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Attack on Digital Multi-Signature Scheme Based on elliptic curve Cryptosystem

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Journal of Computer Science & Technology 2007年第1期22卷 92-94页

作者：刘铎罗平戴一奇 Department of Computer Science and Technology Tsinghua University Bcijing 100084 China

The concept of multisignature, in which multiple signers can cooperate to sign the same message and any verifier can verify the validity of the multi-signature, was first introduced by Itakura and Nakamura. Several multisignature schemes have been proposed since. Chen et al. proposed a new digital multi-signature scheme based on the elliptic curve cryptosystem recently. In this paper, we show that their scheme is insecure, for it is vulnerable to the so-called active attacks, such as the substitution of a ＂false＂ public key to a ＂true＂ one in a key directory or during transmission. And then the attacker can sign a legal signature which other users have signed and forge a signature himself which can be accepted by the verifier.

关键词： digital signature multi-signature elliptic curve cryptography

Design of Nonlinear Components Over a Mordell elliptic curve on Galois Fields

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Computers, Materials & Continua 2022年第4期71卷 1313-1329页

作者： Hafeez ur Rehman Tariq Shah Amer Aljaedi Mohammad Mazyad Hazzazi Adel RAlharbi Department of Mathematics Quaid-i-Azam UniversityIslamabadPakistan College of Computing and Information Technology University of TabukTabuk71491Saudi Arabia Department of Mathematics College of ScienceKing Khalid UniversityAbhaSaudi Arabia

elliptic curve cryptography ensures more safety and reliability than other public key cryptosystems of the same key *** recent years,the use of elliptic curves in public-key cryptography has increased due to their complexity and *** kinds of substitution boxes are proposed to address the substitution process in the cryptosystems,including dynamical,static,and elliptic curve-based ***,elliptic curve-based S-boxes are based on prime field GF(p)but in this manuscript;we propose a new technique of generating S-boxes based on mordell elliptic curves over the Galois field GF(2n).This technique affords a higher number of possibilities to generate S-boxes,which helps to increase the security of the *** robustness of the proposed S-boxes against the well-known algebraic and statistical attacks is analyzed to classify its potential to generate confusion and achieve up to the mark results compared to the various *** majority logic criterion results determine that the proposed S-boxes have up to the mark cryptographic strength.

关键词： Galois field elliptic curve S-box nonlinearity

Rational Points of elliptic curve y2 = x3＋ k3

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Algebra Colloquium 2018年第1期25卷 133-138页

作者： Xia Wu Yan Qin School of Mathematics Southeast University Nanjing 210096 China Nanjing University Business School Nanjing 210093 China

Let E be an elliptic curve defined over the field of rational numbers ~. Let d be a square-free integer and let Ed be the quadratic twist of E determined by d. Mai, Murty and Ono have proved that there are infinitely many square-free integers d such that the rank of Ed（Q） is zero. Let E（k） denote the elliptic curve y2 = x3 ＋ k. Then the quadratic twist E（1）d of E（1） by d is the elliptic curve E（d3）： y2 = x3＋ k3. Let r = 1, 2, 5, 10, 13, 14, 17, 22. Ono proved that there are infinitely many square-free integers d = r （rood 24） such that rankE（-d3）（Q） = 0, using the theory of modular forms. In this paper, we use the class number of quadratic field and Pell equation to describe these square-free integers k such that E（k3）（Q） has rank zero.

关键词： elliptic curve rational point class number Pell equation

Asymmetric Key Cryptosystem for Image Encryption by elliptic curve over Galois Field GF(2^(n))

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Computers, Materials & Continua 2023年第8期76卷 2033-2060页

作者： Mohammad Mazyad Hazzazi Hafeez Ur Rehman Tariq Shah Hajra Younas Department of Mathematics College of ScienceKing Khalid UniversityAbha61421Saudi Arabia Department of Mathematics Quaid-i-Azam UniversityIslamabadPakistan

Protecting the integrity and secrecy of digital data transmitted through the internet is a growing *** this paper,we introduce an asymmetric key algorithm for specifically processing images with larger bit *** overcome the separate flaws of elliptic curve cryptography(ECC)and the Hill cipher(HC),we present an approach to picture encryption by combining these two encryption *** addition,to strengthen our scheme,the group laws are defined over the rational points of a given elliptic curve(EC)over a Galois field(GF).The exclusive-or(XOR)function is used instead of matrix multiplication to encrypt and decrypt the data which also refutes the need for the inverse of the key *** integrating the inverse function on the pixels of the image,we have improved system security and have a wider key ***,through comprehensive analysis of the proposed scheme with different available analyses and standard attacks,it is confirmed that our proposed scheme provides improved speed,security,and efficiency.

关键词： elliptic curve Galois field group law hill cipher

Mathieu Equation and elliptic curve

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Communications in Theoretical Physics 2012年第12期58卷 827-834页

作者：贺伟缪炎刚 School of Physics Nankai University

We present a relation between the Mathieu equation and a particular elliptic curve. We find that the Floquet exponent of the Mathieu equation, for both q《1 and q》1, can be obtained from the integral of a differential one form along the two homology cycles of the elliptic curve. Certain higher order differential operators are needed to generate the WKB expansion. We make a few conjectures about the general structure of these differential operators.

关键词： N= 2 super-Yang-Mills elliptic curve Mathieu equation WKB method

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elliptic curve Scalar Multiplication with x-Coordinate

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Wuhan University Journal of Natural Sciences 2007年第1期12卷 163-166页

作者： ZHANG Ning PEI Qingqi XIAO Guozhen State Key Laboratory of Integrated Service Networks Xidian University Xi＇an 710071 Shaanxi China Ministry of Education Key Laboratory of ComputerNetworks and Information Security Xidian University Xi＇an710071 Shaanxi China

This paper gives a comprehensive method to do elliptic curve Scalar Multiplication with only x-coordinate. Explicit point operation formulae for all types of defining equations of the curves are derived. For each type of curve, the performance is analyzed. The formulae are applied in Montgomery Ladder to get scalar multiplication algorithm operated with only x-coordinate. The new scalar multiplication has the same security level and computation amount with protected binary scalar multiplication （PBSM） against side channel attack, and has the advantages of higher security and little memory needed.

关键词： elliptic curve scalar multiplication Montgomery ladder x-coordinate

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New Collective Signatures Based on the elliptic curve Discrete Logarithm Problem

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Computers, Materials & Continua 2022年第10期73卷 595-610页

作者： Tuan Nguyen Kim Duy Ho Ngoc Nikolay A.Moldovyan School of Computer Science Duy Tan UniversityDa NangVietnam Department of Information Technology Ha NoiVietnam ITMO University St.PetersburgRussia

There have been many digital signature schemes were developed based on the discrete logarithm problem on a finite *** this study,we use the elliptic curve discrete logarithm problem to build new collective signature *** cryptosystem on elliptic curve allows to generate digital signatures with the same level of security as other cryptosystems but with smaller *** extend practical applicability and enhance the security level of the group signature protocols,we propose two new types of collective digital signature schemes based on the discrete logarithm problem on the elliptic curve:i)the collective digital signature scheme shared by several signing groups and ii)the collective digital signature scheme shared by several signing groups and several individual *** two new types of collective signatures have combined the advantages of group digital signatures and collective digital *** signatures have a fixed size and do not depend on the number of members participating in the creation of the final collective *** of the advantages of the proposed collective signature protocols is that they can be deployed on top of the available public key infrastructures.

关键词： elliptic curve signing group individual signer collective signature group signature

Secure and Light Weight elliptic curve Cipher Suites in SSL/TLS

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Computer Systems Science & Engineering 2022年第1期40卷 179-190页

作者： B.Arunkumar G.Kousalya Coimbatore Institute of Technology Coimbatore641014India

In the current circumstance,e-commerce through an online banking system plays a significant *** may either buy goods from E-Commerce websites or use online banking to move money to other *** a user participates in these types of behaviors,their sensitive information is sent to an untrust-worthy *** a consequence,when transmitting data from an internal browser to an external E-commerce web server using the cryptographic protocol SSL/TLS,the E-commerce web server ensures the security of the user’s *** user should be pleased with the confidentiality,authentication,and authenticity properties of the SSL/TLS on both the user’s web browser and the remote E-commerce web server.E-Commerce web servers should choose the best SSL/TLS cipher suites for negotiating the user in order to attain such optimistic scenarios,as the cipher suite used in SSL/TLS plays an important role in securing E-Commerce web *** paper primarily focuses on analyzing the SSL/TLS cipher and elliptic *** paper also recommends the best elliptic curve cipher suites for E-Commerce and online banking servers,based on their power consumption,handshake execution time,and key exchange and signature verification time.

关键词： elliptic curve cipher suites secp256r1 curve25519 ed25519

On the elliptic curve y^2=x^3-2r Dx and factoring integers

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Science China Mathematics 2014年第4期57卷 719-728页

作者： LI XiuMei ZENG JinXiang Department of Mathematical Sciences Tsinghua University

Let D=pq be the product of two distinct odd *** the parity conjecture,we construct infinitely many r≥1 such that E2rD:y2=x3-2rDx has conjectural rank one and vp(x([k]Q))≠vq(x([k]Q))for any odd integer k,where Q is the generator of the free part of E(Q).Furthermore,under the generalized Riemann hypothesis,the minimal value of r is less than c log4 D for some absolute constant *** a corollary,one can factor D by computing the generator Q.

关键词： elliptic curve integer factoring Selmer group

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