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

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…

A mathematical topology with matrix is a natural representation of a coding relational structure that is found in many fields of the world. Matrices are very important in computation of real applications, s ce matrices are easy saved in…

We present a mechanism to manifest unobtainable secrets using a nested Shamir secret sharing scheme to create public/private key pairs for elliptic curves. A threshold secret sharing scheme can be used as a decentralised trust mechanism…

General cryptographic schemes are presented where keys can be one-time or ephemeral. Processes for key exchange are derived. Public key cryptographic schemes based on the new systems are easily established. Authentication and signature…

Cryptographic primitives have been used for various non-cryptographic objectives, such as eliminating or reducing randomness and interaction. We show how to use cryptography to improve the time complexity of solving computational problems.…

In 2021, the $p$-adic signature scheme and public-key encryption cryptosystem were introduced. These schemes have good efficiency but are shown to be not secure. The attack succeeds because the extension fields used in these schemes are…

There is a natural question to ask whether the rich mathematical theory of the hyperelliptic curves can be extended to all superelliptic curves. Moreover, one wonders if all of the applications of hyperelliptic curves such as cryptography,…

Pairings have been widely used since their introduction to cryptography. They can be applied to identity-based encryption, tripartite Diffie-Hellman key agreement, blockchain and other cryptographic schemes. The Acceleration of pairing…

Let $p\ge5$ be a prime and $T$ a Kodaira type of the special fiber of an elliptic curve. We estimate the number of elliptic curves over $\mathbb Q$ up to height $X$ with Kodaira type $T$ at $p$. This enables us find the proportion of…

Let $p$ be a prime and let $K$ be a finite extension of $\mathbb{Q}_p$. Let $E/K$ be an elliptic curve with additive reduction. In this paper, we study the topological group structure of the set of points of good reduction of $E(K)$. In…

The Discrete Logarithm Problem is well-known among cryptographers, for its computational hardness that grants security to some of the most commonly used cryptosystems these days. Still, many of these are limited to a small number of…

One of the methods used in order to protect a secret K is a secret sharing scheme. In this scheme the secret K is distributed among a finite set of participants P by a special participant called the dealer, in such a way that only…

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…

The paper studies cryptographically useful properties of the sequence of the sizes of Goldbach ellipses. We show that binary subsequences based on this sequence have useful properties. They can be used to generate keys and to provide an…

Pairing-based inner product functional encryption provides an efficient theoretical construction for privacy-preserving edge computing secured by widely deployed elliptic curve cryptography. In this work, an efficient software…

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…

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…

The security of the Elliptic Curve Digital Signature Algorithm (ECDSA) depends on the uniqueness and secrecy of the nonce, which is used in each signature. While it is well understood that nonce $k$ reuse across two distinct messages can…

Applying machine learning algorithms to private data, such as financial or medical data, while preserving their confidentiality, is a difficult task. Homomorphic Encryption (HE) is acknowledged for its ability to allow computation on…

Cryptography protects users by providing functionality for the encryption of data and authentication of other users. This technology lets the receiver of an electronic message verify the sender, ensures that a message can be read only by…