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A new attack on three variants of the RSA cryptosystem

Abstract : In 1995, Kuwakado, Koyama and Tsuruoka presented a new RSA-type scheme based on singular cubic curves y^2 ≡ x^3 + bx^2 (mod N) where N = pq is an RSA modulus. Then, in 2002, Elkamchouchi, Elshenawy and Shaban introduced an extension of the RSA scheme to the field of Gaussian integers using a modulus N = P Q where P and Q are Gaussian primes such that p = |P | and q = |Q| are ordinary primes. Later, in 2007, Castagnos's proposed a scheme over quadratic fields quotients with an RSA modulus N = pq. In the three schemes, the public exponent e is an integer satisfying the key equation ed − k^(p^2 − 1) (q^2 − 1) = 1. In this paper, we apply the continued fraction method to launch an attack on the three schemes when the private exponent d is sufficiently small. Our attack can be considered as an extension of the famous Wiener attack on RSA.
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Submitted on : Sunday, October 20, 2019 - 10:45:02 AM
Last modification on : Monday, April 27, 2020 - 4:14:03 PM
Long-term archiving on: : Tuesday, January 21, 2020 - 12:53:44 PM

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Martin Bunder, Abderrahmane Nitaj, Willy Susilo, Joseph Tonien. A new attack on three variants of the RSA cryptosystem. 21st Australasian Conference on Information Security and Privacy ACISP 2016, 2016, Sydney, Australia. ⟨10.1007/978-3-319-40367-0_16⟩. ⟨hal-02321009⟩

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