Andrew Mendelsohn

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

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

Publications

Publications (11)
Article
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...
Chapter
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...
Chapter
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,...
Preprint
Full-text available
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...
Preprint
Full-text available
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.
Article
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.
Preprint
Full-text available
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...
Article
Full-text available
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...
Preprint
Full-text available
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...

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