Related papers: Post-quantum hash functions using $\mathrm{SL}_n(\…

Over the recent months it has become clear that the current generation of cryptographic hashing algorithms are insufficient to meet future needs. The ASH family of algorithms provides modifications to the existing SHA-2 family. These…

In this paper we present an algorithm to compute keyed hash function (message authentication code MAC). Our approach uses a family of expander graphs of large girth denoted $D(n,q)$, where $n$ is a natural number bigger than one and $q$ is…

Shor's algorithm efficiently solves factoring and discrete logarithm problems using quantum computers, compromising all public key schemes used today. These schemes rely on assumptions on their computational complexity, which quantum…

Consistent Hashing functions are widely used for load balancing across a variety of applications. However, the original presentation and typical implementations of Consistent Hashing rely on randomised allocation of hash codes to keys which…

We obtain an effective enumeration of the family of finitely generated groups admitting a faithful, properly discontinuous action on some 2-manifold contained in the sphere. This is achieved by introducing a type of group presentation…

The authors lay the foundations for the study of normal families of holomorphic functions and mappings on an infinite-dimensional normed linear space. Characterizations of normal families, in terms of value distribution, spherical…

We propose a hash function based on arithmetic coding and public-key cryptography. The resistance of the hash function to second preimage attack, collision and differential cryptanalysis is based on the properties of arithmetic coding as a…

We describe a consistent hashing algorithm which performs multiple lookups per key in a hash table of nodes. It requires no additional storage beyond the hash table, and achieves a peak-to-average load ratio of 1 + epsilon with just 1 +…

In this paper we consider an application of the recently proposed quantum hashing technique for computing Boolean functions in the quantum communication model. The combination of binary functions on non-binary quantum hash function is done…

We propose a novel construction of finite hypergraphs and relational structures that is based on reduced products with Cayley graphs of groupoids. To this end we construct groupoids whose Cayley graphs have large girth not just in the usual…

Hashing is a basic tool for dimensionality reduction employed in several aspects of machine learning. However, the perfomance analysis is often carried out under the abstract assumption that a truly random unit cost hash function is used,…

Supervised hashing aims to map the original features to compact binary codes that are able to preserve label based similarity in the Hamming space. Non-linear hash functions have demonstrated the advantage over linear ones due to their…

In comparison to graphs, combinatorial methods for the isomorphism problem of finite groups are less developed than algebraic ones. To be able to investigate the descriptive complexity of finite groups and the group isomorphism problem, we…

For a formation $\mathfrak{F}$ of finite groups, tight connections are established between the pro-$\mathfrak{F}$-topology of a finitely generated free group $F$ and the geometry of the Cayley graph $\Gamma(\hat{F_{\mathfrak{F}}})$ of the…

A Cayley graph of a group $H$ is a finite simple graph $\Gamma$ such that its automorphism group ${\rm Aut}(\Gamma)$ contains a subgroup isomorphic to $H$ acting regularly on $V(\Gamma)$, while a Haar graph of $H$ is a finite simple…

Quantum hashing is a widely used technique in quantum computation that allows us to design space-efficient algorithms and protocols. Recently, Vasiliev has shown that the phase form of shallow quantum hashing can be implemented by a circuit…

We propose theoretical and empirical improvements for two-stage hashing methods. We first provide a theoretical analysis on the quality of the binary codes and show that, under mild assumptions, a residual learning scheme can construct…

We discuss the problem of performing similarity search over function spaces. To perform search over such spaces in a reasonable amount of time, we use {\it locality-sensitive hashing} (LSH). We present two methods that allow LSH functions…

An overview on current developments in post quantum cryptography

We prove that all isometric actions of higher rank simple Lie groups and their lattices on arbitrary uniformly convex Banach spaces have a fixed point. This vastly generalises a recent breakthrough of Oppenheim. Combined with earlier work…