Abstract
We propose an algorithm that, given an arbitrary N of unknown factorization and prime \(e \geq N^{\frac{1}{4}+\varepsilon}\), certifies whether the RSA function RSA N,e (x) : = x e mod N defines a permutation over \({\mathbb Z}_{N}^{*}\) or not. The algorithm uses Coppersmith’s method to find small solutions of polynomial equations and runs in time O(ε − 8 log2 N). Previous certification techniques required e > N.
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Kakvi, S.A., Kiltz, E., May, A. (2012). Certifying RSA. In: Wang, X., Sako, K. (eds) Advances in Cryptology – ASIACRYPT 2012. ASIACRYPT 2012. Lecture Notes in Computer Science, vol 7658. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34961-4_25
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