# Andrew MendelsohnImperial College London | Imperial · Department of Electrical and Electronic Engineering

Andrew Mendelsohn

Doctor of Philosophy

Postdoctoral researcher at Imperial College London

## About

11

Publications

501

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18

Citations

Introduction

Working in post-quantum cryptography

**Skills and Expertise**

## Publications

Publications (11)

Let [Formula: see text] be a totally real number field of degree [Formula: see text] over [Formula: see text], with discriminant and regulator [Formula: see text], respectively. In this paper, using a similar method to van Woerden, we prove that the number of classes of perfect unary forms, up to equivalence and scaling, can be bounded above by [Fo...

We extend the middle product to skew polynomials, which we use to define a skew middle-product Learning with Errors (LWE) variant. We also define a skew polynomial LWE problem, which we connect to Cyclic LWE (CLWE), a variant of LWE in cyclic division algebras. We then reduce a family of skew polynomial LWE problems to skew middle-product LWE, for...

The NTRU assumption provides one of the most prominent problems on which to base post-quantum cryptography. Because of the efficiency and security of NTRU-style schemes, structured variants have been proposed, using modules. In this work, we create a structured form of NTRU using lattices obtained from orders in cyclic division algebras of index 2,...

We obtain an inequality for the kissing number in 16 dimensions. We do this by generalising a sum-product bound of Solymosi and Wong for quaternions to a semialgebra in dimension 16. In particular, we obtain the inequality $$k_{16}\geq \frac{\sum_{x \in \mathcal{R}}\left|\mathcal{S}_{x}\right|}{\left|\bigcup_{x \in \mathcal{R}} \mathcal{S}_{x}\righ...

It is shown that the commuting probability of a finite ring cannot be a fraction with square-free denominator, resolving a conjecture of Buckley and MacHale.

It is shown that the commuting probability of a finite ring cannot be a fraction with square-free denominator, resolving a conjecture of Buckley and MacHale.

Let $K$ be a totally real number field of degree $n$ over $\mathbb{Q}$, with discriminant and regulator $\Delta_K, R_K$ respectively. In this paper, using a similar method to van Woerden, we prove that the number of classes of perfect unary forms, up to equivalence and scaling, can be bounded above by $O( \Delta_K \exp(2n \log(n)+f(n,R_K)))$, where...

The Learning with Errors (LWE) problem is the fundamental backbone of modern lattice-based cryptography, allowing one to establish cryptography on the hardness of well-studied computational problems. However, schemes based on LWE are often impractical, so Ring LWE was introduced as a form of ‘structured’ LWE, trading off a hard to quantify loss of...

Whilst lattice-based cryptosystems are believed to be resistant to quantum attack, they are often forced to pay for that security with inefficiencies in implementation. This problem is overcome by ring- and module-based schemes such as Ring-LWE or Module-LWE, whose keysize can be reduced by exploiting its algebraic structure, allowing for neater an...