Abstract
Message recovery attacks against the Classic McEliece proposal to the NIST standardization process, have recently made use of the Integer syndrome decoding problem. It was demonstrated the one can modify or find extra information about the encrypted data, by means of physical attacks. The question raised by these modifications gave birth to the integer syndrome decoding problem. Here, we propose an algorithm that works as an optimized exhaustive-search, and thus finds all the solutions to the aforementioned problem. The key idea in the complexity gain is to split the binomial coefficient into product of smaller binomial coefficients. We show that this can be achieved using a permutation decomposition of the input matrix. Simulations are provided for small length and dimension matrices.
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Acknowledgment
V-F. Drăgoi was supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS/CCCDI - UEFISCDI, project number PN-III-P1-1.1-PD-2019-0285, within PNCDI III.
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Dragoi, VF., Lacatus, A.T., Popoviciu, A. (2023). Combinatorial Algorithms for Integer Syndrome Decoding Problem. In: Balas, V.E., Jain, L.C., Balas, M.M., Baleanu, D. (eds) Soft Computing Applications. SOFA 2020. Advances in Intelligent Systems and Computing, vol 1438. Springer, Cham. https://doi.org/10.1007/978-3-031-23636-5_50
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