How RSA and AES Algorithms Work
Introduction
In today's digital age, cryptography plays a crucial role in securing sensitive information. Among the various cryptographic algorithms, RSA and AES stand out for their unique approaches to data security. This article aims to explain the theoretical foundations of these algorithms and demonstrate their practical applications.
1. Basics of Cryptography
1.1. Definition of Cryptography and Its Main Goals
Cryptography is the science of encoding and decoding information to protect it from unauthorized access. Its primary goals include confidentiality, integrity, authentication, and non-repudiation.
1.2. Difference Between Symmetric and Asymmetric Algorithms
Symmetric algorithms use the same key for both encryption and decryption, while asymmetric algorithms use a pair of keys: a public key for encryption and a private key for decryption.
1.3. Brief Overview of Other Popular Algorithms
Other notable algorithms include DES (Data Encryption Standard) and ECC (Elliptic Curve Cryptography), each with its own strengths and weaknesses.
2. RSA Algorithm
2.1. History and Development of RSA
RSA (Rivest-Shamir-Adleman) was developed in 1977 and is one of the first public-key cryptosystems. It revolutionized secure communication over the internet.
2.2. Theoretical Foundations:
2.2.1. Principles of Working with Prime Numbers
RSA relies on the mathematical properties of prime numbers. The security of RSA is based on the difficulty of factoring the product of two large prime numbers.
2.2.2. Key Generation (Public and Private Key)
To generate keys, select two large prime numbers \( p \) and \( q \), compute \( n = p \times q \), and calculate the totient \( \phi
= (p-1)(q-1) \). Choose a public exponent \( e \) such that \( 1 < e < \phi \) and \( \gcd(e, \phi) = 1 \). The private key \( d \) is calculated as the modular multiplicative inverse of \( e \) modulo \( \phi \).2.2.3. Encryption and Decryption of Data
Encryption is performed using the formula:
\[ c = m^e \mod n \]
where \( m \) is the plaintext message and \( c \) is the ciphertext. Decryption is done using:
\[ m = c^d \mod n \]
2.3. Application of RSA in Real Systems
RSA is widely used in SSL/TLS protocols to secure communications over the internet.
3. AES Algorithm
3.1. History and Development of AES
AES (Advanced Encryption Standard) was established in 2001 as a replacement for DES, providing enhanced security and efficiency.
3.2. Theoretical Foundations:
3.2.1. Structure of AES (Blocks, Keys, Rounds)
AES operates on 128-bit blocks and supports key sizes of 128, 192, or 256 bits. It consists of multiple rounds of processing, depending on the key size.
3.2.2. Encryption and Decryption Process (SubBytes, ShiftRows, MixColumns, AddRoundKey)
The encryption process involves several steps:
- **SubBytes**: Non-linear substitution step.
- **ShiftRows**: Row-wise permutation.
- **MixColumns**: Mixing of the columns.
- **AddRoundKey**: XORing with the round key.
Decryption reverses these steps in the opposite order.
3.2.3. Difference Between Operating Modes (ECB, CBC, GCM)
AES can operate in various modes, such as ECB (Electronic Codebook), CBC (Cipher Block Chaining), and GCM (Galois/Counter Mode), each with different security properties.
3.3. Application of AES in Real Systems
AES is commonly used for file encryption, VPNs, and securing sensitive data in transit.
4. Practical Part
4.1. Installing Required Libraries (e.g., PyCryptodome for Python)
To get started with cryptography in Python, install the PyCryptodome library:
```
pip install pycryptodome
```
4.2. Example Code for RSA Implementation:
4.2.1. Key Generation
```python
from Crypto.PublicKey import RSA
key = RSA.generate(2048)
private_key = key.export_key()
public_key = key.publickey().export_key()
```
4.2.2. Encrypting a Message
```python
from Crypto.Cipher import PKCS1_OAEP
from Crypto.PublicKey import RSA
cipher = PKCS1_OAEP.new(RSA.import_key(public_key))
ciphertext = cipher.encrypt(b'Hello, World!')
```
4.2.3. Decrypting a Message
```python
from Crypto.Cipher import PKCS1_OAEP
from Crypto.PublicKey import RSA
cipher = PKCS1_OAEP.new(RSA.import_key(private_key))
plaintext = cipher.decrypt(ciphertext)
```
4.3. Example Code for AES Implementation:
4.3.1. Encrypting Text Using AES
```python
from Crypto.Cipher import AES
from Crypto.Util.Padding import pad
from Crypto.Random import get_random_bytes
key = get_random_bytes(16) # AES-128
cipher = AES.new(key, AES.MODE_CBC)
ciphertext = cipher.encrypt(pad(b'Hello