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A new attack on three variants of the RSA cryptosystem

Journal Article


Abstract


  • In 1995, Kuwakado, Koyama and Tsuruoka presented a new RSA-type scheme based on singular cubic curves y2 = x3+bx2 (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 = PQ where P and Q are Gaussian primes such that p = jPj and q = jQj are ordinary primes. Later, in 2007, Castagnos proposed a scheme over quadratic field quotients with an RSA modulus N = pq. In the three schemes,

    the public exponent e is an integer satisfying the key equation ed - k(p2-1) (q2-1) = 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 the RSA.

Publication Date


  • 2016

Citation


  • Bunder, M. W., Nitaj, A., Susilo, W. & Tonien, J. (2016). A new attack on three variants of the RSA cryptosystem. Lecture Notes in Computer Science, (9723), 258-268. Melbourne, Australia 21st Australasian Conference, ACISP 2016

Scopus Eid


  • 2-s2.0-84978821812

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5648

Has Global Citation Frequency


Number Of Pages


  • 10

Start Page


  • 258

End Page


  • 268

Issue


  • 9723

Place Of Publication


  • Germany

Abstract


  • In 1995, Kuwakado, Koyama and Tsuruoka presented a new RSA-type scheme based on singular cubic curves y2 = x3+bx2 (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 = PQ where P and Q are Gaussian primes such that p = jPj and q = jQj are ordinary primes. Later, in 2007, Castagnos proposed a scheme over quadratic field quotients with an RSA modulus N = pq. In the three schemes,

    the public exponent e is an integer satisfying the key equation ed - k(p2-1) (q2-1) = 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 the RSA.

Publication Date


  • 2016

Citation


  • Bunder, M. W., Nitaj, A., Susilo, W. & Tonien, J. (2016). A new attack on three variants of the RSA cryptosystem. Lecture Notes in Computer Science, (9723), 258-268. Melbourne, Australia 21st Australasian Conference, ACISP 2016

Scopus Eid


  • 2-s2.0-84978821812

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5648

Has Global Citation Frequency


Number Of Pages


  • 10

Start Page


  • 258

End Page


  • 268

Issue


  • 9723

Place Of Publication


  • Germany