Fixedhas

Fixedhas is a hypothetical construct used in information theory and cryptography to describe a variant of a hash function in which the output space is fixed or substantially constrained by design. The term is not part of standard cryptographic practice and is mainly found in educational materials and speculative discussions about hash properties.

Definition and model: Let H be a standard hash function mapping a data domain D to a large output space O. A fixedhas variant H_f restricts the usable output to a fixed subset F of O, with |F| = m much smaller than |O|. A common approach is to define H_f(x) by applying H(x) and then projecting or mapping into F (for example by modular reduction, truncation, or a deterministic remapping). The result is a function whose outputs lie entirely within F regardless of the input.

Security and implications: With a reduced output space, birthday bound effects appear earlier, increasing the likelihood of collisions for a given number of inputs. Preimage resistance is correspondingly affected, and the function is not appropriate for cryptographic security. Fixedhas is therefore treated as a teaching or modelling tool rather than a practical primitive.

Applications and variations: It is used in classroom demonstrations of hash properties, in simulations of constrained-hash protocols, or in toy models of commitment schemes. Some discussions imagine adjustable fixed subsets to study how different output sizes influence performance and collision behavior.

See also: Hash function, Collision resistance, Preimage resistance, Constrained-output hashing, Toy models in cryptography.