Low exponent attack against elliptic curve RSA

  • Kaoru Kurosawa
  • Koji Okada
  • Shigeo Tsujii
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 917)


Hastad showed that low exponent RSA is not secure if the same message is encrypted to several receivers. This is true even if time-stamp is used for each receiver. For example, let e=3. Then if the number of receivers =7, the eavesdropper can find the plaintext from the seven ciphertexts of each receiver.

This paper shows that elliptic curve RSA is not secure in the same scenario. It is shown that the KMOV scheme and Demytko's scheme are not secure if e=5, n≥21024 and the number of receivers =428. In Demytko's scheme, e can take the value of 2. In this case, this system is not secure if the number of receiver =11 for n≥2175.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J.Hastad: On using RSA with low exponent in a public key network. Proc. of Crypto'85, pp.403–408 (1985)Google Scholar
  2. 2.
    K.Koyama, U.M.Maurer, T.Okamoto and S.A.Vanstone: New public-key schemes based on elliptic curves over the ring Z n. Proc. of Crypto'91 (1991)Google Scholar
  3. 3.
    N.Demytko: A new elliptic curve based analogue of RSA. Proc. of Eurocrypt'93, pp.39–48, May 24 (1993)Google Scholar
  4. 4.
    D.M.Bressoud: Factorization and primality testing. Springer-Verlag (1989)Google Scholar
  5. 5.
    K.Kurosawa and S.Tsujii: Low exponent attack against elliptic curve RSA. Technical Report of IEICE, ISEC94-2, pp.11–17 (1994)Google Scholar
  6. 6.
    H.Kuwakado and K.Koyama: On the security of RSA-type schemes over cubic curves against the Hastad attack. Technical report of IEICE, ISEC94-10, pp.23–30 (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Kaoru Kurosawa
    • 1
  • Koji Okada
    • 1
  • Shigeo Tsujii
    • 2
  1. 1.Department of Electrical and Electronic Engineering, Faculty of EngineeringTokyo Institute of TechnologyTokyoJapan
  2. 2.Department of Information Systems EngineeringChuo UniversityTokyoJapan

Personalised recommendations