Related papers: Duffing oscillator and elliptic curve cryptography
Cryptography is the study of techniques for ensuring the secrecy and authentication of the information. Public-key encryption schemes are secure only if the authenticity of the public-key is assured. Elliptic curve arithmetic can be used to…
The Discrete Logarithm Problem (DLP) for elliptic curves has been extensively studied since, for instance, it is the core of the security of cryptosystems like Elliptic Curve Cryptography (ECC). In this paper, we present an attack to the…
Privacy Preserving Data Mining is a method which ensures privacy of individual information during mining. Most important task involves retrieving information from multiple data bases which is distributed. The data once in the data warehouse…
This paper presents an overview of the use of elliptic curves in cryptography. The security of this cryptosystem is based on the discrete logarithm problem, which appears to be much harder compared to the discrete logarithm problem in other…
Short Weierstrass's elliptic curves with underlying hard Elliptic Curve Discrete Logarithm Problems was widely used in Cryptographic applications. This paper introduces a new security notation 'trusted security' for computation methods of…
We discuss the use of elliptic curves in cryptography on high-dimensional surfaces. In particular, instead of a Diffie-Hellman key exchange protocol written in the form of a bi-dimensional row, where the elements are made up with 256 bits,…
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…
The elliptic curve discrete logarithm problem is of fundamental importance in public-key cryptography. It is in use for a long time. Moreover, it is an interesting challenge in computational mathematics. Its solution is supposed to provide…
A directly public verifiable signcryption scheme is introduced in this paper that provides the security attributes of message confidentiality, authentication, integrity, non-repudiation, unforgeability, and forward secrecy of message…
The Weil pairing on elliptic curves has deep links with discrete logarithm problems. In practice, to better suit the functionalities of cryptosystems, one often needs to modify the original Weil pairing via what is called a distortion map.…
The elliptic curve discrete logarithm problem is considered a secure cryptographic primitive. The purpose of this paper is to propose a paradigm shift in attacking the elliptic curve discrete logarithm problem. In this paper, we will argue…
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…
Pairing based cryptography is in a dangerous position following the breakthroughs on discrete logarithms computations in finite fields of small characteristic. Remaining instances are built over finite fields of large characteristic and…
Confidentiality in our digital world is based on the security of cryptographic algorithms. These are usually executed transparently in the background, with people often relying on them without further knowledge. In the course of…
The signcryption is a relatively new cryptographic technique that is supposed to fulfill the functionalities of encryption and digital signature in a single logical step. Several signcryption schemes are proposed throughout the years, each…
We introduce the notion of isolated genus two curves. As there is no known efficient algorithm to explicitly construct isogenies between two genus two curves with large conductor gap, the discrete log problem (DLP) cannot be efficiently…
We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under…
In this work, a new 4-D hyperchaotic system for image encryption is proposed and its effectiveness is demonstrated by incorporating it into an existing Elliptic Curve Cryptography (ECC) mapping scheme. The proposed system is considered…
We construct the equation of Duffing oscillator in a dissipative medium using certain concepts from elementary mechanics. The Duffing equation (DE) without damping can be solved analytically. This is not true for a DE that involves a…
The problem of discretization of Darboux integrable equations is considered. Given a Darboux integrable continuous equation, one can obtain a Darboux integrable differential-discrete equation, using the integrals of the continuous equation.…