Cryptography

Cryptography is the study and practice of securing information by transforming it so that only authorized parties can read or modify it. It uses algorithms, keys, and protocols to convert plaintext into ciphertext and back, with goals such as confidentiality, integrity, authentication, and non-repudiation.

There are two main types: symmetric-key cryptography, which uses a single shared key, and public-key cryptography, which uses a public key for encryption and a private key for decryption. Hash functions provide fixed-size digests for data integrity, while digital signatures confirm authorship and non-repudiation. Certificates and trusted authorities help establish identities in networks.

Modern cryptography relies on mathematical problems that are easy to perform in one direction but hard to reverse without a key, such as factoring or discrete logarithms. Public-key systems enable secure key exchange; symmetric systems are typically faster for bulk data. Common algorithms include RSA and elliptic-curve cryptography, as well as block ciphers like DES and its successor AES, and hash families such as SHA-2.

Historically, techniques date to ancient ciphers; the 20th century brought formal security goals and major cryptanalytic advances. The 1970s saw the advent of public-key cryptography (Diffie-Hellman) and RSA, with later decades standardizing DES and AES and expanding hash functions and signatures.

Applications include securing internet traffic (TLS), email and file encryption, authentication protocols, and digital wallets and blockchains. The field continues to evolve toward post-quantum cryptography and ongoing research in randomness, protocol design, and formal security proofs.