Chris Monico

Using low density parity check codes in the McEliece cryptosystem

We examine the implications of using a low density parity check code (LDPCC) in place of the usual Goppa code in McElieces cryptosystem. Using a LDPCC allows for larger block lengths and the possibility of a combined error correction/encryption protocol.

PUBLIC KEY CRYPTOGRAPHY BASED ON SEMIGROUP ACTIONS

A generalization of the original Diffie-Hellman key exchange in

Computing the Primary Decomposition of Zero-dimensional Ideals

(\mathbb Z

Cryptanalysis of a system using matrices over group rings

∕

Markov source based test length optimized SCAN-BIST architecture

p\mathbb Z)

Diffie-HellmanA public key cryptosystem based on actions by semigroups

* found a new depth when Miller [27] and Koblitz [16] suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further vast generalization where abelian semigroups act on finite sets. We define a Diffie-Hellman key exchange in this setting and we illustrate how to build interesting semigroup actions using finite (simple) semirings. The practicality of the proposed extensions rely on the orbit sizes of the semigroup actions and at this point it is an open question how to compute the sizes of these orbits in general and also if there exists a square root attack in general. In Section 5 a concrete practical semigroup action built from simple semirings is presented. It will require further research to analyse this system.

Cryptanalysis of a Matrix-based MOR System

Let K be an infinite perfect computable field and let I�Kx ] be a zero-dimensional ideal represented by a Gr�bner basis. We derive a new algorithm for computing the reduced primary decomposition of I using only standard linear algebra and univariate polynomial factorization techniques. In practice, the algorithm generally works in finite fields of large characteristic as well.

Nonlinear codes for belief propagation

Abstract In several recent works of D. Kahrobaei, C. Koupparis, and V. Shpilrain, public-key protocols have been proposed which depend on the difficulty of computing discrete logarithms in matrix rings over group rings. In particular, the specific ring of 3×3 matrices over 𝔽 7 S 5

On finite congruence-simple semirings

{\mathbb {F}_7S_5}

Semirings and Semigroup Actions in Public-Key Cryptography

has been proposed for use in some of these protocols. In this paper, we show that the discrete logarithm problem in this matrix ring can be solved on a modern PC in seconds, and we give a solution to the challenge problem over 𝔽 2 S 5