Computer Science Notes: Mathematical Cryptography

Asymmetric Encryption Architectures (RSA & Prime Factoring)

Asymmetric cryptosystems rely on a mathematical keypair construct (Public/Private). The RSA algorithm leverages the deep computational intractability of prime factorization.

• Public Key: Broadcasted publicly; utilized exclusively to encrypt incoming plaintext payloads.
• Private Key: Safeguarded within secure memory vault; utilized strictly to decrypt ciphertext.

       [ ENCRYPTION ]                          [ DECRYPTION ]
PlainText ---> (Public Key) ---> CipherText ---> (Private Key) ---> PlainText

High-Velocity Symmetric Ciphers (AES-256)

While asymmetric cryptography is perfect for initial trust handshakes, it incurs heavy CPU overhead. Once symmetric keys are negotiated, systems immediately switch to ciphers like AES-256, where a single shared secret key encrypts and decrypts bulk network streams with immediate hardware acceleration.

Cryptographic Hash Functions & Integrity Auditing

• Deterministic Execution: Transforming arbitrary-length inputs into a fixed-length hexadecimal digest (e.g., SHA-256).
• The Avalanche Effect: Flipping a single bit in the source payload causes a catastrophic, sweeping alteration of the output digest, providing ironclad assurance against silent tampering or injection.