Related papers: Criptografia com Curvas El\'ipticas
Let $E$ be an elliptic curve over $\F_p$ without complex multiplication, and for each prime $p$ of good reduction, let $n_E(p) = | E(\F_p) |$. Let $Q_{E,b}(x)$ be the number of primes $p \leq x$ such that $b^{n_E(p)} \equiv b\,({\rm…
Historically, Elliptic Curve Cryptography (ECC) is an active field of applied cryptography where recent focus is on high speed, constant time, and formally verified implementations. While there are a handful of outliers where all these…
In this paper we discuss the Hidden Subgroup Problem (HSP) in relation to post-quantum group-based cryptography. We review the relationship between HSP and other computational problems discuss an optimal solution method, and review the…
Recent advances in cryptography promise to enable secure statistical computation on encrypted data, whereby a limited set of operations can be carried out without the need to first decrypt. We review these homomorphic encryption schemes in…
In the past years, research on Shor's algorithm for solving elliptic curves for discrete logarithm problems (Shor's ECDLP), the basis for cracking elliptic curve-based cryptosystems (ECC), has started to garner more significant interest. To…
Diffie-Hellman key-agreement and RSA cryptosystem are widely used to provide security in internet protocols. But both of the two algorithms are totally breakable using Shor's algorithms. This paper proposes two connected matrix-based…
The task of this paper is to introduce a new lightweight identification protocol based on biometric data and elliptic curves. In fact, we combine biometric data and asymetric cryptography, namely elliptic curves and standard tools to design…
As the number of hacking events and cyber threats keeps going up, it is getting harder and harder to communicate securely and keep personal information safe on the Internet. Cryptography is a very important way to deal with these problems…
Many graph mining and analysis services have been deployed on the cloud, which can alleviate users from the burden of implementing and maintaining graph algorithms. However, putting graph analytics on the cloud can invade users' privacy. To…
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…
Solving the Elliptic Curve Discrete Logarithm Problem (ECDLP) is critical for evaluating the quantum security of widely deployed elliptic-curve cryptosystems. Consequently, minimizing the number of logical qubits required to execute this…
The trend towards delegating data processing to a remote party raises major concerns related to privacy violations for both end-users and service providers. These concerns have attracted the attention of the research community, and several…
We provide a survey on the Hidden Subgroup Problem (HSP), which plays an important role in studying the security of public-key cryptosystems. We first review the abelian case, where Kitaev's algorithm yields an efficient quantum solution to…
The ECDSA (Elliptic Curve Digital Signature Algorithm) is used in many blockchain networks for digital signatures. This includes the Bitcoin and the Ethereum blockchains. While it has good performance levels and as strong current security,…
We consider representations of algebraic tori $T_n(F_q)$ over finite fields. We make use of normal elliptic bases to show that, for infinitely many squarefree integers $n$ and infinitely many values of $q$, we can encode $m$ torus elements,…
We consider an application to the discrete log problem using completely regular semigroups which may provide a more secure symmetric cryptosystem than the classic system based on groups. In particular we describe a scheme that would appear…
Elliptic curves with a known number of points over a given prime field with n elements are often needed for use in cryptography. In the context of primality proving, Atkin and Morain suggested the use of the theory of complex multiplication…
This experiment breaks a 5-bit elliptic curve cryptographic key using a Shor-style quantum attack. Executed on IBM's 133-qubit ibm_torino with Qiskit Runtime 2.0, a 15-qubit circuit, comprised of 10 logical qubits and 5 ancilla, interferes…
In this paper, we have studied on adapting to asymmetric cryptography power Fibonacci sequence module m . To do this, We have restructed Discreate Logarithm Problem which is one of mathematical difficult problems by using power Fibonacci…
To ensure the secure transmission of data, cryptography is treated as the most effective solution. Cryptographic key is an important entity in this procedure. In general, randomly generated cryptographic key (of 256 bits) is difficult to…