Recent progress on the elliptic curve discrete logarithm problem [PDF]
Designs, Codes, and Cryptography, 2015 International audienceWe survey recent work on the elliptic curve discrete logarithm problem. In particular we review index calculus algorithms using summation polynomials, and claims about their ...
Steven D. Galbraith +4 more
core +5 more sources
Hardware acceleration of number theoretic transform for zk‐SNARK
Engineering Reports, EarlyView., 2023 An FPGA‐based hardware accelerator with a multi‐level pipeline is designed to support the large‐bitwidth and large‐scale NTT tasks in zk‐SNARK. It can be flexibly scaled to different scales of FPGAs and has been equipped in the heterogeneous acceleration system with the help of HLS and OpenCL.
Haixu Zhao +6 more
wiley +1 more source
The elliptic curve discrete logarithm problem and equivalent hard problems for elliptic divisibility sequences [PDF]
, 2008 . We define three hard problems in the theory of elliptic divisibility sequences (EDS Association, EDS Residue and EDS Discrete Log), each of which is solvable in sub-exponential time if and only if the elliptic curve discrete logarithm problem is ...
E. Stange +5 more
core +2 more sources
Trace zero varieties in cryptography : optimal representation and index calculus [PDF]
, 2014 The trace zero variety associated to an elliptic or hyperelliptic curve is an abelian variety defined over a finite field F_q. Its F_q-rational points yield a finite group, the trace zero subgroup of the degree zero Picard group of the original curve ...
Massierer, Maike
core +1 more source
Minors solve the elliptic curve discrete logarithm problem [PDF]
, 2023 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.
Abdullah, Ansari, Mahalanobis, Ayan
core +1 more source
Generalized Fibonacci Sequences for Elliptic Curve Cryptography
Mathematics, 2023 The Fibonacci sequence is a well-known sequence of numbers with numerous applications in mathematics, computer science, and other fields. In recent years, there has been growing interest in studying Fibonacci-like sequences on elliptic curves.
Zakariae Cheddour +2 more
doaj +1 more source
A NEW PROPOSED METHOD FOR SOLVING AN ELLIPTIC CURVE DISCRETE LOGARITHM PROBLEM
Journal of Kufa for Mathematics and Computer, 2012 In this work, we present a new approach for solving Elliptic Curve Discrete Logarithm Problem. This method provides a new access to the field of attacking methods the Elliptic Curve Cryptosystems.
Ammar Ali Neamah
doaj +1 more source
Implications of the Arithmetic Ratio of Prime Numbers for RSA Security
International Journal of Applied Mathematics and Computer Science, 2023 The most commonly used public key cryptographic algorithms are based on the difficulty in solving mathematical problems such as the integer factorization problem (IFP), the discrete logarithm problem (DLP) and the elliptic curve discrete logarithm ...
Ivanov Andrey, Stoianov Nikolai
doaj +1 more source
Smart Contract E-Voting Protocol with Linkable Ring Signcryption [PDF]
Jisuanji gongcheng, 2022 Compared with traditional voting methods, electronic voting is more economical but is not open, nontransparent, and too centralized.Blockchain technology has broad application prospects and has been applied to electronic voting protocols.However ...
WANG Jiechang, ZHANG Ping, GAO Yuan, LIU Yuling
doaj +1 more source
An Efficient Double Parameter Elliptic Curve Digital Signature Algorithm for Blockchain
IEEE Access, 2021 The classic Elliptic curve digital Signature Algorithm (ECDSA) uses one inversion operation in the process of signature and verification, which greatly reduces the efficiency of digital signatures.
Shuang-Gen Liu, Wan-Qi Chen, Jia-Lu Liu
doaj +1 more source