## Cryptology ePrint Archive: Report 2006/178

A New Cryptosystem Based On Hidden Order Groups

Amitabh Saxena and 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.

Category / Keywords: public-key cryptography /

Publication Info: arXiv report archive (eprint arXiv:cs/0605003)

Date: received 19 May 2006, last revised 5 Mar 2007

Contact author: asaxena at cs latrobe edu au

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

Note: Updates on 05/03/07: A few typos corrected.

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