mirror of https://github.com/TheAlgorithms/C
feat: added Affine Cipher (#1245)
* feat: added affine cipher * chore: applied clang-format * docs: fixed typo Co-authored-by: Sharon "Cass" Cassidy <monadicdiffusive@proton.me> * docs: added brief qualifier Co-authored-by: Sharon "Cass" Cassidy <monadicdiffusive@proton.me> * chore: added const qualifier to test_string input * test: added checks for correct ciphertext * chore: removed asserts in modular_multiplicative_inverse and defined the ASCII conversion character * removed previous_remainder variable in modular_multiplicative_inverse() * chore: added brackets Co-authored-by: David Leal <halfpacho@gmail.com> * chore: made test function static Co-authored-by: David Leal <halfpacho@gmail.com> * docs: added back quotes to variable `a` Co-authored-by: David Leal <halfpacho@gmail.com> * docs: added back quotes to more variables Co-authored-by: David Leal <halfpacho@gmail.com> * chore: Added capitalization to string indicating passing tests Co-authored-by: David Leal <halfpacho@gmail.com> * chore: apply suggestions from code review --------- Co-authored-by: Sharon "Cass" Cassidy <monadicdiffusive@proton.me> Co-authored-by: David Leal <halfpacho@gmail.com>
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/**
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* @file
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* @brief An [affine cipher](https://en.wikipedia.org/wiki/Affine_cipher) is a
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* letter substitution cipher that uses a linear transformation to substitute
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* letters in a message.
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* @details Given an alphabet of length M with characters with numeric values
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* 0-(M-1), an arbitrary character x can be transformed with the expression (ax
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* + b) % M into our ciphertext character. The only caveat is that a must be
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* relatively prime with M in order for this transformation to be invertible,
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* i.e., gcd(a, M) = 1.
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* @author [Daniel Murrow](https://github.com/dsmurrow)
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*/
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#include <assert.h> /// for assertions
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#include <stdio.h> /// for IO
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#include <stdlib.h> /// for div function and div_t struct as well as malloc and free
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#include <string.h> /// for strlen, strcpy, and strcmp
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/**
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* @brief number of characters in our alphabet (printable ASCII characters)
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*/
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#define ALPHABET_SIZE 95
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/**
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* @brief used to convert a printable byte (32 to 126) to an element of the
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* group Z_95 (0 to 94)
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*/
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#define Z95_CONVERSION_CONSTANT 32
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/**
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* @brief a structure representing an affine cipher key
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*/
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typedef struct
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{
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int a; ///< what the character is being multiplied by
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int b; ///< what is being added after the multiplication with `a`
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} affine_key_t;
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/**
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* @brief finds the value x such that (a * x) % m = 1
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*
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* @param a number we are finding the inverse for
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* @param m the modulus the inversion is based on
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*
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* @returns the modular multiplicative inverse of `a` mod `m`
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*/
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int modular_multiplicative_inverse(unsigned int a, unsigned int m)
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{
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int x[2] = {1, 0};
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div_t div_result;
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if (m == 0) {
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return 0;
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}
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a %= m;
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if (a == 0) {
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return 0;
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}
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div_result.rem = a;
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while (div_result.rem > 0)
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{
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div_result = div(m, a);
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m = a;
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a = div_result.rem;
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// Calculate value of x for this iteration
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int next = x[1] - (x[0] * div_result.quot);
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x[1] = x[0];
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x[0] = next;
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}
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return x[1];
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}
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/**
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* @brief Given a valid affine cipher key, this function will produce the
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* inverse key.
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*
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* @param key They key to be inverted
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*
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* @returns inverse of key
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*/
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affine_key_t inverse_key(affine_key_t key)
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{
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affine_key_t inverse;
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inverse.a = modular_multiplicative_inverse(key.a, ALPHABET_SIZE);
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// Turn negative results positive
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inverse.a += ALPHABET_SIZE;
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inverse.a %= ALPHABET_SIZE;
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inverse.b = -(key.b % ALPHABET_SIZE) + ALPHABET_SIZE;
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return inverse;
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}
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/**
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* @brief Encrypts character string `s` with key
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*
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* @param s string to be encrypted
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* @param key affine key used for encryption
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*
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* @returns void
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*/
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void affine_encrypt(char *s, affine_key_t key)
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{
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for (int i = 0; s[i] != '\0'; i++)
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{
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int c = (int)s[i] - Z95_CONVERSION_CONSTANT;
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c *= key.a;
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c += key.b;
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c %= ALPHABET_SIZE;
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s[i] = (char)(c + Z95_CONVERSION_CONSTANT);
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}
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}
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/**
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* @brief Decrypts an affine ciphertext
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*
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* @param s string to be decrypted
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* @param key Key used when s was encrypted
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*
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* @returns void
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*/
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void affine_decrypt(char *s, affine_key_t key)
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{
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affine_key_t inverse = inverse_key(key);
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for (int i = 0; s[i] != '\0'; i++)
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{
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int c = (int)s[i] - Z95_CONVERSION_CONSTANT;
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c += inverse.b;
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c *= inverse.a;
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c %= ALPHABET_SIZE;
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s[i] = (char)(c + Z95_CONVERSION_CONSTANT);
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}
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}
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/**
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* @brief Tests a given string
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*
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* @param s string to be tested
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* @param a value of key.a
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* @param b value of key.b
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*
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* @returns void
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*/
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void test_string(const char *s, const char *ciphertext, int a, int b)
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{
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char *copy = malloc((strlen(s) + 1) * sizeof(char));
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strcpy(copy, s);
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affine_key_t key = {a, b};
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affine_encrypt(copy, key);
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assert(strcmp(copy, ciphertext) == 0); // assert that the encryption worked
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affine_decrypt(copy, key);
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assert(strcmp(copy, s) ==
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0); // assert that we got the same string we started with
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free(copy);
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}
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/**
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* @brief Test multiple strings
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*
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* @returns void
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*/
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static void tests()
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{
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test_string("Hello!", "&3ddy2", 7, 11);
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test_string("TheAlgorithms/C", "DNC}=jHS2zN!7;E", 67, 67);
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test_string("0123456789", "840,($ {ws", 91, 88);
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test_string("7W@;cdeRT9uL", "JDfa*we?z&bL", 77, 76);
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test_string("~Qr%^-+++$leM", "r'qC0$sss;Ahf", 8, 90);
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test_string("The quick brown fox jumps over the lazy dog",
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"K7: .*6<4 =-0(1 90' 5*2/, 0):- +7: 3>%& ;08", 94, 0);
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test_string(
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"One-1, Two-2, Three-3, Four-4, Five-5, Six-6, Seven-7, Eight-8, "
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"Nine-9, Ten-10",
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"H&60>\\2*uY0q\\2*p4660E\\2XYn40x\\2XDB60L\\2VDI0 "
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"\\2V6B6&0S\\2%D=p;0'\\2tD&60Z\\2*6&0>j",
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51, 18);
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printf("All tests have successfully passed!\n");
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}
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/**
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* @brief main function
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*
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* @returns 0 upon successful program exit
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*/
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int main()
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{
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tests();
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return 0;
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}
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