Bulletin of the
Korean Mathematical Society BKMS

In this paper, we analyze the security of the KMOV public key cryptosystem. KMOV is based on elliptic curves over the ring $\mathbb{Z}_n$ where $n=pq$ is the product of two large unknown primes of equal bit-size. We consider KMOV with a public key $(n,e)$ where the exponent $e$ satisfies an equation $ ex-(p+1)(q+1)y=z, $ with unknown parameters $x$, $y$, $z$. Using Diophantine approximations and lattice reduction techniques, we show that KMOV is insecure when $x$, $y$, $z$ are suitably small.

Keywords: cryptanalysis, factorization, Coppersmith's method, continued fraction

MSC numbers: 11T71, 94A60, 14G50