@inbook {IOPORT.06059170, author = {Herold, Gottfried}, title = {Polly cracker, revisited, revisited.}, year = {2012}, booktitle = {Public key cryptography -- PKC 2012. 15th international conference on practice and theory in public key cryptography, Darmstadt, Germany, May 21--23, 2012. Proceedings}, isbn = {978-3-642-30056-1}, pages = {17-33}, publisher = {Berlin: Springer}, doi = {10.1007/978-3-642-30057-8_2}, abstract = {Summary: In this paper, we consider the polly cracker with noise (PCN) cryptosystem by Albrecht, Farshim, Faug\`ere, and Perret (Asiacrypt 2011), which is a public-key cryptosystem based on the hardness of computing Gr\"obner 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.}, identifier = {06059170}, }