Solving DLP with Auxiliary Input over an Elliptic Curve Used in TinyTate Library

Abstract : The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α from G, αG, αd G 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 DLPwAI. 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.
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Claudio A. Ardagna; Jianying Zhou. 5th Workshop on Information Security Theory and Practices (WISTP), Jun 2011, Heraklion, Crete, Greece. Springer, Lecture Notes in Computer Science, LNCS-6633, pp.116-127, 2011, Information Security Theory and Practice. Security and Privacy of Mobile Devices in Wireless Communication. 〈10.1007/978-3-642-21040-2_8〉
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Yumi Sakemi, Tetsuya Izu, Masahiko Takenaka, Masaya Yasuda. Solving DLP with Auxiliary Input over an Elliptic Curve Used in TinyTate Library. Claudio A. Ardagna; Jianying Zhou. 5th Workshop on Information Security Theory and Practices (WISTP), Jun 2011, Heraklion, Crete, Greece. Springer, Lecture Notes in Computer Science, LNCS-6633, pp.116-127, 2011, Information Security Theory and Practice. Security and Privacy of Mobile Devices in Wireless Communication. 〈10.1007/978-3-642-21040-2_8〉. 〈hal-01573301〉

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