A new attack on three variants of the RSA cryptosystem - Normandie Université Accéder directement au contenu
Communication Dans Un Congrès Année : 2016

A new attack on three variants of the RSA cryptosystem

Martin Bunder
  • Fonction : Auteur
  • PersonId : 1056339
Joseph Tonien
  • Fonction : Auteur
  • PersonId : 1056341

Résumé

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.
Fichier principal
Vignette du fichier
singular1.pdf (287.24 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02321009 , version 1 (20-10-2019)

Identifiants

Citer

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⟩
21 Consultations
89 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More