Field Guide · algorithm

Also known as: hash, message digest, SHA

A cryptographic hash function maps input of any length to a fixed-size digest in a way that is easy to compute but practically impossible to invert, so the digest acts as a compact, tamper-evident fingerprint of the data.1 It is one of the workhorses of cryptography, underpinning integrity checks, digital signatures, password storage, and message authentication.

message (any length) hash function fixed-sizedigest
A hash function compresses any input into a fixed-size digest that is easy to compute but hard to reverse.

How it works

A good cryptographic hash behaves like a deterministic but unpredictable function. Flipping a single input bit changes roughly half the output bits (the avalanche effect), and the function is designed to resist three distinct attacks:

  • Pre-image resistance — given a digest h, you cannot feasibly find any input m with hash(m) = h (the function is one-way). For an n-bit digest this should cost about 2ⁿ work.
  • Second-pre-image resistance — given one input m₁, you cannot find a different m₂ with the same digest. Also ~2ⁿ work.
  • Collision resistance — you cannot feasibly find any two distinct inputs that hash to the same digest. The birthday paradox halves the exponent here: collisions cost only ~2^(n/2) work, which is why SHA-256 (128-bit collision strength) is chosen where 128-bit security is wanted.

Because the output is fixed-size and the input is unbounded, collisions must exist in principle; the security claim is only that they are computationally infeasible to find. When one of these properties breaks, the hash is “broken” — MD5 and SHA-1 both fell to practical collision attacks and are now unsafe for signatures, though pre-image resistance held longer. A hash uses no key and does not hide the data, so it is not encryption — anyone can recompute it.

Variants — how the pieces fit together

Two dominant construction styles turn a fixed-size mixing primitive into a hash for arbitrary-length input:

  • Merkle–Damgård — used by MD5, SHA-1, and the SHA-2 family. The message is padded and split into blocks; a compression function absorbs one block at a time into a running chaining value, starting from a fixed initialization vector. It is simple and provably collision-resistant if the compression function is, but its length-extension property (an attacker who knows hash(m) can compute hash(m ‖ suffix)) is a footgun.
  • Sponge — used by SHA-3 (Keccak). A single wide permutation alternately absorbs message blocks into part of its state and then squeezes out the digest. Sponges avoid length extension and can emit output of any length (extendable-output functions, XOFs).2

Many SHA-2 compression functions are themselves built like a block cipher run in a one-way (Davies–Meyer) mode, so the same confusion-and-diffusion machinery that powers ciphers also powers hashes.

In practice — MACs and authentication

A bare hash proves a file was not accidentally changed, but anyone can recompute a digest, so it does not prove who produced it. To authenticate a message you combine the hash with a secret key. HMAC does this by hashing the key together with the message in a nested construction (roughly hash(key ⊕ opad ‖ hash(key ⊕ ipad ‖ msg))), which is secure even on length-extendable Merkle–Damgård hashes. The result — a message authentication code — lets a receiver who shares the key verify both integrity and origin. Hashes also derive keys (HKDF), store passwords (with deliberately slow variants like bcrypt or Argon2), and bind data in digital signatures.

Relevance to SDR

Hashing is about integrity, which on the radio is usually handled by something simpler. A cyclic redundancy check protects P25/DMR frames against accidental bit errors, but a CRC is not a cryptographic hash: it is short, linear, and trivial to forge on purpose, so it detects noise, not tampering. GopherTrunk uses CRCs to validate decoded frames, and the distinction matters — a valid CRC means “probably not corrupted by the channel,” never “authenticated.” Cryptographic hashes proper live in the key-management and authentication layers of secure systems (deriving or checking AES keys, signing firmware, authenticating control messages), which a scanner observes only as opaque encrypted or signed traffic.

Sources

  1. Cryptographic hash function — Wikipedia, for pre-image and collision resistance, the avalanche effect, Merkle–Damgård, HMAC, and the integrity-not-secrecy distinction. ↩

  2. SHA-3 — Wikipedia, for the Keccak sponge construction and its contrast with Merkle–Damgård. ↩

See also