A key exchange protocol using matrices over group ring

2019 ◽  
Vol 12 (05) ◽  
pp. 1950075
Author(s):  
Indivar Gupta ◽  
Atul Pandey ◽  
Manish Kant Dubey
Keyword(s):  
Group Ring ◽  
Complexity Analysis ◽  
Discrete Logarithm ◽  
Key Exchange ◽  
Group Rings ◽  
Secret Key ◽  
Key Exchange Protocol ◽  
Diffie Hellman ◽  
Shared Secret ◽  
Invertible Matrices

The first published solution to key distribution problem is due to Diffie–Hellman, which allows two parties that have never communicated earlier, to jointly establish a shared secret key over an insecure channel. In this paper, we propose a new key exchange protocol in a non-commutative semigroup over group ring whose security relies on the hardness of Factorization with Discrete Logarithm Problem (FDLP). We have also provided its security and complexity analysis. We then propose a ElGamal cryptosystem based on FDLP using the group of invertible matrices over group rings.

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

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 ◽  
Diffie Hellman Key Exchange ◽  
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.

scholarly journals A Novel Provably Secure Key-Agreement Using Secret Subgroup Generator

2021 ◽  
Author(s):  
Abdelhaliem Babiker
Keyword(s):  
Prime Order ◽  
Key Agreement ◽  
Discrete Logarithm ◽  
Key Exchange ◽  
Security Requirement ◽  
Secret Key ◽  
Diffie Hellman ◽  
Shared Secret ◽  
Shared Secret Key ◽  
Provably Secure

Abstract In this paper, a new key-agreement scheme is proposed and analyzed. In addition to being provably secure in the shared secret key indistinguishability model under Decisional Diffie-Hellman assumption for subgroup of matrices over GF(2) with prime order, which considered as basic security requirement, the scheme has an interesting feature; it uses exponentiations over cyclic group using hidden secret subgroup generator as a platform for the key exchange, whereby - unlike many other exponentiation based key exchange schemes - it transcends the reliance on intractability of Discrete Logarithm Problem in its security.

scholarly journals A Novel Provably Secure Key-Agreement Using Secret Subgroup Generator

2021 ◽  
Author(s):  
Abdelhaliem Babiker
Keyword(s):  
Key Agreement ◽  
Cyclic Subgroup ◽  
Discrete Logarithm ◽  
Key Exchange ◽  
Discrete Logarithm Problem ◽  
Secret Key ◽  
Shared Secret ◽  
Shared Secret Key ◽  
Provably Secure

Abstract In this paper, a new key-agreement scheme is proposed and analyzed. In addition to being provably secure in shared secret key indistinguishability model, the scheme has an interesting feature: while using exponentiation over a cyclic subgroup to establish the key-agreement, the generator of that subgroup is hidden to secure the scheme against adversaries that are capable of solving the Discrete Logarithm Problem, which means that the scheme might be candidate as a post-quantum key exchange scheme.

scholarly journals Network Security System with Optimized Randomized Multiple Key Exchange Algorithm

2020 ◽  
Vol 9 (3) ◽  
pp. 1075-1080
Keyword(s):  
Network Security ◽  
Elliptic Curve ◽  
Key Exchange ◽  
Memory Requirement ◽  
Secret Key ◽  
Diffie Hellman ◽  
Shared Secret ◽  
Security Properties ◽  
Diffie Hellman Key Exchange ◽  
Shared Secret Key

This paper illustrates three different algorithms to provide shared secret key for security of the system. The proposed three algorithms namely 1) Modified Simple Password Key Exchange Scheme 2) Modified Diffie-Hellman Key exchange Scheme 3) Modified Elliptic Curve Scheme are meant to provide shared secret key for authentication process. Enhancements in terms of memory requirement, storage and other security properties such as authentication among mutual users, fraud prevention, attack etc., prove the validity of the proposed algorithms in proving authentication for the cryptographic identification of networks

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

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 ◽  
Diffie Hellman Key Exchange ◽  
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.

scholarly journals QKD Based on Symmetric Entangled Bernstein-Vazirani

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 870
Author(s):  
Michael Ampatzis ◽  
Theodore Andronikos
Keyword(s):  
Key Distribution ◽  
Key Exchange ◽  
Small Scale ◽  
Secret Key ◽  
Key Exchange Protocol ◽  
Epr Pairs ◽  
Diffie Hellman ◽  
Symmetric Version ◽  
Diffie Hellman Key Exchange

This paper introduces a novel entanglement-based QKD protocol, that makes use of a modified symmetric version of the Bernstein-Vazirani algorithm, in order to achieve secure and efficient key distribution. Two variants of the protocol, one fully symmetric and one semi-symmetric, are presented. In both cases, the spatially separated Alice and Bob share multiple EPR pairs, each one qubit of the pair. The fully symmetric version allows both parties to input their tentative secret key from their respective location and acquire in the end a totally new and original key, an idea which was inspired by the Diffie-Hellman key exchange protocol. In the semi-symmetric version, Alice sends her chosen secret key to Bob (or vice versa). The performance of both protocols against an eavesdroppers attack is analyzed. Finally, in order to illustrate the operation of the protocols in practice, two small scale but detailed examples are given.

scholarly journals An Improved Diffie-Hellman Protocol Security Using Video Entropy

2020 ◽  
Vol 55 (6) ◽  
Author(s):  
Rasha M. Mohsin ◽  
Rasha I. Ahmed ◽  
Zinah R. Hussein
Keyword(s):  
Discrete Logarithm ◽  
Key Exchange ◽  
High Definition ◽  
Video Frames ◽  
Diffie Hellman ◽  
Man In The Middle ◽  
Secret Keys ◽  
Shared Secret ◽  
Diffie Hellman Key Exchange ◽  
Secure Channels

The Diffie-Hellman is a key exchange protocol to provide a way to transfer shared secret keys between two parties, although those parties might never have communicated together. This paper suggested a new way to transfer keys through public or non-secure channels depending on the sent video files over the channel and then extract keys. The proposed method of key generation depends on the video file content by using the entropy value of the video frames. The proposed system solves the weaknesses in the Diffie-Hellman key exchange algorithm, which is MIMA (Man-in-the-Middle attack) and DLA( Discrete logarithm attack). When the method used high definition videos with a vast amount of data, the keys generated with a large number up to 500 per frame, and each number value reaches more than 1000 to be used or switched when needed. The method also provides some difficulty in guessing the keys from the transmitted video and the reason for the development and emergence of many communication programs Viber, WhatsApp, and other programs, enabling to use the proposed method in these programs.

scholarly journals Non-Commutative Key Exchange Protocol

2021 ◽  
Author(s):  
Luis Adrián Lizama-Pérez ◽  
José Mauricio López Romero
Keyword(s):  
Discrete Logarithm ◽  
Matrix Multiplication ◽  
Key Exchange ◽  
Secret Key ◽  
Key Exchange Protocol ◽  
Promising Alternative ◽  
Private Key ◽  
Secret Communication ◽  
Perfect Forward Secrecy ◽  
Commutative Matrix

We introduce a novel key exchange protocol based on non-commutative matrix multiplication. The security of our method does not rely on computational problems as integer factorization or discrete logarithm whose difficulty is conjectured. We claim that the unique opportunity for the eavesdropper to get the private key is by means of an exhaustive search which is equivalent to searching an unsorted database problem. Therefore, the algorithm becomes a promising candidate to be used in the quantum era to establish shared keys and achieve secret communication. Furthermore, to establish a 256-bit secret key the size of the public key only requires 256 bits while the private key occupies just 384 bits. Matrix multiplications can be done over a reduced 4-bit size modulo. Also, we show that in a generalized method, private numbers become indistinguishable and we discuss how to achieve Perfect Forward Secrecy (PFS). As a consequence, Lizama's protocol becomes a promising alternative for Internet-of-Things (IoT) computational devices in the quantum era.

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.

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