A new attack on the KMOV cryptosystem
Bull. Korean Math. Soc. 2014 Vol. 51, No. 5, 1347-1356
Printed September 30, 2014
Abderrahmane Nitaj
Universit\'e de Caen
Abstract : 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
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