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The problem of computing an explicit isogeny between two given elliptic curves over F_q, originally motivated by point counting, has recently awaken new interest in the cryptology community thanks to the works of Teske and Rostovstev &…
An elliptic curve-based signcryption scheme is introduced in this paper that effectively combines the functionalities of digital signature and encryption, and decreases the computational costs and communication overheads in comparison with…
Let C be a 2-connected Gorenstein curve either reduced or contained in a smooth algebraic surface and let S be a subcanonical cluster (i.e. a 0-dim scheme such that the space H^0(C, I_S K_C) contains a generically invertible section). Under…
We introduce a new type of sparse CSS quantum error correcting code based on the homology of hypermaps. Sparse quantum error correcting codes are of interest in the building of quantum computers due to their ease of implementation and the…
We construct a modular desingularisation of $\overline{\mathcal{M}}_{2,n}(\mathbb{P}^r,d)^{\text{main}}$. The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers: with this enhanced…
We consider families of smooth projective curves of genus 2 with a single point removed and study their integral points. We show that in many such families there is a dense set of fibres for which the integral points can be effectively…
We design new differentially private algorithms for the Euclidean k-means problem, both in the centralized model and in the local model of differential privacy. In both models, our algorithms achieve significantly improved error guarantees…
We introduce a computational problem of distinguishing between two specific quantum states as a new cryptographic problem to design a quantum cryptographic scheme that is "secure" against any polynomial-time quantum adversary. Our problem,…
In arithmetic and algebraic geometry, superspecial (s.sp.\ for short) curves are one of the most important objects to be studied, with applications to cryptography and coding theory. If $g \geq 4$, it is not even known whether there exists…
We introduce the separating semigroup of a real algebraic curve of dividing type. The elements of this semigroup record the possible degrees of the covering maps obtained by restricting separating morphisms to the real part of the curve. We…
We call an order $O$ in a quadratic field $K$ odd (resp. even) if its discriminant is an odd (resp. even) integer. We call an elliptic curve $E$ over the field $C$ of complex numbers with CM odd (resp. even) if its endomorphism ring…
We introduce a new tool for the study of isogeny-based cryptography, namely pairings which are sesquilinear (conjugate linear) with respect to the $\mathcal{O}$-module structure of an elliptic curve with CM by an imaginary quadratic order…
Iterative clustering algorithms help us to learn the insights behind the data. Unfortunately, this may allow adversaries to infer the privacy of individuals with some background knowledge. In the worst case, the adversaries know the…
Encrypted control seeks confidential controller evaluation in cloud-based or networked systems. Many existing approaches build on homomorphic encryption (HE) that allow simple mathematical operations to be carried out on encrypted data.…
The paper analyzes a new public key cryptosystem whose security is based on a matrix version of the discrete logarithm problem over an elliptic curve. It is shown that the complexity of solving the underlying problem for the proposed system…
We show that $\mathbb{C}^2$ contains pairs of properly embedded, smooth complex curves that are isotopic through homeomorphisms but not diffeomorphisms of $\mathbb{C}^2$. The construction is based on realizing corks as branched covers of…
In todays world, Cloud computing has attracted research communities as it provides services in reduced cost due to virtualizing all the necessary resources. Even modern business architecture depends upon Cloud computing .As it is a internet…
We determine all genus 2 curves, defined over $\mathbb C$, which have simultaneously degree 2 and 3 elliptic subcovers. The locus of such curves has three irreducible 1-dimensional genus zero components in $\mathcal M_2$. For each component…
Differential Privacy is the gold standard in privacy-preserving data analysis. This paper addresses the challenge of producing a differentially edge-private vertex coloring. In this paper, we present two novel algorithms to approach this…
Solving the discrete logarithm problem (DLP) with quantum computers is a fundamental task with important implications. Beyond Shor's algorithm, many researchers have proposed alternative solutions in recent years. However, due to current…