相关论文: Cryptographic Application of Elliptic Curve with H…

Most cryptocurrency systems or systems based on blockchain technology are currently using the elliptic curves digital signature algorithm (ECDSA) on the secp256k1 curve, which is susceptible to backdoors implemented by the curve creator…

The technique of hiding secret messages within seemingly harmless covertext to evade examination by censors with rigorous security proofs is known as provably secure steganography (PSS). PSS evolves from symmetric key steganography to…

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…

We present a rank metric code-based encryption scheme with key and ciphertext sizes comparable to that of isogeny-based cryptography for an equivalent security level. The system also benefits from efficient encryption and decryption…

The SECP256K1 elliptic curve algorithm is fundamental in cryptocurrency wallets for generating secure public keys from private keys, thereby ensuring the protection and ownership of blockchain-based digital assets. However, the literature…

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…

We consider algebraic affine and projective curves of Edwards \cite{E, SkOdProj} over a finite field $\text{F}_{p^n}$. Most cryptosystems of the modern cryptography \cite{SkBlock} can be naturally transform into elliptic curves \cite{Kob}.…

We give a detailed account of the use of $\mathbb{Q}$-curve reductions to construct elliptic curves over $\mathbb{F}\_{p^2}$ with efficiently computable endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in…

In this paper, we present several methods for construction of elliptic curves with large torsion group and positive rank over number fields of small degree. We also discuss potential applications of such curves in the elliptic curve…

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…

In the evolving landscape of cryptographic security, the robustness of Elliptic Curve Cryptography (ECC) against side-channel analysis (SCA) attacks is of paramount importance due to the widespread use of ECC and the growing sophistication…

Elliptic Curve Cryptography (ECC) is an attractive alternative to conventional public key cryptography, such as RSA. ECC is an ideal candidate for implementation on constrained devices where the major computational resources i.e. speed,…

A new approach to discretization of the Duffing equation is presented. Integrable discrete maps are obtained by using well-studied encrypting operations in elliptic curve cryptography and, therefore, they do not depend upon standard small…

Elliptic Curve Cryptography (ECC) is an encryption method that provides security comparable to traditional techniques like Rivest-Shamir-Adleman (RSA) but with lower computational complexity and smaller key sizes, making it a competitive…

We present e cient algorithms for computing isogenies between hyperelliptic curves, leveraging higher genus curves to enhance cryptographic protocols in the post-quantum context. Our algorithms reduce the computational complexity of isogeny…

Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational…

The paper analyzes a new public key cryptosystem whose security is based on a matrix version of the discrete logarithm problem over an elliptic curve. It is shown that the complexity of solving the underlying problem for the proposed system…

Elliptic Curve Scalar Multiplication denoted as kP operation is the basic operation in all Elliptic Curve based cryptographic protocols. The atomicity principle and different atomic patterns for kP algorithms were proposed in the past as…

We describe a novel type of weak cryptographic private key that can exist in any discrete logarithm based public-key cryptosystem set in a group of prime order $p$ where $p-1$ has small divisors. Unlike the weak private keys based on…

Code that is highly optimized poses a problem for program-level verification: programmers can employ various clever tricks that are non-trivial to reason about. For cryptography on low-power devices, it is nonetheless crucial that…