4 research outputs found
A New Cryptosystem Based On Hidden Order Groups
Let be a cyclic multiplicative group of order . It is known that the
Diffie-Hellman problem is random self-reducible in with respect to a
fixed generator if is known. That is, given and
having oracle access to a `Diffie-Hellman Problem' solver with fixed generator
, it is possible to compute in polynomial time (see
theorem 3.2). On the other hand, it is not known if such a reduction exists
when is unknown (see conjuncture 3.1). We exploit this ``gap'' to
construct a cryptosystem based on hidden order groups and present a practical
implementation of a novel cryptographic primitive called an \emph{Oracle Strong
Associative One-Way Function} (O-SAOWF). O-SAOWFs have applications in
multiparty protocols. We demonstrate this by presenting a key agreement
protocol for dynamic ad-hoc groups.Comment: removed examples for multiparty key agreement and join protocols,
since they are redundan
Enforcing and defying associativity, commutativity, totality, and strong noninvertibility for one-way functions in complexity theory
Rabi and Sherman [RS97,RS93] proved that the hardness of factoring is a sufficient condition for there to exist one-way functions (i.e., p-time computable, honest, p-time noninvertible functions) that are total, commutative, and associative but not strongly noninvertible. In this paper we improve the sufficient condition to P = NP. More generally, in this paper we completely characterize which types of one-way functions stand or fall together with (plain) one-way functionsâequivalently, stand or fall together with P = NP. We look at the four attributes used in Rabi and Shermanâs seminal work on algebraic properties of one-way functions (see [RS97,RS93]) and subsequent papersâstrongness (of noninvertibility), totality, commutativity, and associativityâand for each attribute, we allow it to be required to hold, required to fail, or âdonât care. â In this categorization there are 3 4 = 81 potential types of one-way functions. We prove that each of these 81 feature-laden types stand or fall together with the existence of (plain) one-way functions. Key words: computational complexity, complexity-theoretic one-way functions, associativity, 1.