Conference Paper
Polly Cracker, Revisited.
DOI: 10.1007/9783642253850_10 Conference: Advances in Cryptology  ASIACRYPT 2011  17th International Conference on the Theory and Application of Cryptology and Information Security, Seoul, South Korea, December 48, 2011. Proceedings
Source: DBLP

Conference Paper: A fully homomorphic cryptosystem with approximate perfect secrecy
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ABSTRACT: We propose a new fully homomorphic cryptosystem called Symmetric Polly Cracker (SymPC) and we prove its security in the information theoretical settings. Namely, we prove that SymPC approaches perfect secrecy in bounded CPA model as its security parameter grows (which we call approximate perfect secrecy). In our construction, we use a Gröbner basis to generate a polynomial factor ring of ciphertexts and use the underlying field as the plaintext space. The Gröbner basis equips the ciphertext factor ring with a multiplicative structure that is easily algorithmized, thus providing an environment for a fully homomorphic cryptosystem.Proceedings of the 13th international conference on Topics in Cryptology; 02/2013  [Show abstract] [Hide abstract]
ABSTRACT: We provide an alternative method for constructing latticebased digital signatures which does not use the "hashandsign" methodology of Gentry, Peikert, and Vaikuntanathan (STOC 2008). Our resulting signature scheme is secure, in the random oracle model, based on the worstcase hardness of the Õ(n1.5)SIVP problem in general lattices. The secret key, public key, and the signature size of our scheme are smaller than in all previous instantiations of the hashandsign signature, and our signing algorithm is also quite simple, requiring just a few matrixvector multiplications and rejection samplings. We then also show that by slightly changing the parameters, one can get even more efficient signatures that are based on the hardness of the Learning With Errors problem. Our construction naturally transfers to the ring setting, where the size of the public and secret keys can be significantly shrunk, which results in the most practical todate provably secure signature scheme based on lattices.IACR Cryptology ePrint Archive. 01/2011; 2011:537. 
Conference Paper: Polly cracker, revisited, revisited
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ABSTRACT: In this paper, we consider the Polly Cracker with Noise (PCN) cryptosystem by Albrecht, Farshim, Faugère, and Perret (Asiacrypt 2011), which is a publickey 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 zerodegree noise. In the first setting, the PCN cryptosystem is known to be equivalent to Regev's LWEbased 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 keyrecovery attack. Unrelated to the attack, we also fix some flaws in the security proofs of PCN.Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography; 05/2012
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