Abstract
In 2019, Gu Chunsheng introduced Integer-RLWE, a variant of RLWE devoid of some of its efficiency flaws. Most notably, he proposes a setting where n can be an arbitrary positive integer, contrarily to the typical construction \(n = 2^k\). In this paper, we analyze the new problem and implement the classical meet-in-the-middle and lattice-based attacks. We then use the peculiarity of the construction of n to build an improved lattice-based attack in cases where n is composite with an odd divisor. For example, for parameters \(n = 2000\) and \(q = 2^{33}\), we reduce the estimated complexity of the attack from \(2^{288}\) to \(2^{164}\). We also present reproducible experiments confirming our theoretical results.
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We thank Martha Norberg Hovd and Andrea Tenti for proofreading our manuscript in an early stage and providing insightful comments.
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Budroni, A., Chetioui, B., Franch, E. (2020). Attacks on Integer-RLWE. In: Meng, W., Gollmann, D., Jensen, C.D., Zhou, J. (eds) Information and Communications Security. ICICS 2020. Lecture Notes in Computer Science(), vol 12282. Springer, Cham. https://doi.org/10.1007/978-3-030-61078-4_30
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