In this paper, we consider the Polly Cracker with Noise (PCN) cryptosystem by Albrecht, Farshim, Faugère, and Perret (Asiacrypt 2011), which is a public-key cryptosystem based on the hardness of computing Gröbner bases for noisy random systems of multivariate equations. We examine four settings, covering all possible parameter ranges of PCN with zero-degree noise. In the first setting, the PCN cryptosystem is known to be equivalent to Regev's LWE-based scheme. In the second, it is known to be at most as secure as Regev's scheme. We show that for one other settings it is equivalent to a variants of Regev's with less efficiency and in the last setting it is completely insecure and we give an efficient key-recovery attack. Unrelated to the attack, we also fix some flaws in the security proofs of PCN. © 2012 International Association for Cryptologic Research.
CITATION STYLE
Herold, G. (2012). Polly cracker, revisited, revisited. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7293 LNCS, pp. 17–33). https://doi.org/10.1007/978-3-642-30057-8_2
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