منابع مشابه
Lattice Polly Cracker cryptosystems
Using Gröbner bases for the construction of public key cryptosystems has been often attempted, but has always failed. We review the reason for these failures, and show that only ideals generated by binomials may give a successful cryptosystem. As a consequence, we concentrate on binomial ideals that correspond to Euclidean lattices. We show how to build a cryptosystem based on lattice ideals an...
متن کاملPrivate Key Extension of Polly Cracker Cryptosystems
In 1993 Koblitz and Fellows proposed a public key cryptosystem, Polly Cracker, based on the problem of solving multivariate systems of polynomial equations, which was soon generalized to a Gröbner basis formulation. Since then a handful of improvements of this construction has been proposed. In this paper it is suggested that security, and possibly e ciency, of any Polly Cracker-type cryptosyst...
متن کاملNoncommutative Polly Cracker-type cryptosystems and chosen-ciphertext security
In this paper we consider chosen-ciphertext attacks against noncommutative Polly Cracker-type cryptosystems. We present several versions of these attacks, as well as techniques to counter them. First we introduce a chosen-ciphertext attack, which assumes a very simple private key. We then present generalizations of this attack which are valid in more general situations, and propose a simple but...
متن کاملCountering chosen-ciphertext attacks against noncommutative polly cracker-type cryptosystems
In [2], Stanislav Bulygin presents a chosen-ciphertext attack against certain instances of noncommutative polly cracker-type cryptosystems which were proposed in [7] and [9]. In this article, we present generalized versions of this attack, which can be used against virtually all polly cracker-type cryptosystems. We then present a simple but effective techique to counter these attacks. We also p...
متن کاملPolly Cracker, Revisited
In this work, we initiate the formal treatment of cryptographic constructions (“Polly Cracker”) based on the hardness of computing remainders modulo an ideal. We start by formalising and studying the relation between the ideal remainder problem and the problem of computing a Gröbner basis. We show both positive and negative results. On the negative side, we define a symmetric Polly Cracker encr...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2011
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2010.10.004