Related papers: Criptografia com Curvas El\'ipticas

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,…

Specific quantum algorithms exist to-in theory-break elliptic curve cryptographic protocols. Implementing these algorithms requires designing quantum circuits that perform elliptic curve arithmetic. To accurately judge a cryptographic…

A scheme is presented based on numbers that represent a manifold in $d$ dimensions for generalizations of textbook cryptosystems. The interlocking or intersection of geometries, requiring the addition of a series of integers $q_j$, can be…

An important open problem in supersingular isogeny-based cryptography is to produce, without a trusted authority, concrete examples of "hard supersingular curves" that is, equations for supersingular curves for which computing the…

D\'ech\`ene has proposed generalized Jacobians as a source of groups for public-key cryptosystems based on the hardness of the Discrete Logarithm Problem (DLP). Her specific proposal gives rise to a group isomorphic to the semidirect…

In this paper, we will present a new key exchange cryptosystem based on linear algebra, which take less operations but weaker in security than Diffie-Hellman's one.

Nowadays, using cryptographic systems play an effective role in security and safety technologies. One of the most applied kind of cryptography is Symmetric Cryptography and its applications. New aspects of symmetric Cryptography…

In 2022, Persianom, Phan and Yung outlined the creation of Anamorphic Cryptography. With this, we can create a public key to encrypt data, and then have two secret keys. These secret keys are used to decrypt the cipher into different…

In cryptanalysis, solving the discrete logarithm problem (DLP) is key to assessing the security of many public-key cryptosystems. The index-calculus methods, that attack the DLP in multiplicative subgroups of finite fields, require solving…

We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann…

In this document, a privacy-preserving distributed profile matching protocol is proposed in a particular network context called \emph{mobile social network}. Such networks are often deployed in more or less hostile environments, requiring…

The supersingular Endomorphism Ring problem is the following: given a supersingular elliptic curve, compute all of its endomorphisms. The presumed hardness of this problem is foundational for isogeny-based cryptography. The One Endomorphism…

In this paper, we evaluate the different fully homomorphic encryption schemes, propose an implementation, and numerically analyze the applicability of gradient descent algorithms to solve quadratic programming in a homomorphic encryption…

We lay the foundations for a blockchain scheme, whose consensus is reached via a proof of work algorithm based on the solution of consecutive discrete logarithm problems over the point group of elliptic curves. In the considered…

In 1994, P. Shor discovered quantum algorithms which can break both the RSA cryptosystem and the ElGamal cryptosystem. In 2007, D-Wave demonstrated the first quantum computer. These events and further developments have brought a crisis to…

Cryptography is the science of using mathematics to encrypt and decrypt data. Cryptography enables you to store sensitive information or transmit it across insecure networks so that it cannot be read by anyone except the intended recipient.…

In modern critical infrastructure such as power grids, it is crucial to ensure security of data communications between network-connected devices while following strict latency criteria. This necessitates the use of cryptographic hardware…

The Chrysalis project is a proposed method for post-quantum cryptography using the Riemann sphere. To this end, Riemann primitives are introduced in addition to a novel implementation of this new method. Chrysalis itself is the first…

The problem of constructing elliptic curves suitable for pairing applications has received a lot of attention. To solve this, we propose a variant algorithm of a known method by Brezing and Weng. We produce new families of parameters using…

The purpose of the paper is to give new key agreement protocols (a multi-party extension of the protocol due to Anshel-Anshel-Goldfeld and a generalization of the Diffie-Hellman protocol from abelian to solvable groups) and a new…