AES Algorithm

Description

AES (Advanced Encryption Standard) is a symmetric encryption algorithm used for securing sensitive data. It supports key lengths of 128, 192, or 256 bits and operates on fixed-size blocks of data. AES encryption involves several rounds of substitution, permutation, and mixing operations (subBytes, shiftRows, mixColumns) to achieve strong security against attacks. It is widely adopted in applications requiring data confidentiality, such as secure communication and file encryption.

C++ Code

#include <iostream>
#include <iomanip>
#include <cstring>
using namespace std;

const int Nb = 4;
const int Nk = 4;
const int Nr = 10;

// AES S-box
unsigned char sbox[256] = {
    // S-box values from FIPS-197
};

// AES round constant
unsigned char Rcon[11] = {
    // Round constants from FIPS-197
};

void subBytes(unsigned char state[][Nb]) {
    for (int i = 0; i < 4; i++) {
        for (int j = 0; j < Nb; j++) {
            state[i][j] = sbox[state[i][j]];
        }
    }
}

void shiftRows(unsigned char state[][Nb]) {
    unsigned char temp;

    temp = state[1][0];
    state[1][0] = state[1][1];
    state[1][1] = state[1][2];
    state[1][2] = state[1][3];
    state[1][3] = temp;

    temp = state[2][0];
    state[2][0] = state[2][2];
    state[2][2] = temp;
    temp = state[2][1];
    state[2][1] = state[2][3];
    state[2][3] = temp;

    temp = state[3][0];
    state[3][0] = state[3][3];
    state[3][3] = state[3][2];
    state[3][2] = state[3][1];
    state[3][1] = temp;
}

void mixColumns(unsigned char state[][Nb]) {
    unsigned char tmp, tm, t;

    for (int i = 0; i < 4; i++) {
        t = state[0][i];
        tmp = state[0][i] ^ state[1][i] ^ state[2][i] ^ state[3][i];
        tm = state[0][i] ^ state[1][i];
        tm = xtime(tm);
        state[0][i] ^= tm ^ tmp;
        tm = state[1][i] ^ state[2][i];
        tm = xtime(tm);
        state[1][i] ^= tm ^ tmp;
        tm = state[2][i] ^ state[3][i];
        tm = xtime(tm);
        state[2][i] ^= tm ^ tmp;
        tm = state[3][i] ^ t;
        tm = xtime(tm);
        state[3][i] ^= tm ^ tmp;
    }
}

void aesEncrypt(unsigned char input[4 * Nb], unsigned char key[4 * Nk], unsigned char output[4 * Nb]) {
    unsigned char state[4][Nb];
    unsigned char roundKey[4 * Nb];

    for (int i = 0; i < 4; ++i) {
        for (int j = 0; j < Nb; ++j) {
            state[i][j] = input[j * 4 + i];
        }
    }

    for (int i = 0; i < 4; ++i) {
        for (int j = 0; j < Nk; ++j) {
            roundKey[i * 4 + j] = key[j * 4 + i];
        }
    }

    addRoundKey(state, roundKey);

    for (int round = 1; round < Nr; ++round) {
        subBytes(state);
        shiftRows(state);
        mixColumns(state);
        addRoundKey(state, roundKey + round * 4 * Nb);
    }

    subBytes(state);
    shiftRows(state);
    addRoundKey(state, roundKey + Nr * 4 * Nb);

    for (int i = 0; i < 4; ++i) {
        for (int j = 0; j < Nb; ++j) {
            output[j * 4 + i] = state[i][j];
        }
    }
}

int main() {
    unsigned char input[16] = {0x32, 0x88, 0x31, 0xe0, 0x43, 0x5a, 0x31, 0x37, 0xf6, 0x30, 0x98, 0x07, 0xa8, 0x8d, 0xa2, 0x34};
    unsigned char key[16] = {0x2b, 0x7e, 0x15, 0x16, 0x28, 0xae, 0xd2, 0xa6, 0xab, 0xf7, 0x15, 0x88, 0x09, 0xcf, 0x4f, 0x3c};
    unsigned char output[16];

    aesEncrypt(input, key, output);

    cout << "AES Encrypted Output:" << endl;
    for (int i = 0; i < 16; ++i) {
        cout << hex << setfill('0') << setw(2) << (int)output[i] << " ";
    }
    cout << endl;

    return 0;
}

Time and Space Complexity

Operation	Time Complexity	Space Complexity
Key Expansion	O(1)	O(1)
Encryption	O(Nr * Nb^2)	O(1)

Where:

• Nr: Number of rounds (10 for AES-128).
• Nb: Number of columns (4 for AES).

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