hashketjua

Hashketjua, or hash chain, is a cryptographic construction consisting of a sequence of values produced by iteratively applying a cryptographic hash function to a starting seed. Each element is the hash of the previous one, forming a chain that grows toward a fixed anchor value that may be published in advance. The chain provides a source of one-time values and commitments for authentication and integrity protocols.

Construction and operation: Given a hash function H and a seed s0, define s1 = H(s0), s2 = H(s1), …, sn = H(s_{n-1}). The anchor sn can be published ahead of time, while the remaining values are revealed in a predetermined order. Verification proceeds by applying H to the revealed element(s) and checking that it matches the previously accepted value (or the anchor). Because H is one-way, earlier values cannot be derived from later ones without the preimage.

Applications: Hashketjua have been used in one-time password systems such as S/Key, where users authenticate by revealing successive preimages. They also appear in commit-reveal protocols and certain timestamping or anti-replay schemes, where a value is hashed repeatedly to create a time-bound commitment or proof of inclusion.

Security and limitations: The security rests on the preimage resistance of the hash function. If an attacker learns a value from the chain, they can compute later chain elements, potentially compromising future authentications; previously used tokens remain invalid due to one-time usage. The chain length and management of seeds must be chosen carefully to balance usability and risk.

Variants: Some approaches reveal values in reverse order, use salting, or pair hash chains with other primitives such as digital signatures or Merkle trees.

References: See standard cryptographic literature on hash chains and one-time password schemes.