A New Cryptosystem Based On Hidden Order Groups
<|reference_start|>A New Cryptosystem Based On Hidden Order Groups: 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.<|reference_end|>
@article{saxena2006a,
    title={A New Cryptosystem Based On Hidden Order Groups},
    author={Amitabh Saxena and Ben Soh},
    journal={arXiv preprint arXiv:cs/0605003},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0605003},
    primaryClass={cs.CR cs.CC}
}