Complete C++ Assignment Solution: Implementing Encryption Techniques

Instructions

Objective

Write a program to implement encryption techniques in C++.

Requirements and Specifications

Electronic copy due date: Tuesday, Oct. 4, 2022, 11:30 pm

• File format - one doc file, and the file should contain source code(s), and output captures.
• Upload your file into the D2L
• Compiles - if it does not compile, it will not be graded
• Electronic submission correct (including file formats) - if not, it will not be graded

Plagiarism / Cheating

• When writing programs, you may consult with me or the GA at any stage of your program development. It helps if you bring a current print-out.
• Any student caught cheating on program will automatically fail the course and may be referred to the department chair and/or dean.
• To avoid cheating via collaboration, do not show any other classmates your code. If a classmate consults you for help with C++ assignment after attempting to run his or her program, you may assist in determining why his or her code doesn't work, but refrain from suggesting specific new code.
• Do not lead your classmates into temptation: guard your print-outs. We intend to use an automatic cheating-verification program that is capable of detecting partial logical similarities. Don't even take the risk.

Classical Encryption Techniques:

1. The following ciphertext was the output of a shift cipher:

LCLLEWLJAZLNNZMVYIYLHRMHZA

By performing a frequency count, guess the key used in the cipher. Use the computer to test your hypothesis. What is the decrypted plaintext?

1. The following was encrypted using by row transposition method. Implemented functions to perform encryption/decryption.
   • Encryption the plaintext = “attack postponed until two am” using double transposition with the key (4, 3, 1, 2, 5, 6, 7).
   • Decrypt the ciphertext “AMRT MOEP EAEG RTFY TZTY XAWE” using double transposition with the key (3 5 1 6 2 4).

Hill cipher:

1. Implement functions to perform encryption/decryption with 2x2 Hill Cipher. The key should be an invertible matrix over the integers mod 26.
   • Show the output of your encrypt function on the following (key, plaintext) pair:

Source Code

#include #include #include #include #include #include #include // Classical Encryption Techniques: // 1. struct CipherFreqTable { char letter[26]; float freq[26]; }; int mod(int x, int y) { if (x < 0) { while (x < 0) x += y; return x; } else { return x % y; } } CipherFreqTable* letter_freq(const char* p) { CipherFreqTable* t = new CipherFreqTable; for (int i = 0; i < 26; i += 1) { t->letter[i] = 'A' + i; t->freq[i] = 0; } for (int i = 0; i < strlen(p); i += 1) { int j = p[i] - 'A'; t->freq[j] += 1; } return t; } char* shift_decrypt(const char* c, int k) { int c_size = (int)strlen(c); char* p = (char*)malloc(sizeof(c) * c_size + 1); p[c_size] = 0; for (size_t i = 0; i < c_size; i += 1) { p[i] = mod((c[i] - 'A') - k, 26) + 'a'; } return p; } //*************************************************************************************// // 2. char* expand_string(char* str, int desired_size) { int str_size = (int)strlen(str); char* s = (char*)malloc(sizeof(char) * desired_size + 1); s[desired_size] = 0; for (int i = 0; i < desired_size; i += 1) { s[i] = (i < str_size) ? str[i] : 'x'; } return s; } char* row_transposition_encrypt(char* _P, int* K, int k_size) { int p_size = strlen(_P); int pad = ((p_size % k_size) != 0) ? k_size - (p_size % k_size) : 0; int c_size = p_size + pad; char* P = expand_string(_P, c_size); char* C = (char*)malloc(c_size + 1); C[c_size] = 0; char** TBL = (char**)malloc(sizeof(char*) * (c_size / k_size)); for (int i = 0; i < (c_size / k_size); i += 1) { char* p_ptr = P + (i * k_size); TBL[i] = (char*)malloc(sizeof(char) * k_size); for (int j = 0; j < k_size; j += 1) { TBL[i][j] = p_ptr[j]; } } int k = 0; for (int i = 0; i < k_size; i += 1) { int c = 0; for (int j = 0; j < k_size; j += 1) { if (K[j] == i + 1) { c = j; break; } } for (int j = 0; j < (c_size / k_size); j += 1) { C[k++] = TBL[j][c]; } } return C; } char* row_transposition_decrypt(char* C, int* K, int k_size) { int c_size = strlen(C); int p_size = c_size; char* P = (char*)malloc(p_size + 1); P[p_size] = 0; char** TBL = (char**)malloc(sizeof(char*) * (c_size / k_size)); for (int i = 0; i < (c_size / k_size); i += 1) { char* c_ptr = C + (i * k_size); TBL[i] = (char*)malloc(sizeof(char) * k_size); } for (int i = 0; i < k_size; i += 1) { char* c_ptr = C + (i * (c_size / k_size)); for (int j = 0; j < (c_size / k_size); j += 1) { TBL[j][K[i] - 1] = c_ptr[j]; } } int k = 0; for (int i = 0; i < (c_size / k_size); i += 1) { for (int j = 0; j < k_size; j += 1) { P[k++] = TBL[i][j]; } } return P; } //*************************************************************************************/ // Hill cipher int mult_inv(int i) { int k = 0; int j = 0; for (j = 0; j < 26; j += 1) { k = (i * j); if (k % 26 == 1) break; } return j; } struct Mat22 { int data[2][2]; }; Mat22* mat22_set(int a, int b, int c, int d) { Mat22* m = (Mat22*)malloc(sizeof(Mat22)); m->data[0][0] = a; m->data[0][1] = b; m->data[1][0] = c; m->data[1][1] = d; return m; } void mat22_print(Mat22* m) { std::cout << "|" << std::setw(2) << (m->data[0][0]) << " " << std::setw(2) << (m->data[0][1]) << "|"; std::cout << "\n"; std::cout << "|" << std::setw(2) << (m->data[1][0]) << " " << std::setw(2) << (m->data[1][1]) << "|"; std::cout << "\n"; } Mat22* mat22_mul(Mat22* m, Mat22* n) { Mat22* o = (Mat22*)malloc(sizeof(Mat22)); o->data[0][0] = mod((m->data[0][0] * n->data[0][0]) + (m->data[0][1] * n->data[1][0]), 26); o->data[0][1] = mod((m->data[0][0] * n->data[0][1]) + (m->data[0][1] * n->data[1][1]), 26); o->data[1][0] = mod((m->data[1][0] * n->data[0][0]) + (m->data[1][1] * n->data[1][0]), 26); o->data[1][1] = mod((m->data[1][0] * n->data[0][1]) + (m->data[1][1] * n->data[1][1]), 26); return o; } Mat22* mat22_adj(Mat22* m) { Mat22* adj = (Mat22*)malloc(sizeof(Mat22)); adj->data[0][0] = m->data[1][1]; adj->data[0][1] = m->data[0][1] * -1; adj->data[1][0] = m->data[1][0] * -1; adj->data[1][1] = m->data[0][0]; return adj; } // inv = (1/(ad - bc))[a1 a2] // [b1 b2] Mat22* mat22_inv(Mat22* m) { Mat22* inv = mat22_adj(m); int denom = mod((m->data[0][0] * m->data[1][1]) - (m->data[0][1] * m->data[1][0]), 26); int inverse = mult_inv(denom); inv->data[0][0] = mod(inv->data[0][0] * inverse, 26); inv->data[0][1] = mod(inv->data[0][1] * inverse, 26); inv->data[1][0] = mod(inv->data[1][0] * inverse, 26); inv->data[1][1] = mod(inv->data[1][1] * inverse, 26); return inv; } char* hillcipher_encrypt(char* P, Mat22* K) { int p_size = (int)strlen(P); char* C = (char*)malloc(sizeof(char) * p_size + 1); C[p_size] = 0; // encode C = P*K int i = 0; int j = 0; for (; i < p_size; i += 4) { Mat22* p_mat = mat22_set(P[i + 0] - 'a', (i + 1 < p_size) ? P[i + 1] - 'a' : 0, (i + 2 < p_size) ? P[i + 2] - 'a' : 0, (i + 3 < p_size) ? P[i + 3] - 'a' : 0); Mat22* c_mat = mat22_mul(p_mat, K); if (i < p_size) C[j++] = c_mat->data[0][0] + 'A'; if (i + 1 < p_size) C[j++] = c_mat->data[0][1] + 'A'; if (i + 2 < p_size) C[j++] = c_mat->data[1][0] + 'A'; if (i + 3 < p_size) C[j++] = c_mat->data[1][1] + 'A'; free(p_mat); free(c_mat); } return C; } char* hillcipher_decrypt(char* C, Mat22* inv_K) { int c_size = (int)strlen(C); char* P = (char*)malloc(sizeof(char)* c_size + 1); P[c_size] = 0; // add padding to C int pad = 0; while ((c_size + pad) % 4 != 0) { pad += 1; C = (char*)realloc(C, c_size + pad); C[c_size + pad - 1] = ' '; } // decode P = C*K^(-1) int i = 0; int j = 0; for (; i < c_size; i += 4) { Mat22* c_mat = mat22_set((i + 0 < c_size) ? C[i + 0] - 'A' : 0, (i + 1 < c_size) ? C[i + 1] - 'A' : 0, (i + 2 < c_size) ? C[i + 2] - 'A' : 0, (i + 3 < c_size) ? C[i + 3] - 'A' : 0); Mat22* p_mat = mat22_mul(c_mat, inv_K); if (i + 0 < c_size) P[j++] = p_mat->data[0][0] + 'a'; if (i + 1 < c_size) P[j++] = p_mat->data[0][1] + 'a'; if (i + 2 < c_size) P[j++] = p_mat->data[1][0] + 'a'; if (i + 3 < c_size) P[j++] = p_mat->data[1][1] + 'a'; free(c_mat); free(p_mat); } return P; } //*************************************************************************************// int main() { { const char* ciphertext = "LCLLEWLJAZLNNZMVYIYLHRMHZA"; // frequency analysis int k = -1; CipherFreqTable* freq_table = letter_freq(ciphertext); int score = 0; char letter = ' '; for (size_t j = 0; j < 26; j += 1) { if (score < freq_table->freq[j]) { score = freq_table->freq[j]; letter = freq_table->letter[j]; } } letter += 32; k = letter - 'e'; char* plaintext = shift_decrypt(ciphertext, k); std::cout << "\n"; std::cout << "Question 1 " << "\n"; std::cout << "Using a frequency count the key was foudn to be " << k << "\n"; std::cout << "The message was encrypted to:" << plaintext << "\n\n"; } //********************************* { int key[] = {4, 3, 1, 2, 5, 6, 7}; char P[] = "attackpostponeduntiltwoam"; char* C1 = row_transposition_encrypt(P, key, 7); char* C = row_transposition_encrypt(C1, key, 7); std::cout << "\n"; std::cout << "Question 2.a " << "\n"; // char str[] = C1; char ch[]={}; for (int i = 0; i < strlen(C); i++) { ch[i] = toupper(C[i]); } std::cout << "The message was encrypted to: " << ch << "\n\n"; char* _P = row_transposition_decrypt(row_transposition_decrypt(C, key, 7), key, 7); } { int key[] = {3, 5, 1, 6, 2, 4}; char C[] = "amrtmoepeaegrtfytztyxawe"; char* P = row_transposition_decrypt(row_transposition_decrypt(C, key, 6), key, 6); //std::cout << "Key :: "; for (int i = 0; i < 6; i += 1) { //std::cout << key[i] << " "; } std::cout << "\n"; std::cout << "Question 2.b " << "\n"; std::cout << "The message was encrypted to: " << P << "\n\n"; } //********************************* { Mat22* K = mat22_set(9, 4, 5, 7); char P[] = "meetmeattheusualplaceattenratherthaneightoclockx"; char* C = hillcipher_encrypt(P, K); std::cout << "\n"; std::cout << "Question 3.a " << "\n"; std::cout << "Ciphertext: " << C << "\n\n"; free(K); free(C); } //********************************* { Mat22* K = mat22_set(9, 13, 2, 3); char* C = (char*)malloc(sizeof(char) * 6); memcpy(C, "YIFZMA", 6); Mat22* inv_K = mat22_inv(K); Mat22* identity = mat22_mul(K, inv_K); char* P = hillcipher_decrypt(C, inv_K); std::cout << "\n"; std::cout << "Question 3.b " << "\n"; std::cout << "Plaintext: " << P << "\n"; free(inv_K); free(K); free(P); } //********************************* { // known plaintext attack char P[] = "howareyoutoday"; char C[] = "ZWSENIUSPLJVEU"; Mat22* p_mat = mat22_set(P[0] - 'a', P[1] - 'a', P[8] - 'a', P[9] - 'a'); Mat22* inv_p_mat = mat22_inv(p_mat); Mat22* identity_of_p = mat22_mul(p_mat, inv_p_mat); Mat22* c_mat = mat22_set(C[0] - 'A', C[1] - 'A', C[8] - 'A', C[9] - 'A'); Mat22* K = mat22_mul(inv_p_mat, c_mat); std::cout << "\n"; std::cout << "Question 4 " << "\n"; std::cout << "Key: \n"; mat22_print(K); std::cout << "\n"; } return 0; }