Cryptography Basics: Key Exchange, Encryption, and Signing

This repository demonstrates basic cryptographic concepts using simplified implementations of Diffie-Hellman and RSA algorithms. It showcases key exchange, encryption, decryption, and digital signing processes, highlighting the roles of Alice, Bob, and Eve (an eavesdropper) in each scenario.

Disclaimer

IMPORTANT: The implementations in this repository are greatly simplified and use small numbers for demonstration purposes only. They are NOT secure and should NEVER be used in real-world applications. This code is purely for educational purposes to illustrate basic cryptographic concepts.

Motivating Work

Diffie-Hellman vs. RSA Encryption Algorithms- What's the Difference- - YouTube https://www.youtube.com/watch?v=VY4EouzyJS0

Scenarios

1. Diffie-Hellman Key Exchange

Demonstrates how two parties can establish a shared secret over an insecure channel.

Principles:

• Uses the difficulty of the discrete logarithm problem
• Allows key agreement without prior shared secret

Steps:

1. Alice and Bob agree on public parameters (prime p and base g)
2. Each generates a private key
3. Each computes and exchanges public keys
4. Each computes the shared secret

Process:

• Alice and Bob: Can compute the shared secret
• Eve: Can see all public information but cannot compute the shared secret

2. RSA Key Exchange

Shows how RSA can be used to exchange a symmetric key securely.

Principles:

• Uses the difficulty of factoring large numbers
• Allows secure key transmission using public-key cryptography

Steps:

1. Alice and Bob generate RSA key pairs
2. They exchange public keys
3. Bob generates a symmetric key
4. Bob encrypts the symmetric key with Alice's public key
5. Bob sends the encrypted key to Alice
6. Alice decrypts the key with her private key

Process:

• Alice: Can decrypt the symmetric key
• Bob: Can create and encrypt the symmetric key
• Eve: Can see the encrypted key but cannot decrypt it

3. RSA Encryption and Decryption

Demonstrates secure message transmission using RSA.

Principles:

• Asymmetric encryption
• Message confidentiality

Steps:

1. Bob prepares a message
2. Bob encrypts the message with Alice's public key
3. Bob sends the encrypted message to Alice
4. Alice decrypts the message with her private key

Process:

• Alice: Can decrypt the message
• Bob: Can encrypt the message
• Eve: Can see the encrypted message but cannot decrypt it

4. RSA Signing

Illustrates digital signature creation and verification.

Principles:

• Message integrity
• Non-repudiation
• Sender authentication

Steps:

1. Alice prepares a message
2. Alice signs the message with her private key
3. Alice sends the message and signature to Bob
4. Bob verifies the signature using Alice's public key

Process:

• Alice: Can sign messages
• Bob: Can verify Alice's signatures
• Eve: Can see signed messages and verify signatures, but cannot forge Alice's signature

Results

Remember, never implement your own cryptography for real-world applications. Always use well-vetted, standard cryptographic libraries.