The multi-variable modular polynomial and its applications to cryptography

  • Tsuyoshi Takagi
  • Shozo Naito
Session 9b: Invited Presentation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1178)


We prove the extension of the Håstad algorithm to the multi-variable modular polynomial. Although the Håstad attack is one of the strongest known attacks on RSA-type cryptosystems, the original Håstad attack is generally not applicable to multi-variable cryptosystems, where the plain text space (the encryption domain) is multi-variable. As an application of our extension, we attack RSA-type cryptosystems over elliptic curves and show the critical number of encrypted texts.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Tsuyoshi Takagi
    • 1
  • Shozo Naito
    • 1
  1. 1.NTT Software LaboratoriesTokyo

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