::from_word(((rng.next_byte() % 2) ? 5 : 7));	2✔
126	} else if(bits == 4) {	13✔
127	return BigInt::from_word(((rng.next_byte() % 2) ? 11 : 13));	1✔
128	} else {
129	for(;;) {	8,306✔
130	// This is slightly biased, but for small primes it does not seem to matter
131	uint8_t b[4];	4,159✔
132	rng.randomize(b, 4);	4,159✔
133	const size_t idx = load_le<uint32_t>(b, 0) % PRIME_TABLE_SIZE;	4,159✔
134	const uint16_t small_prime = PRIMES[idx];	4,159✔
135
136	if(high_bit(small_prime) == bits) {	8,318✔
137	return BigInt::from_word(small_prime);	12✔
138	}
139	}	4,147✔
140	}
141	}
142
143	const size_t MAX_ATTEMPTS = 32 * 1024;	233✔
144
145	const size_t mr_trials = miller_rabin_test_iterations(bits, prob, true);	233✔
146
147	while(true) {	233✔
148	BigInt p(rng, bits);	233✔
149
150	// Force lowest and two top bits on
151	p.set_bit(bits - 1);	233✔
152	p.set_bit(bits - 2);	233✔
153	p.set_bit(0);	233✔
154
155	// Force p to be equal to equiv mod modulo
156	p += (modulo - (p % modulo)) + equiv;	233✔
157
158	Prime_Sieve sieve(p, bits, modulo, true);	233✔
159
160	for(size_t attempt = 0; attempt <= MAX_ATTEMPTS; ++attempt) {	615,933✔
161	p += modulo;	615,933✔
162
163	if(!sieve.next()) {	615,933✔
164	continue;	615,700✔
165	}
166
167	// here p can be even if modulo is odd, continue on in that case
168	if(p.is_even()) {	35,834✔
169	continue;	8,802✔
170	}
171
172	BOTAN_DEBUG_ASSERT(no_small_multiples(p, sieve));	9,115✔
173
174	Modular_Reducer mod_p(p);	9,115✔
175
176	if(coprime > 1) {	9,115✔
177	/*
178	First do a single M-R iteration to quickly elimate most non-primes,
179	before doing the coprimality check which is expensive
180	*/
181	if(is_miller_rabin_probable_prime(p, mod_p, rng, 1) == false) {	99✔
182	continue;	93✔
183	}
184
185	/*
186	* Check if p - 1 and coprime are relatively prime, using gcd.
187	* The gcd computation is const-time
188	*/
189	if(gcd(p - 1, coprime) > 1) {	24✔
190	continue;	×
191	}
192	}
193
194	if(p.bits() > bits) {	9,022✔
195	break;
196	}
197
198	if(is_miller_rabin_probable_prime(p, mod_p, rng, mr_trials) == false) {	9,022✔
199	continue;	8,789✔
200	}
201
202	if(prob > 32 && !is_lucas_probable_prime(p, mod_p)) {	233✔
203	continue;	×
204	}
205
206	return p;	233✔
207	}	9,115✔
208	}	233✔
209	}
210
211	BigInt generate_rsa_prime(RandomNumberGenerator& keygen_rng,	132✔
212	RandomNumberGenerator& prime_test_rng,
213	size_t bits,
214	const BigInt& coprime,
215	size_t prob) {
216	if(bits < 512) {	132✔
217	throw Invalid_Argument("generate_rsa_prime bits too small");	×
218	}
219
220	/*
221	* The restriction on coprime <= 64 bits is arbitrary but generally speaking
222	* very large RSA public exponents are a bad idea both for performance and due
223	* to attacks on small d.
224	*/
225	if(coprime <= 1 \|\| coprime.is_even() \|\| coprime.bits() > 64) {	264✔
226	throw Invalid_Argument("generate_rsa_prime coprime must be small odd positive integer");	×
227	}
228
229	const size_t MAX_ATTEMPTS = 32 * 1024;	132✔
230
231	const size_t mr_trials = miller_rabin_test_iterations(bits, prob, true);	132✔
232
233	while(true) {	132✔
234	BigInt p(keygen_rng, bits);	132✔
235
236	/*
237	Force high two bits so multiplication always results in expected n bit integer
238
239	Force the two low bits, and step by 4, so the generated prime is always == 3 (mod 4).
240	This way when we perform the inversion modulo phi(n) it is always of the form 2*o
241	with o odd, which allows a fastpath and avoids leaking any information about the
242	structure of the prime.
243	*/
244	p.set_bit(bits - 1);	132✔
245	p.set_bit(bits - 2);	132✔
246	p.set_bit(1);	132✔
247	p.set_bit(0);	132✔
248
249	const word step = 4;	132✔
250
251	Prime_Sieve sieve(p, bits, step, false);	132✔
252
253	for(size_t attempt = 0; attempt <= MAX_ATTEMPTS; ++attempt) {	36,176✔
254	p += step;	36,176✔
255
256	if(!sieve.next()) {	36,176✔
257	continue;	36,044✔
258	}
259
260	BOTAN_DEBUG_ASSERT(no_small_multiples(p, sieve));	4,745✔
261
262	Modular_Reducer mod_p(p);	4,745✔
263
264	/*
265	* Do a single primality test first before checking coprimality, since
266	* currently a single Miller-Rabin test is faster than computing gcd,
267	* and this eliminates almost all wasted gcd computations.
268	*/
269	if(is_miller_rabin_probable_prime(p, mod_p, prime_test_rng, 1) == false) {	4,745✔
270	continue;	4,613✔
271	}
272
273	/*
274	* Check if p - 1 and coprime are relatively prime.
275	*/
276	if(gcd(p - 1, coprime) > 1) {	528✔
277	continue;	×
278	}
279
280	if(p.bits() > bits) {	132✔
281	break;
282	}
283
284	if(is_miller_rabin_probable_prime(p, mod_p, prime_test_rng, mr_trials) == true) {	132✔
285	return p;	132✔
286	}
287	}	4,745✔
288	}	132✔
289	}
290
291	/*
292	* Generate a random safe prime
293	*/
294	BigInt random_safe_prime(RandomNumberGenerator& rng, size_t bits) {	8✔
295	if(bits <= 64) {	8✔
296	throw Invalid_Argument("random_safe_prime: Can't make a prime of " + std::to_string(bits) + " bits");	×
297	}
298
299	const size_t error_bound = 128;	8✔
300
301	BigInt q, p;	8✔
302	for(;;) {	199✔
303	/*
304	Generate q == 2 (mod 3), since otherwise [in the case of q == 1 (mod 3)],
305	2*q+1 == 3 (mod 3) and so certainly not prime.
306	*/
307	q = random_prime(rng, bits - 1, BigInt::zero(), 2, 3, error_bound);	390✔
308	p = (q << 1) + 1;	589✔
309
310	if(is_prime(p, rng, error_bound, true)) {	199✔
311	return p;	8✔
312	}
313	}
314	}	8✔
315
316	} // namespace Botan

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