82 lines
2.2 KiB
C
82 lines
2.2 KiB
C
#pragma once
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#include <stdbool.h>
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#include <stdint.h>
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/**
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* @brief Calculates greatest common divider of two integers using the euclidean
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* algorithm
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*
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* @param a First number
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* @param b Second number
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* @return The greatest common divider
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*/
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uint64_t gcd(uint64_t a, uint64_t b);
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/**
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* @brief Computes Euler's Totient function φ(n), which counts the number of
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* integers from 1 to n that are coprime to n.
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*
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* @param n The input number.
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* @return The number of integers from 1 to n that are coprime to n.
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*/
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int totient(int n);
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/**
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* @brief Modular exponentiation (a^b) mod m
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*
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* @param a The base
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* @param b The exponent
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* @param m The modulus
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*/
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uint64_t modexp(uint64_t a, uint64_t b, uint64_t m);
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/**
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* @brief Computes the modular inverse of a modulo m.
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*
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* @param a The integer whose modular inverse is to be found.
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* @param m The modulus.
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* @return The modular inverse of a modulo m, or -1 if no inverse exists.
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*/
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int mod_inverse(int a, int m);
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/**
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* @brief Generates a random prime number within the given range.
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*
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* @param min The lower bound (inclusive).
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* @param max The upper bound (inclusive).
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* @return A prime number in the range [min, max].
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*/
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uint64_t gen_prime(uint64_t min, uint64_t max);
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/**
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* @brief Checks if a number is prime.
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*
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* @param n The number to check.
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* @return true if n is prime, false otherwise.
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*/
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bool is_prime(int n);
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/**
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* @brief Performs the Miller-Rabin primality test to check if a number is
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* probably prime.
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*
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* @param n The number to test for primality.
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* @param k The number of rounds of testing to perform.
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* @return true if n is probably prime, false if n is composite.
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*/
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bool miller_rabin(uint64_t n, uint64_t k);
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/**
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* @brief Computes the greatest common divisor (GCD) of two integers a and b
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* using the Extended Euclidean Algorithm. Also finds coefficients x and y such
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* that ax + by = gcd(a, b).
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*
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* @param a The first integer.
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* @param b The second integer.
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* @param x Pointer to an integer to store the coefficient x in the equation ax
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* + by = gcd(a, b).
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* @param y Pointer to an integer to store the coefficient y in the equation ax
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* + by = gcd(a, b).
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* @return The greatest common divisor (gcd) of a and b.
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*/
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int extended_euclid(int a, int b, int *x, int *y);
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