/src/botan/build/include/public/botan/numthry.h

Source
/*
* Number Theory Functions
* (C) 1999-2007,2018 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/

#ifndef BOTAN_NUMBER_THEORY_H_
#define BOTAN_NUMBER_THEORY_H_

#include <botan/bigint.h>

namespace Botan {

class RandomNumberGenerator;

/**
* Return the absolute value
* @param n an integer
* @return absolute value of n
*/
inline BigInt abs(const BigInt& n) {
   return n.abs();
}

/**
* Compute the greatest common divisor
* @param x a positive integer
* @param y a positive integer
* @return gcd(x,y)
*/
BigInt BOTAN_PUBLIC_API(2, 0) gcd(const BigInt& x, const BigInt& y);

/**
* Least common multiple
* @param x a positive integer
* @param y a positive integer
* @return z, smallest integer such that z % x == 0 and z % y == 0
*/
BigInt BOTAN_PUBLIC_API(2, 0) lcm(const BigInt& x, const BigInt& y);

/**
* @param x an integer
* @return (x*x)
*/
BigInt BOTAN_PUBLIC_API(2, 0) square(const BigInt& x);

/**
* Modular inversion. This algorithm is const time with respect to x,
* as long as x is less than modulus. It also avoids leaking
* information about the modulus, except that it does leak which of 3
* categories the modulus is in: an odd integer, a power of 2, or some
* other even number, and if the modulus is even, leaks the power of 2
* which divides the modulus.
*
* @param x a positive integer
* @param modulus a positive integer
* @return y st (x*y) % modulus == 1 or 0 if no such value
*/
BigInt BOTAN_PUBLIC_API(2, 0) inverse_mod(const BigInt& x, const BigInt& modulus);

/**
* Compute the Jacobi symbol. If n is prime, this is equivalent
* to the Legendre symbol.
* @see http://mathworld.wolfram.com/JacobiSymbol.html
*
* @param a is a non-negative integer
* @param n is an odd integer > 1
* @return (n / m)
*/
int32_t BOTAN_PUBLIC_API(2, 0) jacobi(const BigInt& a, const BigInt& n);

/**
* Modular exponentation
* @param b an integer base
* @param x a positive exponent
* @param m a positive modulus
* @return (b^x) % m
*/
BigInt BOTAN_PUBLIC_API(2, 0) power_mod(const BigInt& b, const BigInt& x, const BigInt& m);

/**
* Compute the square root of x modulo a prime using the Tonelli-Shanks
* algorithm. This algorithm is primarily used for EC point
* decompression which takes only public inputs, as a consequence it is
* not written to be constant-time and may leak side-channel information
* about its arguments.
*
* @param x the input
* @param p the prime modulus
* @return y such that (y*y)%p == x, or -1 if no such integer
*/
BigInt BOTAN_PUBLIC_API(3, 0) sqrt_modulo_prime(const BigInt& x, const BigInt& p);

/**
* @param x an integer
* @return count of the low zero bits in x, or, equivalently, the
*         largest value of n such that 2^n divides x evenly. Returns
*         zero if x is equal to zero.
*/
size_t BOTAN_PUBLIC_API(2, 0) low_zero_bits(const BigInt& x);

/**
* Check for primality
* @param n a positive integer to test for primality
* @param rng a random number generator
* @param prob chance of false positive is bounded by 1/2**prob
* @param is_random true if n was randomly chosen by us
* @return true if all primality tests passed, otherwise false
*/
bool BOTAN_PUBLIC_API(2, 0)
   is_prime(const BigInt& n, RandomNumberGenerator& rng, size_t prob = 64, bool is_random = false);

/**
* Test if the positive integer x is a perfect square ie if there
* exists some positive integer y st y*y == x
* See FIPS 186-4 sec C.4
* @return 0 if the integer is not a perfect square, otherwise
*         returns the positive y st y*y == x
*/
BigInt BOTAN_PUBLIC_API(2, 8) is_perfect_square(const BigInt& x);

/**
* Randomly generate a prime suitable for discrete logarithm parameters
* @param rng a random number generator
* @param bits how large the resulting prime should be in bits
* @param coprime a positive integer that (prime - 1) should be coprime to
* @param equiv a non-negative number that the result should be
               equivalent to modulo equiv_mod
* @param equiv_mod the modulus equiv should be checked against
* @param prob use test so false positive is bounded by 1/2**prob
* @return random prime with the specified criteria
*/
BigInt BOTAN_PUBLIC_API(2, 0) random_prime(RandomNumberGenerator& rng,
                                           size_t bits,
                                           const BigInt& coprime = BigInt::from_u64(0),
                                           size_t equiv = 1,
                                           size_t equiv_mod = 2,
                                           size_t prob = 128);

/**
* Generate a prime suitable for RSA p/q
* @param keygen_rng a random number generator
* @param prime_test_rng a random number generator
* @param bits how large the resulting prime should be in bits (must be >= 512)
* @param coprime a positive integer that (prime - 1) should be coprime to
* @param prob use test so false positive is bounded by 1/2**prob
* @return random prime with the specified criteria
*/
BigInt BOTAN_PUBLIC_API(2, 7) generate_rsa_prime(RandomNumberGenerator& keygen_rng,
                                                 RandomNumberGenerator& prime_test_rng,
                                                 size_t bits,
                                                 const BigInt& coprime,
                                                 size_t prob = 128);

/**
* Return a 'safe' prime, of the form p=2*q+1 with q prime
* @param rng a random number generator
* @param bits is how long the resulting prime should be
* @return prime randomly chosen from safe primes of length bits
*/
BigInt BOTAN_PUBLIC_API(2, 0) random_safe_prime(RandomNumberGenerator& rng, size_t bits);

/**
* The size of the PRIMES[] array
*/
const size_t PRIME_TABLE_SIZE = 6541;

/**
* A const array of all odd primes less than 65535
*/
extern const uint16_t BOTAN_PUBLIC_API(2, 0) PRIMES[];

}  // namespace Botan

#endif

Coverage Report

Created: 2024-06-28 06:39

Line	Count	Source
1		/*
2		* Number Theory Functions
3		* (C) 1999-2007,2018 Jack Lloyd
4		*
5		* Botan is released under the Simplified BSD License (see license.txt)
6		*/
7
8		#ifndef BOTAN_NUMBER_THEORY_H_
9		#define BOTAN_NUMBER_THEORY_H_
10
11		#include <botan/bigint.h>
12
13		namespace Botan {
14
15		class RandomNumberGenerator;
16
17		/**
18		* Return the absolute value
19		* @param n an integer
20		* @return absolute value of n
21		*/
22	78	inline BigInt abs(const BigInt& n) {
23	78	return n.abs();
24	78	}
25
26		/**
27		* Compute the greatest common divisor
28		* @param x a positive integer
29		* @param y a positive integer
30		* @return gcd(x,y)
31		*/
32		BigInt BOTAN_PUBLIC_API(2, 0) gcd(const BigInt& x, const BigInt& y);
33
34		/**
35		* Least common multiple
36		* @param x a positive integer
37		* @param y a positive integer
38		* @return z, smallest integer such that z % x == 0 and z % y == 0
39		*/
40		BigInt BOTAN_PUBLIC_API(2, 0) lcm(const BigInt& x, const BigInt& y);
41
42		/**
43		* @param x an integer
44		* @return (x*x)
45		*/
46		BigInt BOTAN_PUBLIC_API(2, 0) square(const BigInt& x);
47
48		/**
49		* Modular inversion. This algorithm is const time with respect to x,
50		* as long as x is less than modulus. It also avoids leaking
51		* information about the modulus, except that it does leak which of 3
52		* categories the modulus is in: an odd integer, a power of 2, or some
53		* other even number, and if the modulus is even, leaks the power of 2
54		* which divides the modulus.
55		*
56		* @param x a positive integer
57		* @param modulus a positive integer
58		* @return y st (x*y) % modulus == 1 or 0 if no such value
59		*/
60		BigInt BOTAN_PUBLIC_API(2, 0) inverse_mod(const BigInt& x, const BigInt& modulus);
61
62		/**
63		* Compute the Jacobi symbol. If n is prime, this is equivalent
64		* to the Legendre symbol.
65		* @see http://mathworld.wolfram.com/JacobiSymbol.html
66		*
67		* @param a is a non-negative integer
68		* @param n is an odd integer > 1
69		* @return (n / m)
70		*/
71		int32_t BOTAN_PUBLIC_API(2, 0) jacobi(const BigInt& a, const BigInt& n);
72
73		/**
74		* Modular exponentation
75		* @param b an integer base
76		* @param x a positive exponent
77		* @param m a positive modulus
78		* @return (b^x) % m
79		*/
80		BigInt BOTAN_PUBLIC_API(2, 0) power_mod(const BigInt& b, const BigInt& x, const BigInt& m);
81
82		/**
83		* Compute the square root of x modulo a prime using the Tonelli-Shanks
84		* algorithm. This algorithm is primarily used for EC point
85		* decompression which takes only public inputs, as a consequence it is
86		* not written to be constant-time and may leak side-channel information
87		* about its arguments.
88		*
89		* @param x the input
90		* @param p the prime modulus
91		* @return y such that (y*y)%p == x, or -1 if no such integer
92		*/
93		BigInt BOTAN_PUBLIC_API(3, 0) sqrt_modulo_prime(const BigInt& x, const BigInt& p);
94
95		/**
96		* @param x an integer
97		* @return count of the low zero bits in x, or, equivalently, the
98		* largest value of n such that 2^n divides x evenly. Returns
99		* zero if x is equal to zero.
100		*/
101		size_t BOTAN_PUBLIC_API(2, 0) low_zero_bits(const BigInt& x);
102
103		/**
104		* Check for primality
105		* @param n a positive integer to test for primality
106		* @param rng a random number generator
107		* @param prob chance of false positive is bounded by 1/2**prob
108		* @param is_random true if n was randomly chosen by us
109		* @return true if all primality tests passed, otherwise false
110		*/
111		bool BOTAN_PUBLIC_API(2, 0)
112		is_prime(const BigInt& n, RandomNumberGenerator& rng, size_t prob = 64, bool is_random = false);
113
114		/**
115		* Test if the positive integer x is a perfect square ie if there
116		* exists some positive integer y st y*y == x
117		* See FIPS 186-4 sec C.4
118		* @return 0 if the integer is not a perfect square, otherwise
119		* returns the positive y st y*y == x
120		*/
121		BigInt BOTAN_PUBLIC_API(2, 8) is_perfect_square(const BigInt& x);
122
123		/**
124		* Randomly generate a prime suitable for discrete logarithm parameters
125		* @param rng a random number generator
126		* @param bits how large the resulting prime should be in bits
127		* @param coprime a positive integer that (prime - 1) should be coprime to
128		* @param equiv a non-negative number that the result should be
129		equivalent to modulo equiv_mod
130		* @param equiv_mod the modulus equiv should be checked against
131		* @param prob use test so false positive is bounded by 1/2**prob
132		* @return random prime with the specified criteria
133		*/
134		BigInt BOTAN_PUBLIC_API(2, 0) random_prime(RandomNumberGenerator& rng,
135		size_t bits,
136		const BigInt& coprime = BigInt::from_u64(0),
137		size_t equiv = 1,
138		size_t equiv_mod = 2,
139		size_t prob = 128);
140
141		/**
142		* Generate a prime suitable for RSA p/q
143		* @param keygen_rng a random number generator
144		* @param prime_test_rng a random number generator
145		* @param bits how large the resulting prime should be in bits (must be >= 512)
146		* @param coprime a positive integer that (prime - 1) should be coprime to
147		* @param prob use test so false positive is bounded by 1/2**prob
148		* @return random prime with the specified criteria
149		*/
150		BigInt BOTAN_PUBLIC_API(2, 7) generate_rsa_prime(RandomNumberGenerator& keygen_rng,
151		RandomNumberGenerator& prime_test_rng,
152		size_t bits,
153		const BigInt& coprime,
154		size_t prob = 128);
155
156		/**
157		* Return a 'safe' prime, of the form p=2*q+1 with q prime
158		* @param rng a random number generator
159		* @param bits is how long the resulting prime should be
160		* @return prime randomly chosen from safe primes of length bits
161		*/
162		BigInt BOTAN_PUBLIC_API(2, 0) random_safe_prime(RandomNumberGenerator& rng, size_t bits);
163
164		/**
165		* The size of the PRIMES[] array
166		*/
167		const size_t PRIME_TABLE_SIZE = 6541;
168
169		/**
170		* A const array of all odd primes less than 65535
171		*/
172		extern const uint16_t BOTAN_PUBLIC_API(2, 0) PRIMES[];
173
174		} // namespace Botan
175
176		#endif