Abstract
Finding the solution to a general multivariate modular linear equation plays an important role in cryptanalysis field. Earlier results show that obtaining a relatively short solution is possible in polynomial time. However, one problem arises here that if the equation has a short solution in given bounded range, the results outputted by earlier algorithms are often not the ones we are interested in. In this paper, we present a probability method based on lattice basis reduction to solve the problem. For a general multivariate modular linear equation with short solution in the given bounded range, the new method outputs this short solution in polynomial time, with a high probability. When the number of unknowns is not too large (smaller than 68), the probability is approximating 1. Experimental results show that Knapsack systems and Lu-Lee type systems are easily broken in polynomial time with this new method.
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Supported by the National Natural Science Foundation of China (Grant Nos. 60873249, 60973142), the National High-Tech Research & Development Program of China (Grant Nos. 2008AA10Z419, 2009AA011906), and the Project Funded by Basic Research Foundation of School of Information Science and Technology of Tsinghua University
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Zhou, H., Luo, P., Wang, D. et al. Probability method for cryptanalysis of general multivariate modular linear equation. Sci. China Ser. F-Inf. Sci. 52, 1792–1800 (2009). https://doi.org/10.1007/s11432-009-0159-9
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DOI: https://doi.org/10.1007/s11432-009-0159-9