On Generalization of Cheon's Algorithm

Takakazu Satoh

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Paper 2009/058

On Generalization of Cheon's Algorithm

Takakazu Satoh

Abstract

We consider a generalization of Cheon's algorithm on the strong Diffie-Hellman problem. More specifically, we consider the circumstance that p^k-1 has a small divisor for k>=3, where p is the order of group on which we consider the strong Diffie-Hellman problem. It seems that our algorithm is only effective for k=1, 2, that is, the original Cheon's algorithm.

Note: The exponent in (5) and the proof of Lemma 2 are corrected. The author would like to thank Dr. Sungwook Kim for pointing out them.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. None.
Keywords: strong Diffie-Hellman problem
Contact author(s): satohcgn @ mathpc-satoh math titech ac jp
History: 2010-10-11: last of 2 revisions; 2009-02-06: received; See all versions
Short URL: https://ia.cr/2009/058
License: CC BY

BibTeX

@misc{cryptoeprint:2009/058,
      author = {Takakazu Satoh},
      title = {On Generalization of Cheon's Algorithm},
      howpublished = {Cryptology ePrint Archive, Paper 2009/058},
      year = {2009},
      note = {\url{https://eprint.iacr.org/2009/058}},
      url = {https://eprint.iacr.org/2009/058}
}