A Parameterized Splitting System and Its Application to the Discrete Logarithm Problem with Low Hamming Weight Product Exponents
نویسندگان
چکیده
A low Hamming weight product (LHWP) exponent is used to increase the efficiency of cryptosystems based on the discrete logarithm problem (DLP). In this paper, we introduce a new tool, called a Parameterized Splitting System, to analyze the security of the DLP with LHWP exponents. We apply a parameterized splitting system to attack the GPS identification scheme modified by Coron, Lefranc and Poupard in CHES’05 and obtain an algorithm of 2 time complexity which was expected to be 2. Also a parameterized splitting system can be used to solve the DLP with a LHWP exponent proposed by Hoffstein and Silverman in 2 time complexity, that is smaller than 2 in the recent Cheon-Kim attack.
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