Handbook of Applied Cryptography
Handbook of Applied Cryptography
Some baby-step giant-step algorithms for the low hamming weight discrete logarithm problem
Mathematics of Computation
Random small hamming weight products with applications to cryptography
Discrete Applied Mathematics - Special issue on the 2000 com2MaC workshop on cryptography
Analysis of Low Hamming Weight Products
Discrete Applied Mathematics
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Practical threshold signatures
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
A new baby-step giant-step algorithm and some applications to cryptanalysis
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Parameterized splitting systems for the discrete logarithm
IEEE Transactions on Information Theory
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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 261.6 time complexity which was expected to be 278. Also a parameterized splitting system can be used to solve the DLP with a LHWP exponent proposed by Hoffstein and Silverman in 254.51 time complexity, that is smaller than 259 in the recent Cheon-Kim attack.