Solving DLP with auxiliary input over an elliptic curve used in TinyTate library

Authors:
Yumi Sakemi;Tetsuya Izu;Masahiko Takenaka;Masaya Yasuda
Affiliations:
Okayama University, Kita-ku, Okayama, Japan;Fujitsu Laboratories Ltd., Nakahara-ku, Kawasaki, Japan;Fujitsu Laboratories Ltd., Nakahara-ku, Kawasaki, Japan;Fujitsu Laboratories Ltd., Nakahara-ku, Kawasaki, Japan
Venue:
WISTP'11 Proceedings of the 5th IFIP WG 11.2 international conference on Information security theory and practice: security and privacy of mobile devices in wireless communication
Year:
2011

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Abstract

The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find a from G, αG, αdG in an additive cyclic group generated by G of prime order r and a positive integer d dividing r - 1. The infeasibility of DLPwAI assures the security of some cryptographic schemes. In 2006, Cheon proposed a novel algorithm for solving DLP-wAI. This paper shows our experimental results of Cheon's algorithm by implementing it with some speeding-up techniques. In fact, we succeeded to solve DLPwAI in a group with 128-bit order in 45 hours with a single PC on an elliptic curve defined over a prime finite field with 256-bit elements which is used in the TinyTate library.