Aggarwal, Joux, Prakash and Santha recently introduced a new potentially quantum-safe public-key cryptosystem, and suggested that a brute-force attack is essentially optimal against it. They consider but then dismiss both Meet-in-the-Middle attacks and LLL-based attacks. Very soon after their paper appeared, Beunardeau et al. proposed a practical LLL-based technique that seemed to significantly reduce the security of the AJPS system. In this paper we do two things. First, we show that a Meet-in-the-Middle attack can also be made to work against the AJPS system, using locality-sensitive hashing to overcome the difficulty that Aggarwal et al. saw for such attacks. We also present a quantum version of this attack. Second, we give a more precise analysis of the attack of Beunardeau et al., confirming and refining their results.
CITATION STYLE
de Boer, K., Ducas, L., Jeffery, S., & de Wolf, R. (2018). Attacks on the AJPS mersenne-based cryptosystem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10786 LNCS, pp. 101–120). Springer Verlag. https://doi.org/10.1007/978-3-319-79063-3_5
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