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Title:
A New Cryptosystem Based On Hidden Order Groups
Authors: Amitabh Saxena, Ben Soh
Abstract:Let G_1 be a cyclic multiplicative group of order n. It is known that the Diffie-Hellman problem is random self-reducible in G_1 with respect to a fixed generator g if \phi(n) is known. That is, given g, g^x\in G_1 and having oracle access to a Diffie-Hellman Problem solver'' with fixed generator $g$, it is possible to compute $g^{1/x} \in G_1$ in polynomial time (see theorem 3.2). On the other hand, it is not known if such a reduction exists when $\phi(n)$ 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.
ePrint: https://eprint.iacr.org/2006/178
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