Hash-functions using modulo-n operations

Abstract

Today, there is a need for one-way hash-functions, particularly for use in digital signatures [1]. Following R.S. Winternitz [2], we define that H is a one-way hash-function if it maps messages of arbitrary length to some small fixed length, such that it is computationally infeasible to find two different messages M and M′ hashing to the same value H(M) = H(M′). Now, if Alice wishes to sign M using for example the public-key system RSA, she submits H(M) to her secret function SAlice, and the signature of M is Sig = SAlice [H(M)]. The functions H and PAlice (her RSA public function) being public, anybody who received the plain message M along with its signature Sig, is able to verify the signature by matching PAlice(Sig) against H(M). The one-way property of H is not the only one required [3], but is the essential one: it prevents anybody (including Alice) from claiming that Sig is Alice’s signature of a message M′, different from M.