Modification of Traditional RSA into Symmetric-RSA Cryptosystems

Rsa Cryptography

This paper addresses the modification of RSA cryptography namely Symmetric-RSA, which seem to be equally useful for different cryptographic applications such as encryption, digital signature, etc. In order to design Symmetric-RSA, two prime numbers are negotiated using Diffie-Hellman key exchange protocol followed by RSA algorithm. As the new scheme uses Diffie-Hellman and RSA algorithm, the security of the overall system depends on discrete logarithm as well as factorization problem and thus, its security is more than public-key RSA. Finally, some new cryptographic applications of the proposed modifications are described that certainly extend the applications of the existing RSA.

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 ◽

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.

Algorithmic Strategies for Solving Complex Problems in Cryptography - Advances in Information Security, Privacy, and Ethics ◽

Problems in Cryptography and Cryptanalysis

10.4018/978-1-5225-2915-6.ch002 ◽

2018 ◽

pp. 23-39

Author(s):

Kannan Balasubramanian ◽

Rajakani M.

Keyword(s):

Elliptic Curve ◽

Optimization Problems ◽

Discrete Logarithm ◽

Random Number Generators ◽

Factorization Problem ◽

Diffie Hellman ◽

Integer Factorization Problem ◽

Membership Problems

The integer factorization problem used in the RSA cryptosystem, the discrete logarithm problem used in Diffie-Hellman Key Exchange protocol and the Elliptic Curve Discrete Logarithm problem used in Elliptic Curve Cryptography are traditionally considered the difficult problems and used extensively in the design of cryptographic algorithms. We provide a number of other computationally difficult problems in the areas of Cryptography and Cryptanalysis. A class of problems called the Search problems, Group membership problems, and the Discrete Optimization problems are examples of such problems. A number of computationally difficult problems in Cryptanalysis have also been identified including the Cryptanalysis of Block ciphers, Pseudo-Random Number Generators and Hash functions.

Using P systems to Solve the Discrete Logarithm Problem used in Diffie-Hellman Key Exchange Protocol

International Journal of Computer Network and Information Security ◽

10.5815/ijcnis.2009.01.04 ◽

2009 ◽

Vol 1 (1) ◽

pp. 24-31

Author(s):

Xiaojing Ma ◽

Zhitang Li ◽

Hao Tu

Keyword(s):

Discrete Logarithm ◽

Key Exchange ◽

P Systems ◽

Key Exchange Protocol ◽

Diffie Hellman ◽

Diffie Hellman Key Exchange

Enhancement of Security of Diffie-Hellman Key Exchange Protocol using RSA Cryptography.

Journal of Physics Conference Series ◽

10.1088/1742-6596/2161/1/012014 ◽

2022 ◽

Vol 2161 (1) ◽

pp. 012014

Author(s):

Chiradeep Gupta ◽

N V Subba Reddy

Keyword(s):

Key Exchange ◽

Secret Key ◽

Key Exchange Protocol ◽

Diffie Hellman ◽

Shared Secret ◽

Intended Receiver ◽

Rsa Cryptography ◽

Shared Secret Key ◽

Mitm Attack

Abstract Cryptography is related and referred to as the secured transmission of messages amongst the sender and the intended receiver by ensuring confidentiality, integrity, and authentication. Diffie – Hellman (DH) key exchange protocol is a well-known algorithm that would generate a shared secret key among the sender and the intended receiver, and the basis of cryptosystems for using public and private key for encryption and decryption process. But it is severely affected by the Man in the Middle (MITM) attack that would intercept and manipulate thus eavesdropping the shared secret key. This paper proposes a model of integrating the public-key RSA cryptography system with the DH key exchange to prevent the MITM attack. The performance of the proposed work has been compared to the DH Key Exchange algorithm as well as RSA Cryptosystem to conclude for effectiveness of the proposed model.

Post–Quantum Cryptography – A Primer

10.34048/acc.2020.1.f2 ◽

2020 ◽

Author(s):

P. V. Ananda Mohana

Keyword(s):

Elliptic Curve ◽

Quantum Cryptography ◽

Digital Signature ◽

Information Transfer ◽

Discrete Logarithm ◽

Digital Signatures ◽

Factorization Problem ◽

Rsa Algorithm ◽

Digital Signature Algorithm ◽

Post Quantum Cryptography

Traditionally, information security needed encryption, authentication, key management, non-repudiation and authorization which were being met using several techniques. Standardization of algorithms by National Institute of Standards and Technology (NIST) has facilitated international communication for banking and information transfer using these standards. Encryption can be carried out using Advanced Encryption Standard (AES) using variable block lengths (128, 192 or 256 bits) and variable key lengths (128, 192 or 256 bits). Solutions for light weight applications such as those for Internet of Things (IoT) are also being standardized. Message integrity is possible using host of hash algorithms such as SHA-1, SHA-2 etc., and more recently using SHA-3 algorithm. Authentication is possible using well known Rivest-Shamir-Adleman (RSA) algorithm needing 2048/4096 bit operations. Elliptic Curve Cryptography (ECC) is also quite popular and used in several practical systems such as WhatsApp, Blackberry etc. Key exchange is possible using Diffie-Hellman algorithm and its variations. Digital Signatures can be carried out using RSA algorithm or Elliptic Curve Digital Signature Algorithm (ECDSA) or DSA (Digital Signature Algorithm). All these algorithms derive security from difficulty in solving some mathematical problems such as factorization problem or discrete logarithm problem. Though published literature gives evidence of solving factorization problem upto 768 bits only, it is believed that using Quantum computers, these problems could be solved by the end of this decade. This is due to availability of the pioneering work of Shor and Grover [1]. For factoring an integer of N bits, Shor’s algorithm takes quantum gates. As such, there is ever growing interest in being ready for the next decade with algorithms that may resist attacks in the quantum computer era. NIST has foreseen this need and has invited proposals from researchers all over the world. In the first round, about 66 submissions were received which have been scrutinized for completeness of submissions , novelty of the approach and security and 25 of these were promote to second round to improve based on the comments received on the first round submission. These will be analyzed for security and some will be selected for final recommendation for use by industry. These are for encryption/decryption, key agreement, hashing and Digital Signatures for both hardware and software implementations. In this paper, we present a brief survey of the state of the art in post-Quantum Cryptography (PQC) followed by study of one of technique referred to as Learning With Errors (LWE) in some detail.

Synchronization of chaotic systems using feedback controller: An application to Diffie–Hellman key exchange protocol and ElGamal public key cryptosystem

Journal of the Egyptian Mathematical Society ◽

10.1016/j.joems.2013.10.003 ◽

2014 ◽

Vol 22 (3) ◽

pp. 365-372 ◽

Cited By ~ 10

Author(s):

P. Balasubramaniam ◽

P. Muthukumar

Keyword(s):

Chaotic Systems ◽

Key Exchange ◽

Feedback Controller ◽

Public Key ◽

Public Key Cryptosystem ◽

Key Exchange Protocol ◽

Diffie Hellman ◽

Diffie Hellman Key Exchange

A Summary of Recent and Old Results on the Security of the Diffie-Hellman Key Exchange Protocol in Finite Groups

Handbook of Research on Secure Multimedia Distribution ◽

10.4018/978-1-60566-262-6.ch010 ◽

2011 ◽

pp. 181-200

Author(s):

Ionut Florescu

Keyword(s):

Discrete Logarithm ◽

Key Exchange ◽

Underlying Structure ◽

Key Exchange Protocol ◽

Statistical Concept ◽

Dimensional Group ◽

Diffie Hellman ◽

Recent Developments ◽

The Relationship

Regarding fundamental protocols in cryptography, the Diffie-Hellman (Diffie and Hellman, 1976) public key exchange protocol is one of the oldest and most widely used in today’s applications. Consequently, many specific cryptographic implementations depend on its security. Typically, an underlying (finite dimensional) group is selected to provide candidates for the key. The study of the security of the exchange as depending on the structure of the underlying group is even today poorly understood, with the most common approaches relying on the security of the Discrete Logarithm problem or on the size of the group. Recent developments bring to attention that the relationship is not necessarily valid and that more research is needed that will relate the underlying structure of the group and the security of the Diffie- Hellman exchange. In this chapter, we describe the problem in detail, we present the relationship with the previously studied Discrete Logarithm and Computational Diffie-Hellman problems, we expose the various concepts of security, and we introduce a new statistical concept specifically designed to serve the assessment of the security of the exchange.

Research Anthology on Blockchain Technology in Business, Healthcare, Education, and Government ◽

Problems in Cryptography and Cryptanalysis

10.4018/978-1-7998-5351-0.ch048 ◽

2021 ◽

pp. 837-853

Author(s):

Kannan Balasubramanian ◽

Rajakani M.

Keyword(s):

Elliptic Curve ◽

Optimization Problems ◽

Discrete Logarithm ◽

Random Number Generators ◽

Factorization Problem ◽

Diffie Hellman ◽

Integer Factorization Problem ◽

Membership Problems

The integer factorization problem used in the RSA cryptosystem, the discrete logarithm problem used in Diffie-Hellman Key Exchange protocol and the Elliptic Curve Discrete Logarithm problem used in Elliptic Curve Cryptography are traditionally considered the difficult problems and used extensively in the design of cryptographic algorithms. We provide a number of other computationally difficult problems in the areas of Cryptography and Cryptanalysis. A class of problems called the Search problems, Group membership problems, and the Discrete Optimization problems are examples of such problems. A number of computationally difficult problems in Cryptanalysis have also been identified including the Cryptanalysis of Block ciphers, Pseudo-Random Number Generators and Hash functions.

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 ◽

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.