Abstract. This paper describes a simple candidate one-way hash function which satisfies a quasi-commutative property that allows it to be used aa an accumulator. This property allows protocols to be developed in which the need for a trusted central authority can be eliminated. Spaceefficient distributed protocols are given for document time stamping and for membership testing, and many other applications are possible. One-way hash functions are generally defined as functions of a single argument which (in a "difficult to invert-fashion) reduce their arguments to a predetermined size. We view hash functions, somewhat differently here, as functions which take two arguments from comparably sized domains and produce a result of similar size. In other words, a hash function is a function h with the property that h: A x B + C where [A] x IBI k: I C I . There is, of course, no substantial difference between this view and the traditional view except that this view allows us to define a special quasi-commutative property which, as it turns out, has several applications. The desired property is obtained by considering functions h: X x Y + X and asserting that for all z E X and for all y1,yz E Y, This property is not at all unusual. Addition and multiplication modulo n both have this property as does exponentiation modulo n when written as en(z, y) = xv mod n. Of these, only exponentiation modulo n has the additional property that (under suitable conditions), the function is believed to be difficult to invert. This paper will describe how to use the combination of these two properties (quasi-commutativity and one-wayness) to develop a one-way uccurnulator which (among other applications) can be used to provide space-efficient cryptographic protocols for time stamping and membership testing.
Benaloh and Mare REF presented one-way accumulator, which satisfies a quasi-commutative property that allows it to be used for membership testing.
One-way accumulators: A decentralized alternative to digital signatures
EUROCRYPT
Computer Science