Arithmetic, Geometry, Cryptography, and Coding Theory 2021

Applications of finite geometry in coding theory and cryptography

We present in this article the basic properties of projective geometry, coding theory, and cryptography, and show how finite geometry can contribute to coding theory and cryptography. In this way, we show links between three research areas, and in particular, show that finite geometry is not only interesting from a pure mathematical point of view, but also of interest for applications. We conce...

Arithmetic Coding and Blinding for Lattice Cryptography

In this work we apply information theoretically optimal arithmetic coding and a number of novel side-channel blinding countermeasure techniques to create BLZZRD, a practical, compact, and more quantum-resistant variant of the BLISS Ring-LWE Signature Scheme. We show how the hash-based random oracle can be modified to be more secure against quantum preimage attacks while decreasing signature siz...

Coding Theory & Cryptography

Curves, Cryptography and Coding theory

2 Basic Cryptography 3 2.1 Preliminaries: Ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Modern Cryptography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Block Ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.2 Moving forward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Generalised Jacobians in Cryptography and Coding Theory

The use of generalised Jacobians in discrete logarithm based cryptosystems has so far been rather limited since they offer no advantage over traditional discrete logarithm based systems. In this paper we continue the search for possible applications in two directions. Firstly, we investigate pairings on generalised Jacobians and show that these are insecure. Secondly, generalising and extending...