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A Generalized Attack on Some Variants of the RSA Cryptosystem

Journal Article


Abstract


  • Let N=pq be an RSA modulus with unknown factorization. The RSA cryptosystem can be attacked by using the key equation ed−k(p−1)(q−1)=1 . Similarly, some variants of RSA, such as RSA combined with singular elliptic curves, LUC and RSA with Gaussian primes can be attacked by using the key equation ed−k(p2−1)(q2−1)=1 . In this paper, we consider the more general equation eu−(p2−1)(q2−1)v=w and present a new attack that finds the prime factors p and q in the case that u, v and w satisfy some specific conditions. The attack is based on Coppersmith’s technique and improves the former attacks.

Authors


  •   Nitaj, Abderrahmane (external author)
  •   Pan, Yanbin (external author)
  •   Tonien, Joseph

Publication Date


  • 2019

Citation


  • Nitaj, A., Pan, Y. & Tonien, J. (2019). A Generalized Attack on Some Variants of the RSA Cryptosystem. Lecture Notes in Computer Science, 11349 421-433.

Scopus Eid


  • 2-s2.0-85060681972

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/2316

Number Of Pages


  • 12

Start Page


  • 421

End Page


  • 433

Volume


  • 11349

Place Of Publication


  • Germany

Abstract


  • Let N=pq be an RSA modulus with unknown factorization. The RSA cryptosystem can be attacked by using the key equation ed−k(p−1)(q−1)=1 . Similarly, some variants of RSA, such as RSA combined with singular elliptic curves, LUC and RSA with Gaussian primes can be attacked by using the key equation ed−k(p2−1)(q2−1)=1 . In this paper, we consider the more general equation eu−(p2−1)(q2−1)v=w and present a new attack that finds the prime factors p and q in the case that u, v and w satisfy some specific conditions. The attack is based on Coppersmith’s technique and improves the former attacks.

Authors


  •   Nitaj, Abderrahmane (external author)
  •   Pan, Yanbin (external author)
  •   Tonien, Joseph

Publication Date


  • 2019

Citation


  • Nitaj, A., Pan, Y. & Tonien, J. (2019). A Generalized Attack on Some Variants of the RSA Cryptosystem. Lecture Notes in Computer Science, 11349 421-433.

Scopus Eid


  • 2-s2.0-85060681972

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/2316

Number Of Pages


  • 12

Start Page


  • 421

End Page


  • 433

Volume


  • 11349

Place Of Publication


  • Germany