SHA (Secure Hash Algorithm) is the name given to a series of cryptographic hash function families standardised by NIST under FIPS 180 and FIPS 202. Three generations exist with fundamentally different design lineages. SHA-1 (1995, FIPS 180-1) produces a 160-bit digest and is fully broken for collision resistance: the SHAttered attack (Google and CWI Amsterdam, 2017) produced a chosen-prefix collision — two different PDF files with identical SHA-1 hashes — using approximately 9.2 × 10^18 SHA-1 operations, within practical reach of well-resourced attackers. SHA-1 must not be used for any security purpose; it persists only in legacy Git object identifiers (SHA-1 is being phased out in Git’s object store in favour of SHA-256 under the sha256 object format) and in TOTP’s HMAC-SHA-1 inner construction (where collision resistance is not the relevant security property, but migration to SHA-256 variants is still recommended). SHA-2 (2001, FIPS 180-2 and subsequent revisions) is the Merkle-Damgård family that includes SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224, and SHA-512/256. SHA-256 and SHA-512 are the two variants in universal production use; the others serve niche roles. SHA-3 (2015, FIPS 202) is the Keccak sponge construction — structurally independent of SHA-2 — providing algorithm diversity and including fixed-output variants (SHA3-256, SHA3-512) and extendable output functions (SHAKE128, SHAKE256).
HMAC (Hash-based Message Authentication Code), standardised in RFC 2104 (1997) and FIPS 198-1, is a construction that produces a Message Authentication Code (MAC) by combining a cryptographic hash function with a shared secret key. A plain hash function provides integrity — any modification to a message changes its digest — but anyone can recompute the digest of a modified message, so a hash alone cannot prove that a message came from a specific party who holds a secret. HMAC adds authenticity: only a party who knows the key K can produce a valid HMAC(K, message), and only a party who knows K can verify it. The construction is HMAC(K, m) = H((K ⊕ opad) ∥ H((K ⊕ ipad) ∥ m)) — two rounds of hashing with the key XOR’d against inner and outer padding constants — a design chosen to be provably secure against length-extension attacks that affect naive H(K ∥ m) constructions with Merkle-Damgård hash functions like SHA-256. HMAC is proven secure as long as the underlying hash function is a pseudorandom function, a weaker requirement than collision resistance, meaning HMAC-SHA-256 remains secure even in scenarios where SHA-256 collision resistance might be weakened.
A cryptographic hash function maps an input of arbitrary length (a file, a certificate, a password, a block of network data) to a fixed-length digest (also called a hash or fingerprint) with three security properties that distinguish it from non-cryptographic checksums. Preimage resistance: given a digest h, it is computationally infeasible to find any input m such that H(m) = h. Second preimage resistance: given an input m1, it is computationally infeasible to find a different input m2 such that H(m1) = H(m2). Collision resistance: it is computationally infeasible to find any pair (m1, m2) with m1 ≠ m2 such that H(m1) = H(m2). Collision resistance is the strongest property and implies second preimage resistance but not preimage resistance. These properties together make a hash function a one-way, tamper-evident fingerprint: two inputs that produce the same digest cannot be found by an adversary, and knowing the digest reveals nothing about the input beyond its length.
Diffie-Hellman (DH) is a key exchange protocol published by Whitfield Diffie and Martin Hellman in 1976 — the first public description of asymmetric cryptography and one of the most consequential cryptographic publications in history. Its fundamental contribution is solving the key establishment problem: two parties who have never communicated before, communicating over a channel that an adversary can fully observe, can nonetheless agree on a shared secret that the adversary cannot determine. The security of finite-field DH rests on the discrete logarithm problem: given g^a mod p and g^b mod p (the public values exchanged), computing g^ab mod p (the shared secret) requires solving for either a or b, which is computationally infeasible for sufficiently large groups. The 1976 original uses multiplicative groups of integers modulo a prime p; the security level is determined by the size of p (currently 2048-bit minimum, 3072-bit recommended) and the group’s structure. Finite-field DH is still deployed in TLS 1.2 DHE cipher suites and legacy IPsec configurations, but has been supplanted in new deployments by Elliptic Curve Diffie-Hellman (ECDH) and specifically by X25519, which provide equivalent security at dramatically smaller key sizes.
AES (Advanced Encryption Standard), standardised as NIST FIPS 197 in 2001, is the symmetric block cipher that underlies virtually all data encryption in modern infrastructure. It was selected through a five-year open competition that evaluated 15 candidate algorithms; the winner, Rijndael (designed by Joan Daemen and Vincent Rijmen), became AES. A block cipher takes a fixed-size block of plaintext and a key and produces a fixed-size block of ciphertext — AES always operates on 128-bit (16-byte) blocks, regardless of key size. Three key lengths are standardised: AES-128 (128-bit key, 10 rounds), AES-192 (192-bit key, 12 rounds), and AES-256 (256-bit key, 14 rounds), providing 128, 192, and 256 bits of security respectively against classical attacks. AES-256 is the conservative choice for data with long confidentiality requirements and is mandated by CNSA 2.0 for national security systems; AES-128 is widely deployed in TLS and provides adequate security for most workloads. The internal structure — SubBytes, ShiftRows, MixColumns, AddRoundKey — is fully public and has withstood over two decades of cryptanalysis; the best known attacks against full-round AES are theoretical and computationally infeasible, requiring work far beyond brute force but not threatening practical security.
