Cryptography Lab

Mathematical Principles & Theorems

Examines symmetric and asymmetric cryptosystems. Caesar (\(c \equiv p + k \pmod{26}\)) and Vigenère polyalphabetic ciphers vs modern public-key cryptography. RSA relies on the computational hardness of factoring large semiprimes \(n = pq\): public key \((e, n)\), private key \(d \equiv e^{-1} \pmod{\phi(n)}\), encryption \(c \equiv m^e \pmod n\), decryption \(m \equiv c^d \pmod n\). Diffie-Hellman establishes shared secret keys over insecure channels via discrete logarithms \(g^{ab} \pmod p\).

Operating Instructions

• Choose a cryptographic protocol: Caesar, Vigenère, RSA Public Key, Diffie-Hellman, or SHA-256.
• Enter plaintext message and encryption key parameters.
• For RSA: Generate key pairs \((e, d, n)\) and perform modular exponentiation encryption and decryption.
• Inspect binary hashing output and cryptographic step breakdowns.