Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A NEW ATTACK ON THE KMOV CRYPTOSYSTEM

  • Received : 2012.06.26
  • Published : 2014.09.30
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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.

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Cited by

  1. A new generalization of the KMOV cryptosystem 2017, https://doi.org/10.1007/s12190-017-1103-6