Analysis Review on Public Key Cryptography Algorithms

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.

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Cryptographic Primitives

Cryptographic Primitives in Blockchain Technology ◽

10.1093/oso/9780198862840.003.0003 ◽

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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Committing to quantum resistance: a slow defence for Bitcoin against a fast quantum computing attack

Royal Society Open Science ◽

10.1098/rsos.180410 ◽

2018 ◽

Vol 5 (6) ◽

pp. 180410 ◽

Cited By ~ 9

Author(s):

I. Stewart ◽

D. Ilie ◽

A. Zamyatin ◽

S. Werner ◽

M. F. Torshizi ◽

...

Keyword(s):

Quantum Computing ◽

Digital Signature ◽

Public Key Cryptography ◽

Public Key ◽

Quantum Computers ◽

Signature Scheme ◽

Integer Factorization ◽

Digital Signature Algorithm ◽

Mathematical Problems ◽

Digital Signature Scheme

Quantum computers are expected to have a dramatic impact on numerous fields due to their anticipated ability to solve classes of mathematical problems much more efficiently than their classical counterparts. This particularly applies to domains involving integer factorization and discrete logarithms, such as public key cryptography. In this paper, we consider the threats a quantum-capable adversary could impose on Bitcoin, which currently uses the Elliptic Curve Digital Signature Algorithm (ECDSA) to sign transactions. We then propose a simple but slow commit–delay–reveal protocol, which allows users to securely move their funds from old (non-quantum-resistant) outputs to those adhering to a quantum-resistant digital signature scheme. The transition protocol functions even if ECDSA has already been compromised. While our scheme requires modifications to the Bitcoin protocol, these can be implemented as a soft fork.

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A new RSA public key encryption scheme with chaotic maps

International Journal of Electrical and Computer Engineering (IJECE) ◽

10.11591/ijece.v10i2.pp1430-1437 ◽

2020 ◽

Vol 10 (2) ◽

pp. 1430

Author(s):

Nedal Tahat ◽

Ashraf A. Tahat ◽

Maysam Abu-Dalu ◽

Ramzi B. Albadarneh ◽

Alaa E. Abdallah ◽

...

Keyword(s):

Information Exchange ◽

Chaotic Maps ◽

Discrete Logarithm ◽

Public Key Cryptography ◽

Public Key ◽

Original Text ◽

Public Key Encryption ◽

Integer Factorization ◽

Computational Ability ◽

New System

Public key cryptography has received great attention in the field of information exchange through insecure channels. In this paper, we combine the Dependent-RSA (DRSA) and chaotic maps (CM) to get a new secure cryptosystem, which depends on both integer factorization and chaotic maps discrete logarithm (CMDL). Using this new system, the scammer has to go through two levels of reverse engineering, concurrently, so as to perform the recovery of original text from the cipher-text has been received. Thus, this new system is supposed to be more sophisticated and more secure than other systems. We prove that our new cryptosystem does not increase the overhead in performing the encryption process or the decryption process considering that it requires minimum operations in both. We show that this new cryptosystem is more efficient in terms of performance compared with other encryption systems, which makes it more suitable for nodes with limited computational ability.

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Collective Signature Protocols for Signing Groups based on Problem of Finding Roots Modulo Large Prime Number

International Journal of Network Security & Its Applications ◽

10.5121/ijnsa.2021.13405 ◽

2021 ◽

Vol 13 (04) ◽

pp. 59-69

Author(s):

Tuan Nguyen Kim ◽

Duy Ho Ngoc ◽

Nikolay A. Moldovyan

Keyword(s):

Elliptic Curve ◽

Prime Number ◽

Digital Signature ◽

Discrete Logarithm ◽

Discrete Logarithm Problem ◽

Public Key ◽

Prime Factorization ◽

Factorization Problem ◽

Hybrid Combination ◽

Different Types

Generally, digital signature algorithms are based on a single difficult computational problem like prime factorization problem, discrete logarithm problem, elliptic curve problem. There are also many other algorithms which are based on the hybrid combination of prime factorization problem and discrete logarithm problem. Both are true for different types of digital signatures like single digital signature, group digital signature, collective digital signature etc. In this paper we propose collective signature protocols for signing groups based on difficulty of problem of finding roots modulo large prime number. The proposed collective signatures protocols have significant merits one of which is connected with possibility of their practical using on the base of the existing public key infrastructures.

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Public Key Cryptosystem Research Based on Discrete Group

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.687-691.2984 ◽

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.

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PERSPECTIVES OF ELLIPTICAL CRYPTOGRAPHY TO ENSURE THE INTEGRITY AND CONFIDENTIALITY OF INFORMATION

Visnyk Universytetu “Ukraina” ◽

10.36994/2707-4110-2019-2-23-26 ◽

2019 ◽

Author(s):

Anna ILYENKO ◽

Sergii ILYENKO ◽

Yana MASUR

Keyword(s):

Information Systems ◽

Elliptic Curve ◽

Elliptic Curves ◽

Finite Fields ◽

Computational Efficiency ◽

Digital Signature ◽

Discrete Logarithm ◽

Algebraic Groups ◽

Schnorr Signature ◽

Stability Of Algorithms

In this article, the main problems underlying the current asymmetric crypto algorithms for the formation and verification of electronic-digital signature are considered: problems of factorization of large integers and problems of discrete logarithm. It is noted that for the second problem, it is possible to use algebraic groups of points other than finite fields. The group of points of the elliptical curve, which satisfies all set requirements, looked attractive on this side. Aspects of the application of elliptic curves in cryptography and the possibilities offered by these algebraic groups in terms of computational efficiency and crypto-stability of algorithms were also considered. Information systems using elliptic curves, the keys have a shorter length than the algorithms above the finite fields. Theoretical directions of improvement of procedure of formation and verification of electronic-digital signature with the possibility of ensuring the integrity and confidentiality of information were considered. The proposed method is based on the Schnorr signature algorithm, which allows data to be recovered directly from the signature itself, similarly to RSA-like signature systems, and the amount of recoverable information is variable depending on the information message. As a result, the length of the signature itself, which is equal to the sum of the length of the end field over which the elliptic curve is determined, and the artificial excess redundancy provided to the hidden message was achieved.

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Public-Key Encryption

10.1093/oso/9780198788003.003.0005 ◽

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.

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

Journal of Mathematical Cryptology ◽

10.1515/jmc-2019-0054 ◽

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.

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