The multi-variable modular polynomial and its applications to cryptography

Tsuyoshi Takagi, Shozo Naito

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 7th International Symposium, ISAAC 1996, Proceedings
EditorsTetsuo Asano, Yoshihide Igarashi, Hiroshi Nagamochi, Satoru Miyano, Subhash Suri
PublisherSpringer Verlag
Pages386-396
Number of pages11
ISBN (Print)3540620486, 9783540620488
DOIs
Publication statusPublished - Jan 1 1996
Event7th International Symposium on Algorithms and Computation, ISAAC 1996 - Osaka, Japan
Duration: Dec 16 1996Dec 18 1996

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1178
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other7th International Symposium on Algorithms and Computation, ISAAC 1996
CountryJapan
CityOsaka
Period12/16/9612/18/96

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Takagi, T., & Naito, S. (1996). The multi-variable modular polynomial and its applications to cryptography. In T. Asano, Y. Igarashi, H. Nagamochi, S. Miyano, & S. Suri (Eds.), Algorithms and Computation - 7th International Symposium, ISAAC 1996, Proceedings (pp. 386-396). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1178). Springer Verlag. https://doi.org/10.1007/bfb0009515