Related papers: Extending class group action attacks via sesquilin…

This work introduces a hybrid quantum-classical method to correlation clustering, a graph-based unsupervised learning task that seeks to partition the nodes in a graph based on pairwise agreement and disagreement. In particular, we adapt…

The survey presents the evolution of Short Weierstrass elliptic curves after their introduction in cryptography. Subsequently, this evolution resulted in the establishment of present elliptic curve computational standards. We discuss the…

In this paper, we propose a novel approach for optimizing the linear layer used in symmetric cryptography. It is observed that these matrices often have circulant structure. The basic idea of this work is to utilize the property to…

We classify twisted conjugacy classes in loop groups, restricted to classical groups. The main tool we used is the so-called D_q module, an object which is related to vector bundles over elliptic curves.

A projective moduli space of pairs (C,E) where E is a slope- semistable torsion free sheaf of uniform rank on a Deligne- Mumford stable curve C is constructed via G.I.T. There is a natural SL x SL action on the relative Quot scheme over the…

We present a new class of stochastic, geometrically-driven optimization algorithms on the orthogonal group $O(d)$ and naturally reductive homogeneous manifolds obtained from the action of the rotation group $SO(d)$. We theoretically and…

We consider an application to the discrete log problem using completely regular semigroups which may provide a more secure symmetric cryptosystem than the classic system based on groups. In particular we describe a scheme that would appear…

We construct infinite families of pairs of (geometrically non-isogenous) elliptic curves defined over $\mathbb{Q}$ with $12$-torsion subgroups that are isomorphic as Galois modules. This extends previous work of Chen and Fisher where it is…

We study the complexity of isomorphism problems for d-way arrays, or tensors, under natural actions by classical groups such as orthogonal, unitary, and symplectic groups. Such problems arise naturally in statistical data analysis and…

The present paper proposes a new and systematic approach to the so-called black box group methods in computational group theory. Instead of a single black box, we consider categories of black boxes and their morphisms. This makes new…

By resorting to basic features of topological knot theory we propose a (classical) cryptographic protocol based on the `difficulty' of decomposing complex knots generated as connected sums of prime knots and their mutants. The scheme…

We consider a class of "harmonic variations" for nonsingular curves, obtained as asymptotic degenerations along bitangents. On a geometric level, we obtain an attractive relationship between the class and the genus of $C$. The distribution…

We study isometric Lie group actions on symmetric spaces admitting a section, i.e. a submanifold which meets all orbits orthogonally at every intersection point. We classify such actions on the compact symmetric spaces with simple isometry…

We consider the problems of measurable isomorphisms and joinings, measurable centralizers and quotients for certain classes of ergodic group actions on infinite measure spaces. Our main focus is on systems of algebraic origin: actions of…

In this paper, we improve the cube attack by exploiting low-degree factors of the superpoly w.r.t. certain "special" index set of cube (ISoC). This can be viewed as a special case of the correlation cube attack proposed at Eurocrypt 2018,…

Given a finite group $G$ and an extension of finite chain rings $S|R$, one can consider the group rings $\mathscr{S} = S[G]$ and $\mathscr{R} = R[G]$. The group ring $\mathscr{S}$ can be viewed as an $R$-bimodule, and any of its…

The formal group law of an elliptic curve has seen recent applications to computational algebraic geometry in the work of Couveignes to compute the order of an elliptic curve over finite fields of small characteristic. The purpose of this…

We develop a categorical index calculus for elliptic symbol families. The categorified index problems we consider are a secondary version of the traditional problem of expressing the index class in K-theory in terms of…

This work addresses approximate nearest neighbor search applied in the domain of large-scale image retrieval. Within the group testing framework we propose an efficient off-line construction of the search structures. The linear-time…

In this paper, we propose a novel construction for a symmetric encryption scheme, referred as SEBQ which is based on the structure of quasigroup. We utilize concepts of chaining like mode of operation and present a block cipher with…