Related papers: Criptografia com Curvas El\'ipticas
As quantum computing technology continues to advance, post-quantum cryptographic methods capable of resisting quantum attacks have emerged as a critical area of focus. Given the potential vulnerability of existing homomorphic encryption…
The Internet, a rapidly expanding communication infrastructure, poses significant cybersecurity challenges. A few techniques have been developed to provide security in the OSI model's application, presentation, and network layers. Instead…
The increased use of cryptography to protect our personal information makes us want to understand the security of cryptosystems. The security of many cryptosystems relies on solving the discrete logarithm, which is thought to be relatively…
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…
Multiplication is one of the most important operation in Elliptic Curve Cryptography (ECC) arithmetic. For point addition and point doubling in ECC scalar (integer) multiplication is required. In higher order classical (standard)…
This article is a short introduction to the theory of the groups of points of elliptic curves over finite fields. It is concerned with the elementary theory and practice of elliptic curves cryptography, the new generation of public key…
The need of exchanging messages and images secretly over unsecure networks promoted the creation of cryptosystems to enable receivers to interpret the exchanged information. In this paper, a particular public key cryptosystem called the…
The aim of this paper is to justify the common cryptographic practice of selecting elliptic curves using their order as the primary criterion. We can formalize this issue by asking whether the discrete log problem (DLOG) has the same…
Transparency is one of the key benefits of public blockchains. However, the public visibility of transactions potentially compromises users' privacy. The fundamental challenge is to balance the intrinsic benefits of blockchain openness with…
In this paper, we will present how to find keys elliptic curve cryptosystems (ECC) with simple tools of Delphi 7 console application, using the software problem solving of the scalar point multiplication in the field GF(p), where p is an…
In this thesis, we propose some directed signature schemes. In addition, we have discussed their applications in different situations. In this thesis, we would like to discuss the security aspects during the design process of the proposed…
Since the elliptic curve discrete logarithms problem (ECDLP) was proposed, it has been widely used in cryptosystem because of its strong security. Although the proposal of the extended Shor's algorithm offers hope for cracking ECDLP, it is…
We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and discrete log as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete…
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.…
Nowadays, Internet of Things (IoT) is a trending topic in the computing world. Notably, IoT devices have strict design requirements and are often referred to as constrained devices. Therefore, security techniques and primitives that are…
We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point…
This paper introduces a new public key cryptosystem based on two hard problems : the cube root extraction modulo a composite moduli (which is equivalent to the factorisation of the moduli) and the discrete logarithm problem. These two hard…
We propose an image encryption scheme based on quasi-resonant Rossby/drift wave triads (related to elliptic surfaces) and Mordell elliptic curves (MECs). By defining a total order on quasi-resonant triads, at a first stage we construct…
The widespread use of wireless sensor networks (WSNs) that are consisted of resource-constrained sensor nodes in communication with gateways in open-space environments and industries has highlighted the need for a secure yet fast…
We consider a quantum polynomial-time algorithm which solves the discrete logarithm problem for points on elliptic curves over $GF(2^m)$. We improve over earlier algorithms by constructing an efficient circuit for multiplying elements of…