Related papers: Selmer-Inspired Elliptic Curve Generation

This paper studies the task of two-sources randomness extractors for elliptic curves defined over finite fields $K$, where $K$ can be a prime or a binary field. In fact, we introduce new constructions of functions over elliptic curves which…

Let $p$ be a prime and let $\mathbf{E}$ be an elliptic curve defined over the finite field $\mathbb{F}_p$ of $p$ elements. For a point $G\in\mathbf{E}(\mathbb{F}_p)$ the elliptic curve congruential generator (with respect to the first…

This is the second in a series of papers in which we study the n-Selmer group of an elliptic curve. In this paper, we show how to realize elements of the n-Selmer group explicitly as curves of degree n embedded in P^{n-1}. The main tool we…

The elliptic curve method (ECM) is one of the best factorization methods available. It is possible to use hyperelliptic curves instead of elliptic curves but it is in theory slower. We use special hyperelliptic curves and Kummer surfaces to…

We present an elementary proof of the group properties of the elliptic curve known as "Curve25519", as a component of a comprehensive proof of correctness of a hardware implementation of the associated Diffie-Hellman key agreement…

Cryptographic Protocols (CP) are distributed algorithms intended for secure communication in an insecure environment. They are used, for example, in electronic payments, electronic voting procedures, systems of confidential data processing,…

We propose a novel derived cohomological framework for the Birch and Swinnerton-Dyer (BSD) conjecture for elliptic curves. In our approach, local arithmetic data are encoded in derived sheaves which, when glued via a mapping cone…

Confidentiality and Integrity are two paramount objectives in the evaluation of information and communication technology. In this paper, we propose an arithmetic approach for designing asymmetric key cryptography. Our method is based on the…

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…

As applications of biometric verification proliferate, users become more vulnerable to privacy infringement. Biometric data is very privacy sensitive as it may contain information as gender, ethnicity and health conditions which should not…

Three decades ago, Montgomery introduced a new elliptic curve model for use in Lenstra's ECM factorization algorithm. Since then, his curves and the algorithms associated with them have become foundational in the implementation of elliptic…

An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between elliptic curves efficiently. For ordinary curves of the same…

We present information-theoretic definitions and results for analyzing symmetric-key encryption schemes beyond the perfect secrecy regime, i.e. when perfect secrecy is not attained. We adopt two lines of analysis, one based on lossless…

When deploying wireless sensor networks (WSNs) in public environments it may become necessary to secure their data storage and transmission against possible attacks such as node-compromise and eavesdropping. The nodes feature only small…

The ubiquity of closed-weight language models with public-facing APIs has generated interest in forensic methods, both for extracting hidden model details (e.g., parameters) and for identifying models by their outputs. One successful…

Secret Sharing techniques are now the building blocks of several security protocols. A (t;n) threshold secret sharing scheme is one in which t or more participant can join together to retrieve the secret.Traditional single secret sharing…

Let $p>3$ be a prime and $E$ be a supersingular elliptic curve defined over $\mathbb{F}_{p^2}$. Let $c$ be a prime with $c < 3p/16$ and $G$ be a subgroup of $E[c]$ of order $c$. The pair $(E,G)$ is called a supersingular elliptic curve with…

Anamorphic encryption serves as a vital tool for covert communication, maintaining secrecy even during post-compromise scenarios. Particularly in the receiver-anamorphic setting, a user can shield hidden messages even when coerced into…

We propose a new numerical algorithm to construct a structured numerical elliptic grid of a doubly connected domain. Our method is applicable to domains with boundaries defined by two contour lines of a two-dimensional function. The…

Secret sharing in user hierarchy represents a challenging area for research. Although a lot of work has already been done in this direc- tion, this paper presents a novel approach to share a secret among a hierarchy of users while…