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We analyse the number of occurrences of a fixed non-zero digit in the width-w non-adjacent forms of all elements of a lattice in some region (e.g. a ball). Our result is an asymptotic formula, where its main term coincides with the full…

Number Theory · Mathematics 2013-03-15 Daniel Krenn

This whitepaper seeks to elucidate implications that the capabilities of developing quantum architectures have on blockchain vulnerabilities and mitigation strategies. First, we provide new resource estimates for breaking the 256-bit…

The elliptic curve discrete logarithm problem is considered a secure cryptographic primitive. The purpose of this paper is to propose a paradigm shift in attacking the elliptic curve discrete logarithm problem. In this paper, we will argue…

Cryptography and Security · Computer Science 2023-06-22 Ansari Abdullah , Ayan Mahalanobis , Vivek M. Mallick

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…

Quantum Physics · Physics 2009-12-18 Donny Cheung , Dmitri Maslov , Jimson Mathew , Dhiraj K. Pradhan

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…

Cryptography and Security · Computer Science 2021-09-16 Shiping Cai , Zhi Hu , Zheng-An Yao , Chang-An Zhao

qDSA is a high-speed, high-security signature scheme that facilitates implementations with a very small memory footprint, a crucial requirement for embedded systems and IoT devices, and that uses the same public keys as modern…

Cryptography and Security · Computer Science 2017-09-12 Joost Renes , Benjamin Smith

This paper introduces a novel cryptographic approach based on the continuous logarithm in the complex circle, designed to address the challenges posed by quantum computing. By leveraging its multi-valued and spectral properties, this…

Cryptography and Security · Computer Science 2025-01-22 Jaafar Gaber

In todays world, Cloud computing has attracted research communities as it provides services in reduced cost due to virtualizing all the necessary resources. Even modern business architecture depends upon Cloud computing .As it is a internet…

Cryptography and Security · Computer Science 2014-11-26 Debajyoti Mukhopadhyay , Ashay Shirwadkar , Pratik Gaikar , Tanmay Agrawal

Several aspects of managing a sensor network (e.g., motion planning for data mules, serial data fusion and inference) benefit once the network is linearized to a path. The linearization is often achieved by constructing a space filling…

Computational Geometry · Computer Science 2015-07-21 Mayank Goswami , Siming Li , Junwei Zhang , Emil Saucan , David Xianfeng Gu , Jie Gao

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…

Cryptography and Security · Computer Science 2023-11-29 Kashif Ishaq , Awais Ahmed Qarni

In this paper, we propose a novel approach for optimizing the linear layer used in symmetric cryptography. It is observed that these matrices often have circulant structure. The basic idea of this work is to utilize the property to…

Cryptography and Security · Computer Science 2026-05-26 Buji Xu , Xiaoming Sun

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…

General Mathematics · Mathematics 2012-12-18 N. A. Carella

In recent years, establishing secure visual communications has turned into one of the essential problems for security engineers and researchers. However, only limited novel solutions are provided for image encryption, and limiting the…

Cryptography and Security · Computer Science 2022-04-19 Navid Abapour , Mohsen Ebadpour

In this paper secured wireless communication using fuzzy logic based high speed public key cryptography (FLHSPKC) has been proposed by satisfying the major issues likes computational safety, power management and restricted usage of memory…

Cryptography and Security · Computer Science 2012-11-12 Arindam Sarkar , J. K. Mandal

Post-Quantum Cryptography (PQC) attempts to find cryptographic protocols resistant to attacks using Shor polynomial time algorithm for numerical field problems or Grover search algorithm. A mostly overlooked but valuable line of solutions…

Cryptography and Security · Computer Science 2019-04-23 P. Hecht

We perform a comparison of two protocols for generating a cryptographic key composed from d-valued symbols: one exploiting a string of independent qubits and another one utilizing d-level systems prepared in states belonging to d+1 mutually…

Quantum Physics · Physics 2015-06-26 D. B. Horoshko , S. Ya. Kilin

Molecular communication in nanonetworks is an emerging communication paradigm that uses molecules as information carriers. Achieving a secure information exchange is one of the practical challenges that need to be considered to address the…

Information Theory · Computer Science 2017-09-15 S. M. Riazul Islam , Farman Ali , Hyeonjoon Moon , Kyung-Sup Kwak

In this paper, we have proposed a modified cryptographic scheme based on the application of recursive matrices as key in ECC and ElGamal. For encryption, we consider mapping analogous to affine Hill cipher in which a plaintext matrix has…

Cryptography and Security · Computer Science 2021-12-22 Munesh Kumari , Jagmohan Tanti

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…

Cryptography and Security · Computer Science 2018-05-23 Rudresh Dwivedi , Somnath Dey , Mukul Anand Sharma , Apurv Goel

High-dimensional quantum key distribution (QKD) offers secure communication, with secure key rates that surpass those achievable by QKD protocols utilizing two-dimensional encoding. However, existing high-dimensional QKD protocols require…