A New Cryptosystem Based On Hidden Order Groups

Amitabh Saxena; Ben Soh

Paper 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 $ϕ (n)$ 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 $ϕ (n)$ 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.

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

Metadata

Available format(s): PDF PS
Category: Public-key cryptography
Publication info: Published elsewhere. arXiv report archive (eprint arXiv:cs/0605003)
Contact author(s): asaxena @ cs latrobe edu au
History: 2007-03-05: last of 6 revisions; 2006-05-30: received; See all versions
Short URL: https://ia.cr/2006/178
License: CC BY

BibTeX

@misc{cryptoeprint:2006/178,
      author = {Amitabh Saxena and Ben Soh},
      title = {A New Cryptosystem Based On Hidden Order Groups},
      howpublished = {Cryptology {ePrint} Archive, Paper 2006/178},
      year = {2006},
      url = {https://eprint.iacr.org/2006/178}
}