Private Key Extension of Polly Cracker Cryptosystems

Noncommutative 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...

Countering 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...

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...

Secret Sharing for n-Colorable Graphs with Application to Public Key Cryptography

At the beginning some results from the field of graph theory are presented. Next we show how to share a secret that is proper n-coloring of the graph, with the known structure. The graph is described and converted to the form, where colors assigned to vertices form the number with entries from Zn. A secret sharing scheme (SSS) for the graph coloring is proposed. The proposed method is applied t...

Polly two - a public key cryptosystem based on Polly cracker