Several of the basic cryptographic constructs have associated algebraic structures. Formal models proposed by Dolev and Yao to study the (unconditional) security of public key protocols form a group. The security of some types of protocols can be neatly formulated in this algebraic setting. We investigate classes of two-party protocols. We then consider extension of the formal algebraic framewo...

Recently, Ajtai discovered a fascinating connection between the worst-case complexity and the average-case complexity of some wellknown lattice problems. Later, Ajtai and Dwork proposed a cryptosystem inspired by Ajtai’s work, provably secure if a particular lattice problem is difficult in the worst-case. We present a heuristic attack (to recover the private key) against this celebrated cryptos...

Recently, Ajtai discovered a fascinating connection between the worst-case complexity and the average-case complexity of some well-known lattice problems. Later, Ajtai and Dwork proposed a cryptosystem inspired by Ajtai's work, provably secure if a particular lattice problem is diicult in the worst-case. We present a heuristic attack (to recover the private key) against this celebrated cryptosy...

In 1998 [8], Patarin proposed an efficient cryptosystem called Little Dragon which was a variant a variant of Matsumoto Imai cryptosystem C*. However Patarin latter found that Little Dragon cryptosystem is not secure [8], [3]. In this paper we propose a cryptosystem Little Dragon Two which is as efficient as Little Dragon cryptosystem but secure against all the known attacks. Like Little Dragon...

Baocang and Yupu proposed a relatively fast public key cryptosystem. The authors claim that the security of their system is based on two number-theoretic hard problems, namely the simultaneous Diophantine approximation problem and the integer factorisation problem. In this article we present a polynomial time heuristic attack that enables us to recover the private key from the public key. In pa...

A Sidon space is a subspace of an extension field over base in which the product any two elements can be factored uniquely, up to constants. This paper proposes new public-key cryptosystem multivariate type based on spaces, and has potential remain secure even if quantum supremacy attained. system, whose security relies hardness well-known MinRank problem, shown resilient several straightforwar...