20579846577

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Merge pull request #5167 from randombit/jack/src-size-reductions

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/divide.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] = ct_mod_word(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] = sieve_step_incr(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:
      // Return (v + step) % mod
      //
      // This assumes v is already < mod, which is an invariant of the sieve
      static constexpr word sieve_step_incr(word v, word step, word mod) {
         BOTAN_DEBUG_ASSERT(v < mod);
         // The sieve step and primes are public so this modulo is ok
         const word stepmod = (step >= mod) ? (step % mod) : step;

         // This sum is at most 2*(mod-1)
         const word next = (v + stepmod);
         return next - CT::Mask<word>::is_gte(next, mod).if_set_return(mod);
      }

      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");
   }
   // TODO(Botan4) reduce this to ~1000
   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);

      auto scope = CT::scoped_poison(p);

      /*
      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/divide.h>
16	#include <botan/internal/loadstor.h>
17
18	namespace Botan {
19
20	namespace {
21
22	class Prime_Sieve final {	×
23	public:
24	Prime_Sieve(const BigInt& init_value, size_t sieve_size, word step, bool check_2p1) :	885✔
25	m_sieve(std::min(sieve_size, PRIME_TABLE_SIZE)), m_step(step), m_check_2p1(check_2p1) {	885✔
26	for(size_t i = 0; i != m_sieve.size(); ++i) {	468,300✔
27	m_sieve[i] = ct_mod_word(init_value, PRIMES[i]);	467,415✔
28	}
29	}	885✔
30
31	size_t sieve_size() const { return m_sieve.size(); }
32
33	bool check_2p1() const { return m_check_2p1; }	1,002,941,118✔
34
35	bool next() {	1,203,980✔
36	auto passes = CT::Mask<word>::set();	1,203,980✔
37	for(size_t i = 0; i != m_sieve.size(); ++i) {	1,004,145,098✔
38	m_sieve[i] = sieve_step_incr(m_sieve[i], m_step, PRIMES[i]);	1,002,941,118✔
39
40	// If m_sieve[i] == 0 then val % p == 0 -> not prime
41	passes &= CT::Mask<word>::expand(m_sieve[i]);	1,002,941,118✔
42
43	if(this->check_2p1()) {	1,002,941,118✔
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);	973,312,190✔
54	}
55	}
56
57	return passes.as_bool();	1,203,980✔
58	}
59
60	private:
61	// Return (v + step) % mod
62	//
63	// This assumes v is already < mod, which is an invariant of the sieve
64	static constexpr word sieve_step_incr(word v, word step, word mod) {	1,002,941,118✔
65	BOTAN_DEBUG_ASSERT(v < mod);	1,002,941,118✔
66	// The sieve step and primes are public so this modulo is ok
67	const word stepmod = (step >= mod) ? (step % mod) : step;	1,002,941,118✔
68
69	// This sum is at most 2*(mod-1)
70	const word next = (v + stepmod);	1,002,941,118✔
71	return next - CT::Mask<word>::is_gte(next, mod).if_set_return(mod);	1,002,941,118✔
72	}
73
74	std::vector<word> m_sieve;
75	const word m_step;
76	const bool m_check_2p1;
77	};
78
79	#if defined(BOTAN_ENABLE_DEBUG_ASSERTS)
80
81	bool no_small_multiples(const BigInt& v, const Prime_Sieve& sieve) {
82	const size_t sieve_size = sieve.sieve_size();
83	const bool check_2p1 = sieve.check_2p1();
84
85	if(v.is_even())
86	return false;
87
88	const BigInt v_x2_p1 = 2 * v + 1;
89
90	for(size_t i = 0; i != sieve_size; ++i) {
91	if((v % PRIMES[i]) == 0)
92	return false;
93
94	if(check_2p1) {
95	if(v_x2_p1 % PRIMES[i] == 0)
96	return false;
97	}
98	}
99
100	return true;
101	}
102
103	#endif
104
105	} // namespace
106
107	/*
108	* Generate a random prime
109	*/
110	BigInt random_prime(	759✔
111	RandomNumberGenerator& rng, size_t bits, const BigInt& coprime, size_t equiv, size_t modulo, size_t prob) {
112	if(bits <= 1) {	759✔
113	throw Invalid_Argument("random_prime: Can't make a prime of " + std::to_string(bits) + " bits");	8✔
114	}
115	if(coprime.is_negative() \|\| (!coprime.is_zero() && coprime.is_even()) \|\| coprime.bits() >= bits) {	1,521✔
116	throw Invalid_Argument("random_prime: invalid coprime");	×
117	}
118	// TODO(Botan4) reduce this to ~1000
119	if(modulo == 0 \|\| modulo >= 100000) {	757✔
120	throw Invalid_Argument("random_prime: Invalid modulo value");	×
121	}
122
123	equiv %= modulo;	757✔
124
125	if(equiv == 0) {	757✔
126	throw Invalid_Argument("random_prime Invalid value for equiv/modulo");	1✔
127	}
128
129	// Handle small values:
130
131	if(bits <= 16) {	756✔
132	if(equiv != 1 \|\| modulo != 2 \|\| coprime != 0) {	38✔
133	throw Not_Implemented("random_prime equiv/modulo/coprime options not usable for small primes");	×
134	}
135
136	if(bits == 2) {	19✔
137	return BigInt::from_word(((rng.next_byte() % 2) == 0 ? 2 : 3));	1✔
138	} else if(bits == 3) {	18✔
139	return BigInt::from_word(((rng.next_byte() % 2) == 0 ? 5 : 7));	1✔
140	} else if(bits == 4) {	17✔
141	return BigInt::from_word(((rng.next_byte() % 2) == 0 ? 11 : 13));	1✔
142	} else {
143	for(;;) {	4,520✔
144	// This is slightly biased, but for small primes it does not seem to matter
145	uint8_t b[4] = {0};	2,268✔
146	rng.randomize(b, 4);	2,268✔
147	const size_t idx = load_le<uint32_t>(b, 0) % PRIME_TABLE_SIZE;	2,268✔
148	const uint16_t small_prime = PRIMES[idx];	2,268✔
149
150	if(high_bit(small_prime) == bits) {	4,536✔
151	return BigInt::from_word(small_prime);	16✔
152	}
153	}	2,252✔
154	}
155	}
156
157	const size_t MAX_ATTEMPTS = 32 * 1024;	737✔
158
159	const size_t mr_trials = miller_rabin_test_iterations(bits, prob, true);	737✔
160
161	while(true) {	×
162	BigInt p(rng, bits);	737✔
163
164	// Force lowest and two top bits on
165	p.set_bit(bits - 1);	737✔
166	p.set_bit(bits - 2);	737✔
167	p.set_bit(0);	737✔
168
169	// Force p to be equal to equiv mod modulo
170	p += (modulo - (p % modulo)) + equiv;	737✔
171
172	Prime_Sieve sieve(p, bits, modulo, true);	737✔
173
174	for(size_t attempt = 0; attempt <= MAX_ATTEMPTS; ++attempt) {	1,167,710✔
175	p += modulo;	1,167,710✔
176
177	if(!sieve.next()) {	1,167,710✔
178	continue;	1,166,973✔
179	}
180
181	// here p can be even if modulo is odd, continue on in that case
182	if(p.is_even()) {	52,402✔
183	continue;	9,190✔
184	}
185
186	BOTAN_DEBUG_ASSERT(no_small_multiples(p, sieve));	17,011✔
187
188	auto mod_p = Barrett_Reduction::for_secret_modulus(p);	17,011✔
189
190	if(coprime > 1) {	17,011✔
191	/*
192	First do a single M-R iteration to quickly eliminate most non-primes,
193	before doing the coprimality check which is expensive
194	*/
195	if(!is_miller_rabin_probable_prime(p, mod_p, rng, 1)) {	99✔
196	continue;	93✔
197	}
198
199	/*
200	* Check if p - 1 and coprime are relatively prime, using gcd.
201	* The gcd computation is const-time
202	*/
203	if(gcd(p - 1, coprime) > 1) {	12✔
204	continue;	×
205	}
206	}
207
208	if(p.bits() > bits) {	16,918✔
209	break;
210	}
211
212	if(!is_miller_rabin_probable_prime(p, mod_p, rng, mr_trials)) {	16,918✔
213	continue;	16,181✔
214	}
215
216	if(prob > 32 && !is_lucas_probable_prime(p, mod_p)) {	737✔
217	continue;	×
218	}
219
220	return p;	737✔
221	}	17,011✔
222	}	737✔
223	}
224
225	BigInt generate_rsa_prime(RandomNumberGenerator& keygen_rng,	148✔
226	RandomNumberGenerator& prime_test_rng,
227	size_t bits,
228	const BigInt& coprime,
229	size_t prob) {
230	if(bits < 512) {	148✔
231	throw Invalid_Argument("generate_rsa_prime bits too small");	×
232	}
233
234	/*
235	* The restriction on coprime <= 64 bits is arbitrary but generally speaking
236	* very large RSA public exponents are a bad idea both for performance and due
237	* to attacks on small d.
238	*/
239	if(coprime <= 1 \|\| coprime.is_even() \|\| coprime.bits() > 64) {	296✔
240	throw Invalid_Argument("generate_rsa_prime coprime must be small odd positive integer");	×
241	}
242
243	const size_t MAX_ATTEMPTS = 32 * 1024;	148✔
244
245	const size_t mr_trials = miller_rabin_test_iterations(bits, prob, true);	148✔
246
247	while(true) {	×
248	BigInt p(keygen_rng, bits);	148✔
249
250	auto scope = CT::scoped_poison(p);	148✔
251
252	/*
253	Force high two bits so multiplication always results in expected n bit integer
254
255	Force the two low bits, and step by 4, so the generated prime is always == 3 (mod 4).
256	This way when we perform the inversion modulo phi(n) it is always of the form 2*o
257	with o odd, which allows a fastpath and avoids leaking any information about the
258	structure of the prime.
259	*/
260	p.set_bit(bits - 1);	148✔
261	p.set_bit(bits - 2);	148✔
262	p.set_bit(1);	148✔
263	p.set_bit(0);	148✔
264
265	const word step = 4;	148✔
266
267	Prime_Sieve sieve(p, bits, step, false);	148✔
268
269	for(size_t attempt = 0; attempt <= MAX_ATTEMPTS; ++attempt) {	36,270✔
270	p += step;	36,270✔
271
272	if(!sieve.next()) {	36,270✔
273	continue;	36,122✔
274	}
275
276	BOTAN_DEBUG_ASSERT(no_small_multiples(p, sieve));	4,886✔
277
278	auto mod_p = Barrett_Reduction::for_secret_modulus(p);	4,886✔
279
280	/*
281	* Do a single primality test first before checking coprimality, since
282	* currently a single Miller-Rabin test is faster than computing gcd,
283	* and this eliminates almost all wasted gcd computations.
284	*/
285	if(!is_miller_rabin_probable_prime(p, mod_p, prime_test_rng, 1)) {	4,886✔
286	continue;	4,738✔
287	}
288
289	/*
290	* Check if p - 1 and coprime are relatively prime.
291	*/
292	if(gcd(p - 1, coprime) > 1) {	296✔
293	continue;	×
294	}
295
296	if(p.bits() > bits) {	148✔
297	break;
298	}
299
300	if(is_miller_rabin_probable_prime(p, mod_p, prime_test_rng, mr_trials)) {	148✔
301	return p;	296✔
302	}
303	}	4,886✔
304	}	296✔
305	}
306
307	/*
308	* Generate a random safe prime
309	*/
310	BigInt random_safe_prime(RandomNumberGenerator& rng, size_t bits) {	8✔
311	if(bits <= 64) {	8✔
312	throw Invalid_Argument("random_safe_prime: Can't make a prime of " + std::to_string(bits) + " bits");	×
313	}
314
315	const size_t error_bound = 128;	8✔
316
317	BigInt q;	8✔
318	BigInt p;	8✔
319	for(;;) {	207✔
320	/*
321	Generate q == 2 (mod 3), since otherwise [in the case of q == 1 (mod 3)],
322	2*q+1 == 3 (mod 3) and so certainly not prime.
323	*/
324	q = random_prime(rng, bits - 1, BigInt::zero(), 2, 3, error_bound);	207✔
325	p = (q << 1) + 1;	414✔
326
327	if(is_prime(p, rng, error_bound, true)) {	207✔
328	return p;	8✔
329	}
330	}
331	}	8✔
332
333	} // namespace Botan

randombit / botan / 20579846577

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