Public Key Cryptosystem Research Based on Discrete Group

2014 ◽  
Vol 687-691 ◽  
pp. 2984-2988
Author(s):  
Lan Bai ◽  
Jian Zhang ◽  
Li Zhu
Keyword(s):  
Information System ◽  
Elliptic Curve ◽  
Rapid Development ◽  
Discrete Logarithm ◽  
Modern Society ◽  
Public Key Cryptography ◽  
Public Key ◽  
Elliptic Curve Cryptosystem ◽  
Digital Form ◽  
Defensive Measures

In modern society with Internet rapid development, information system takes digital form of 0 and 1, this information system and public channel are very fragile in the case of without defensive measures, and they are easily attacked and destructed by hackers and intruders. This article is mainly based on the knowledge of discrete logarithm, studies public key cipher algorithm, especially elliptic curve cryptosystem. First this paper introduces the basic concepts and knowledge of cryptography, and discusses the relation between discrete logarithm and public key cryptography algorithms. Finally in detail it discusses elliptic curve cryptosystem, and presents the realization and running effect of encryption system.

scholarly journals Analysis Review on Public Key Cryptography Algorithms

2018 ◽  
Vol 12 (2) ◽  
pp. 447 ◽  
Author(s):  
Jasmin Ilyani Ahmad ◽  
Roshidi Din ◽  
Mazida Ahmad
Keyword(s):  
Elliptic Curve ◽  
Digital Signature ◽  
Coding Theory ◽  
Discrete Logarithm ◽  
Public Key Cryptography ◽  
Hybrid Algorithms ◽  
Public Key ◽  
Integer Factorization

This paper presents several Public Key Cryptography (PKC) algorithms based on the perspective of researchers’ effort since it was invented in the last four decades. The categories of the algorithms had been analyzed which are Discrete Logarithm, Integer Factorization, Coding Theory, Elliptic Curve, Lattices, Digital Signature and Hybrid algorithms. This paper reviewed the previous schemes in different PKC algorithms. The aim of this paper is to present the comparative trends of PKC algorithms based on number of research for each algorithm in last four decades, the roadmap of PKC algorithms since they were invented and the most chosen algorithms among previous researchers. Finally, the strength and drawback of proposed schemes and algorithms also presented in this paper.

Public-Key Encryption

2017 ◽  
Author(s):  
Keith M. Martin
Keyword(s):  
Elliptic Curve ◽  
Public Key Cryptography ◽  
Public Key ◽  
Public Key Encryption ◽  
Hybrid Encryption ◽  
Public Key Cryptosystems ◽  
Encryption And Decryption ◽  
Encryption Schemes ◽  
Hard Problems ◽  
Set Up

In this chapter, we introduce public-key encryption. We first consider the motivation behind the concept of public-key cryptography and introduce the hard problems on which popular public-key encryption schemes are based. We then discuss two of the best-known public-key cryptosystems, RSA and ElGamal. For each of these public-key cryptosystems, we discuss how to set up key pairs and perform basic encryption and decryption. We also identify the basis for security for each of these cryptosystems. We then compare RSA, ElGamal, and elliptic-curve variants of ElGamal from the perspectives of performance and security. Finally, we look at how public-key encryption is used in practice, focusing on the popular use of hybrid encryption.

scholarly journals Improved cryptanalysis of a ElGamal Cryptosystem Based on Matrices Over Group Rings

2020 ◽  
Vol 15 (1) ◽  
pp. 266-279
Author(s):  
Atul Pandey ◽  
Indivar Gupta ◽  
Dhiraj Kumar Singh
Keyword(s):  
Discrete Logarithm ◽  
Public Key Cryptography ◽  
Public Key ◽  
Quantum Computers ◽  
Group Rings ◽  
Diffie Hellman ◽  
Algebra Approach ◽  
Elgamal Cryptosystem ◽  
Diffie Hellman Key Exchange ◽  
Equivalent Keys

AbstractElGamal cryptosystem has emerged as one of the most important construction in Public Key Cryptography (PKC) since Diffie-Hellman key exchange protocol was proposed. However, public key schemes which are based on number theoretic problems such as discrete logarithm problem (DLP) are at risk because of the evolution of quantum computers. As a result, other non-number theoretic alternatives are a dire need of entire cryptographic community.In 2016, Saba Inam and Rashid Ali proposed a ElGamal-like cryptosystem based on matrices over group rings in ‘Neural Computing & Applications’. Using linear algebra approach, Jia et al. provided a cryptanalysis for the cryptosystem in 2019 and claimed that their attack could recover all the equivalent keys. However, this is not the case and we have improved their cryptanalysis approach and derived all equivalent key pairs that can be used to totally break the ElGamal-like cryptosystem proposed by Saba and Rashid. Using the decomposition of matrices over group rings to larger size matrices over rings, we have made the cryptanalysing algorithm more practical and efficient. We have also proved that the ElGamal cryptosystem proposed by Saba and Rashid does not achieve the security of IND-CPA and IND-CCA.

A General Threshold Signature Scheme Based on Elliptic Curve

2013 ◽  
Vol 756-759 ◽  
pp. 1339-1343
Author(s):  
Yu Lian Shang ◽  
Xiu Juan Wang ◽  
Yu Juan Li ◽  
Yu Fei Zhang
Keyword(s):  
Elliptic Curve ◽  
Communication System ◽  
Public Key ◽  
Threshold Scheme ◽  
Elliptic Curve Cryptosystem ◽  
Signature Scheme ◽  
Threshold Signature ◽  
Private Key ◽  
Generating Polynomial ◽  
Directional Transmission

Based on Elliptic Curve cryptosystem, a threshold signature scheme characterized by (k,l) joint verification for (t,n) signature is put forward. After being signed by a signer company employing (t, n) threshold signature scheme, the informationmis transmitted to a particular verifier company, and then the signature is verified through the cooperation ofkones from the verifier company withlmembers, so as to realize a directional transmission between different companies. Finally, the application examples of the company encryption communication system, the generating polynomial of company private key and public key were given. The security of this scheme is based on Shamir threshold scheme and Elliptic Curve system, and due to the advantages of Elliptic Curve, the scheme enjoys wider application in practice.

scholarly journals A Group Law on the Projective Plane with Applications in Public Key Cryptography

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 734
Author(s):  
Raúl Durán Díaz ◽  
Luis Hernández Encinas ◽  
Jaime Muñoz Masqué
Keyword(s):  
Projective Plane ◽  
Multiplicative Group ◽  
Mathematical Problem ◽  
Discrete Logarithm ◽  
Public Key Cryptography ◽  
Public Key ◽  
Arbitrary Field ◽  
Base Field ◽  
Computational Difficulty ◽  
Group Law

In the context of new threats to Public Key Cryptography arising from a growing computational power both in classic and in quantum worlds, we present a new group law defined on a subset of the projective plane F P 2 over an arbitrary field F , which lends itself to applications in Public Key Cryptography and turns out to be more efficient in terms of computational resources. In particular, we give explicitly the number of base field operations needed to perform the mentioned group law. Based on it, we present a Diffie-Hellman-like key agreement protocol. We analyze the computational difficulty of solving the mathematical problem underlying the proposed Abelian group law and we prove that the security of our proposal is equivalent to the discrete logarithm problem in the multiplicative group of the cubic extension of the finite field considered. We present an experimental setup in order to show real computation times along a comparison with the group operation in the group of points of an elliptic curve. Based on current state-of-the-art algorithms, we provide parameter ranges suitable for real world applications. Finally, we present a promising variant of the proposed group law, by moving from the base field F to the ring Z / p q Z , and we explain how the security becomes enhanced, though at the cost of a longer key length.

Design of Digital Signature Scheme Based on Elliptic Curve Cryptosystem

2014 ◽  
Vol 685 ◽  
pp. 579-582
Author(s):  
Shi Guo Jin ◽  
Guang Jiang Wang
Keyword(s):  
Elliptic Curve ◽  
Digital Signature ◽  
Public Key Cryptography ◽  
Elliptic Curve Cryptosystem ◽  
Generation Process ◽  
Signature Scheme ◽  
Technical Performance ◽  
Elliptic Curve Cryptosystems ◽  
Process System ◽  
Digital Signature Scheme

Digital signature is electronically password technique for electronic document signature. Elliptic curve cryptography is a method of public key cryptography based on elliptic curve mathematical. Digital signature scheme consists of three processes: initialization process, the signature generation process and signature verification process system. This paper analyzes the elliptic curve cryptosystems mathematical principle and technical performance. The paper proposes design of digital signature scheme based on elliptic curve cryptosystem.

Cryptographic Primitives

2020 ◽  
pp. 57-134
Author(s):  
Andreas Bolfing
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Public Key ◽  
Public Key Encryption ◽  
Cryptographic Primitives ◽  
Digital Signature Algorithm ◽  
Digital Signature Scheme ◽  
Current Standards

This chapter provides a very detailed introduction to cryptography. It first explains the cryptographic basics and introduces the concept of public-key encryption which is based on one-way and trapdoor functions, considering the three major public-key encryption families like integer factorization, discrete logarithm and elliptic curve schemes. This is followed by an introduction to hash functions which are applied to construct Merkle trees and digital signature schemes. As modern cryptoschemes are commonly based on elliptic curves, the chapter then introduces elliptic curve cryptography which is based on the Elliptic Curve Discrete Logarithm Problem (ECDLP). It considers the hardness of the ECDLP and the possible attacks against it, showing how to find suitable domain parameters to construct cryptographically strong elliptic curves. This is followed by the discussion of elliptic curve domain parameters which are recommended by current standards. Finally, it introduces the Elliptic Curve Digital Signature Algorithm (ECDSA), the elliptic curve digital signature scheme.

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