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Improved Cryptanalysis of the KMOV Elliptic Curve Cryptosystem

Abstract : This paper presents two new improved attacks on the KMOV cryptosystem. KMOV is an encryption algorithm based on elliptic curves over the ring ZN where N = pq is a product of two large primes of equal bit size. The first attack uses the properties of the convergents of the continued fraction expansion of a specific value derived from the KMOV public key. The second attack is based on Coppersmith's method for finding small solutions of a multivariate polynomial modular equation. Both attacks improve the existing attacks on the KMOV cryptosystem.
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https://hal-normandie-univ.archives-ouvertes.fr/hal-02320906
Contributor : Abderrahmane Nitaj <>
Submitted on : Saturday, October 19, 2019 - 7:25:34 PM
Last modification on : Monday, April 27, 2020 - 4:14:03 PM
Long-term archiving on: : Monday, January 20, 2020 - 1:32:53 PM

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Abderrahmane Nitaj, Willy Susilo, Joseph Tonien. Improved Cryptanalysis of the KMOV Elliptic Curve Cryptosystem. Provable Security ProvSec 2019, 2019, Cairns, Australia. ⟨10.1007/978-3-030-31919-9_12⟩. ⟨hal-02320906⟩

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