20295000893

Committed 17 Dec 2025 07:24AM UTC coverage: 90.52% (+0.2%) from 90.36%

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Merge 70b91cb18 into 3d96b675e

Pull Request Pull Request #5167: Changes to reduce unnecessary inclusions

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/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/rng.h>
#include <botan/internal/barrett.h>
#include <botan/internal/bit_ops.h>
#include <botan/internal/ct_utils.h>
#include <botan/internal/loadstor.h>

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.as_bool();
      }

   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) == 0 ? 2 : 3));
      } else if(bits == 3) {
         return BigInt::from_word(((rng.next_byte() % 2) == 0 ? 5 : 7));
      } else if(bits == 4) {
         return BigInt::from_word(((rng.next_byte() % 2) == 0 ? 11 : 13));
      } else {
         for(;;) {
            // This is slightly biased, but for small primes it does not seem to matter
            uint8_t b[4] = {0};
            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));

         auto mod_p = Barrett_Reduction::for_secret_modulus(p);

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

         auto mod_p = Barrett_Reduction::for_secret_modulus(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)) {
            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)) {
            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;
   BigInt 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/rng.h>
12	#include <botan/internal/barrett.h>
13	#include <botan/internal/bit_ops.h>
14	#include <botan/internal/ct_utils.h>
15	#include <botan/internal/loadstor.h>
16
17	namespace Botan {
18
19	namespace {
20
21	class Prime_Sieve final {	×
22	public:
23	Prime_Sieve(const BigInt& init_value, size_t sieve_size, word step, bool check_2p1) :	880✔
24	m_sieve(std::min(sieve_size, PRIME_TABLE_SIZE)), m_step(step), m_check_2p1(check_2p1) {	880✔
25	for(size_t i = 0; i != m_sieve.size(); ++i) {	461,255✔
26	m_sieve[i] = init_value % PRIMES[i];	460,375✔
27	}
28	}	880✔
29
30	size_t sieve_size() const { return m_sieve.size(); }
31
32	bool check_2p1() const { return m_check_2p1; }	970,160,958✔
33
34	bool next() {	1,141,216✔
35	auto passes = CT::Mask<word>::set();	1,141,216✔
36	for(size_t i = 0; i != m_sieve.size(); ++i) {	971,302,174✔
37	m_sieve[i] = (m_sieve[i] + m_step) % PRIMES[i];	970,160,958✔
38
39	// If m_sieve[i] == 0 then val % p == 0 -> not prime
40	passes &= CT::Mask<word>::expand(m_sieve[i]);	970,160,958✔
41
42	if(this->check_2p1()) {	970,160,958✔
43	/*
44	If v % p == (p-1)/2 then 2*v+1 == 0 (mod p)
45
46	So if potentially generating a safe prime, we want to
47	avoid this value because 2*v+1 will certainly not be prime.
48
49	See "Safe Prime Generation with a Combined Sieve" M. Wiener
50	https://eprint.iacr.org/2003/186.pdf
51	*/
52	passes &= ~CT::Mask<word>::is_equal(m_sieve[i], (PRIMES[i] - 1) / 2);	940,645,310✔
53	}
54	}
55
56	return passes.as_bool();	1,141,216✔
57	}
58
59	private:
60	std::vector<word> m_sieve;
61	const word m_step;
62	const bool m_check_2p1;
63	};
64
65	#if defined(BOTAN_ENABLE_DEBUG_ASSERTS)
66
67	bool no_small_multiples(const BigInt& v, const Prime_Sieve& sieve) {
68	const size_t sieve_size = sieve.sieve_size();
69	const bool check_2p1 = sieve.check_2p1();
70
71	if(v.is_even())
72	return false;
73
74	const BigInt v_x2_p1 = 2 * v + 1;
75
76	for(size_t i = 0; i != sieve_size; ++i) {
77	if((v % PRIMES[i]) == 0)
78	return false;
79
80	if(check_2p1) {
81	if(v_x2_p1 % PRIMES[i] == 0)
82	return false;
83	}
84	}
85
86	return true;
87	}
88
89	#endif
90
91	} // namespace
92
93	/*
94	* Generate a random prime
95	*/
96	BigInt random_prime(	754✔
97	RandomNumberGenerator& rng, size_t bits, const BigInt& coprime, size_t equiv, size_t modulo, size_t prob) {
98	if(bits <= 1) {	754✔
99	throw Invalid_Argument("random_prime: Can't make a prime of " + std::to_string(bits) + " bits");	8✔
100	}
101	if(coprime.is_negative() \|\| (!coprime.is_zero() && coprime.is_even()) \|\| coprime.bits() >= bits) {	1,511✔
102	throw Invalid_Argument("random_prime: invalid coprime");	×
103	}
104	if(modulo == 0 \|\| modulo >= 100000) {	752✔
105	throw Invalid_Argument("random_prime: Invalid modulo value");	×
106	}
107
108	equiv %= modulo;	752✔
109
110	if(equiv == 0) {	752✔
111	throw Invalid_Argument("random_prime Invalid value for equiv/modulo");	1✔
112	}
113
114	// Handle small values:
115
116	if(bits <= 16) {	751✔
117	if(equiv != 1 \|\| modulo != 2 \|\| coprime != 0) {	38✔
118	throw Not_Implemented("random_prime equiv/modulo/coprime options not usable for small primes");	×
119	}
120
121	if(bits == 2) {	19✔
122	return BigInt::from_word(((rng.next_byte() % 2) == 0 ? 2 : 3));	1✔
123	} else if(bits == 3) {	18✔
124	return BigInt::from_word(((rng.next_byte() % 2) == 0 ? 5 : 7));	1✔
125	} else if(bits == 4) {	17✔
126	return BigInt::from_word(((rng.next_byte() % 2) == 0 ? 11 : 13));	1✔
127	} else {
128	for(;;) {	8,290✔
129	// This is slightly biased, but for small primes it does not seem to matter
130	uint8_t b[4] = {0};	4,153✔
131	rng.randomize(b, 4);	4,153✔
132	const size_t idx = load_le<uint32_t>(b, 0) % PRIME_TABLE_SIZE;	4,153✔
133	const uint16_t small_prime = PRIMES[idx];	4,153✔
134
135	if(high_bit(small_prime) == bits) {	8,306✔
136	return BigInt::from_word(small_prime);	16✔
137	}
138	}	4,137✔
139	}
140	}
141
142	const size_t MAX_ATTEMPTS = 32 * 1024;	732✔
143
144	const size_t mr_trials = miller_rabin_test_iterations(bits, prob, true);	732✔
145
146	while(true) {	×
147	BigInt p(rng, bits);	732✔
148
149	// Force lowest and two top bits on
150	p.set_bit(bits - 1);	732✔
151	p.set_bit(bits - 2);	732✔
152	p.set_bit(0);	732✔
153
154	// Force p to be equal to equiv mod modulo
155	p += (modulo - (p % modulo)) + equiv;	732✔
156
157	Prime_Sieve sieve(p, bits, modulo, true);	732✔
158
159	for(size_t attempt = 0; attempt <= MAX_ATTEMPTS; ++attempt) {	1,104,886✔
160	p += modulo;	1,104,886✔
161
162	if(!sieve.next()) {	1,104,886✔
163	continue;	1,104,154✔
164	}
165
166	// here p can be even if modulo is odd, continue on in that case
167	if(p.is_even()) {	50,320✔
168	continue;	8,962✔
169	}
170
171	BOTAN_DEBUG_ASSERT(no_small_multiples(p, sieve));	16,198✔
172
173	auto mod_p = Barrett_Reduction::for_secret_modulus(p);	16,198✔
174
175	if(coprime > 1) {	16,198✔
176	/*
177	First do a single M-R iteration to quickly eliminate most non-primes,
178	before doing the coprimality check which is expensive
179	*/
180	if(!is_miller_rabin_probable_prime(p, mod_p, rng, 1)) {	99✔
181	continue;	93✔
182	}
183
184	/*
185	* Check if p - 1 and coprime are relatively prime, using gcd.
186	* The gcd computation is const-time
187	*/
188	if(gcd(p - 1, coprime) > 1) {	12✔
189	continue;	×
190	}
191	}
192
193	if(p.bits() > bits) {	16,105✔
194	break;
195	}
196
197	if(!is_miller_rabin_probable_prime(p, mod_p, rng, mr_trials)) {	16,105✔
198	continue;	15,373✔
199	}
200
201	if(prob > 32 && !is_lucas_probable_prime(p, mod_p)) {	732✔
202	continue;	×
203	}
204
205	return p;	732✔
206	}	16,198✔
207	}	732✔
208	}
209
210	BigInt generate_rsa_prime(RandomNumberGenerator& keygen_rng,	148✔
211	RandomNumberGenerator& prime_test_rng,
212	size_t bits,
213	const BigInt& coprime,
214	size_t prob) {
215	if(bits < 512) {	148✔
216	throw Invalid_Argument("generate_rsa_prime bits too small");	×
217	}
218
219	/*
220	* The restriction on coprime <= 64 bits is arbitrary but generally speaking
221	* very large RSA public exponents are a bad idea both for performance and due
222	* to attacks on small d.
223	*/
224	if(coprime <= 1 \|\| coprime.is_even() \|\| coprime.bits() > 64) {	296✔
225	throw Invalid_Argument("generate_rsa_prime coprime must be small odd positive integer");	×
226	}
227
228	const size_t MAX_ATTEMPTS = 32 * 1024;	148✔
229
230	const size_t mr_trials = miller_rabin_test_iterations(bits, prob, true);	148✔
231
232	while(true) {	×
233	BigInt p(keygen_rng, bits);	148✔
234
235	/*
236	Force high two bits so multiplication always results in expected n bit integer
237
238	Force the two low bits, and step by 4, so the generated prime is always == 3 (mod 4).
239	This way when we perform the inversion modulo phi(n) it is always of the form 2*o
240	with o odd, which allows a fastpath and avoids leaking any information about the
241	structure of the prime.
242	*/
243	p.set_bit(bits - 1);	148✔
244	p.set_bit(bits - 2);	148✔
245	p.set_bit(1);	148✔
246	p.set_bit(0);	148✔
247
248	const word step = 4;	148✔
249
250	Prime_Sieve sieve(p, bits, step, false);	148✔
251
252	for(size_t attempt = 0; attempt <= MAX_ATTEMPTS; ++attempt) {	36,330✔
253	p += step;	36,330✔
254
255	if(!sieve.next()) {	36,330✔
256	continue;	36,182✔
257	}
258
259	BOTAN_DEBUG_ASSERT(no_small_multiples(p, sieve));	4,901✔
260
261	auto mod_p = Barrett_Reduction::for_secret_modulus(p);	4,901✔
262
263	/*
264	* Do a single primality test first before checking coprimality, since
265	* currently a single Miller-Rabin test is faster than computing gcd,
266	* and this eliminates almost all wasted gcd computations.
267	*/
268	if(!is_miller_rabin_probable_prime(p, mod_p, prime_test_rng, 1)) {	4,901✔
269	continue;	4,753✔
270	}
271
272	/*
273	* Check if p - 1 and coprime are relatively prime.
274	*/
275	if(gcd(p - 1, coprime) > 1) {	296✔
276	continue;	×
277	}
278
279	if(p.bits() > bits) {	148✔
280	break;
281	}
282
283	if(is_miller_rabin_probable_prime(p, mod_p, prime_test_rng, mr_trials)) {	148✔
284	return p;	296✔
285	}
286	}	4,901✔
287	}	148✔
288	}
289
290	/*
291	* Generate a random safe prime
292	*/
293	BigInt random_safe_prime(RandomNumberGenerator& rng, size_t bits) {	8✔
294	if(bits <= 64) {	8✔
295	throw Invalid_Argument("random_safe_prime: Can't make a prime of " + std::to_string(bits) + " bits");	×
296	}
297
298	const size_t error_bound = 128;	8✔
299
300	BigInt q;	8✔
301	BigInt p;	8✔
302	for(;;) {	202✔
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);	202✔
308	p = (q << 1) + 1;	404✔
309
310	if(is_prime(p, rng, error_bound, true)) {	202✔
311	return p;	8✔
312	}
313	}
314	}	8✔
315
316	} // namespace Botan

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