FRACTAL MAGMAS AND PUBLIC-KEY CRYPTOGRAPHY

2021 ◽  
Vol 26 (2) ◽  
pp. 23-49
Author(s):  
V. P. Tsvetov
Keyword(s):  
Binary Operation ◽  
Public Key Cryptography ◽  
The Self ◽  
Public Key ◽  
Self Similarity ◽  
Key Exchange Protocol ◽  
Binary Operations ◽  
Similarity Principle ◽  
Diffie Hellman ◽  
Cayley Tables

In this paper, we deal with magmas the simplest algebras with a single binary operation. The main result of our research is algorithms for generating chain of finite magmas based on the self-similarity principle of its Cayley tables. In this way the cardinality of a magmas domain is twice as large as the previous one for each magma in the chain, and its Cayley table has a block-like structure. As an example, we consider a cyclic semigroup of binary operations generated by a finite magmas operation with a low-cardinality domain, and a modify the Diffie-Hellman-Merkle key exchange protocol for this case.

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.

scholarly journals Survey on Asymmetric Key Cryptographic Algorithms

2020 ◽  
pp. 404-408
Author(s):  
Sabitha S ◽  
Binitha V Nair
Keyword(s):  
Public Key Cryptography ◽  
Public Key ◽  
The Public ◽  
Private Key ◽  
Design And Implementation ◽  
Diffie Hellman ◽  
Encryption And Decryption ◽  
Cryptographic Algorithms ◽  
Symmetric Key ◽  
Symmetric Key Cryptography

Cryptography is an essential and effective method for securing information’s and data. Several symmetric and asymmetric key cryptographic algorithms are used for securing the data. Symmetric key cryptography uses the same key for both encryption and decryption. Asymmetric Key Cryptography also known as public key cryptography uses two different keys – a public key and a private key. The public key is used for encryption and the private key is used for decryption. In this paper, certain asymmetric key algorithms such as RSA, Rabin, Diffie-Hellman, ElGamal and Elliptical curve cryptosystem, their security aspects and the processes involved in design and implementation of these algorithms are examined.

scholarly journals Certificateless Public Key Encryption Scheme with Hybrid Problems and Its Application to Internet of Things

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Rui Guo ◽  
Qiaoyan Wen ◽  
Huixian Shi ◽  
Zhengping Jin ◽  
Hua Zhang
Keyword(s):  
Internet Of Things ◽  
Public Key Cryptography ◽  
Public Key ◽  
Encryption Scheme ◽  
Public Key Encryption ◽  
Certificateless Cryptography ◽  
Diffie Hellman ◽  
Identity Based ◽  
Certificate Management ◽  
Certificateless Public Key Encryption

Certificateless cryptography aims at combining the advantages of public key cryptography and identity based cryptography to avoid the certificate management and the key escrow problem. In this paper, we present a novel certificateless public key encryption scheme on the elliptic curve over the ring, whose security is based on the hardness assumption of Bilinear Diffie-Hellman problem and factoring the large number as in an RSA protocol. Moreover, since our scheme requires only one pairing operation in decryption, it is significantly more efficient than other related schemes. In addition, based on our encryption system, we also propose a protocol to protect the confidentiality and integrity of information in the scenario of Internet of Things with constrained resource nodes.

Secure and Efficient Certificateless Signature and Blind Signature Scheme from Pairings

2013 ◽  
Vol 457-458 ◽  
pp. 1262-1265
Author(s):  
Min Qin Chen ◽  
Qiao Yan Wen ◽  
Zheng Ping Jin ◽  
Hua Zhang
Keyword(s):  
Random Oracle Model ◽  
Public Key Cryptography ◽  
Random Oracle ◽  
Blind Signature ◽  
Public Key ◽  
Signature Scheme ◽  
Signature Schemes ◽  
Diffie Hellman ◽  
Identity Based ◽  
Certificateless Signature

Based an identity-based signature scheme, we givea certificateless signature scheme. And then we propose a certificateless blind signature (CLBS) scheme in this paper. This schemeis more efficient than those of previous schemes by pre-computing the pairing e (P, P)=g. Based on CL-PKC, it eliminates theusing of certificates in the signature scheme with respect to thetraditional public key cryptography (PKC) and solves key escrowproblems in ID-based signature schemes. Meanwhile it retains themerits of BS schemes. The proposed CLBS scheme is existentialunforgeable in the random oracle model under the intractabilityof the q-Strong Diffie-Hellman problem.

scholarly journals A Certificateless Noninteractive Key Exchange Protocol with Provable Security

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Xuefei Cao ◽  
Lanjun Dang ◽  
Yingzi Luan ◽  
Wei You
Keyword(s):  
Random Oracle Model ◽  
Random Oracle ◽  
Key Exchange ◽  
Public Key ◽  
Communication Overhead ◽  
Key Exchange Protocol ◽  
The Public ◽  
Diffie Hellman ◽  
Message Exchange ◽  
Certificateless Public Key Cryptosystem

In this paper, we propose a certificateless noninteractive key exchange protocol. No message exchange is required in the protocol, and this feature will facilitate the applications where the communication overhead matters, for example, the communications between the satellites and the earth. The public key certificate is removed as well as the key escrow problem using the certificateless public key cryptosystem. The security of the protocol rests on the bilinear Diffie–Hellman problem, and it could be proved in the random oracle model. Compared with previous protocols, the new protocol reduces the running time by at least 33.0%.

scholarly journals Modification of Traditional RSA into Symmetric-RSA Cryptosystems

Cryptography ◽  
2020 ◽  
pp. 120-128
Author(s):  
Prerna Mohit ◽  
G. P. Biswas
Keyword(s):  
Digital Signature ◽  
Discrete Logarithm ◽  
Prime Numbers ◽  
Public Key ◽  
Key Exchange Protocol ◽  
Factorization Problem ◽  
Rsa Algorithm ◽  
Diffie Hellman ◽  
Diffie Hellman Key Exchange ◽  
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.

Modification of Traditional RSA into Symmetric-RSA Cryptosystems

2017 ◽  
Vol 13 (1) ◽  
pp. 66-73
Author(s):  
Prerna Mohit ◽  
G. P. Biswas
Keyword(s):  
Digital Signature ◽  
Discrete Logarithm ◽  
Prime Numbers ◽  
Public Key ◽  
Key Exchange Protocol ◽  
Factorization Problem ◽  
Rsa Algorithm ◽  
Diffie Hellman ◽  
Diffie Hellman Key Exchange ◽  
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.

scholarly journals MAKE: A matrix action key exchange

2022 ◽  
Vol 16 (1) ◽  
pp. 64-72
Author(s):  
Nael Rahman ◽  
Vladimir Shpilrain
Keyword(s):  
Semidirect Product ◽  
Key Exchange ◽  
The Other ◽  
Public Key ◽  
Key Exchange Protocol ◽  
Formula One ◽  
Diffie Hellman

Abstract We offer a public key exchange protocol based on a semidirect product of two cyclic (semi)groups of matrices over Z p {{\mathbb{Z}}}_{p} . One of the (semi)groups is additive, and the other one is multiplicative. This allows us to take advantage of both operations on matrices to diffuse information. We note that in our protocol, no power of any matrix or of any element of Z p {{\mathbb{Z}}}_{p} is ever exposed, so standard classical attacks on Diffie–Hellman-like protocols are not applicable.

scholarly journals SPDH - A Secure Plain Diffie-Hellman Algorithm

2012 ◽  
Author(s):  
Henrik Tange ◽  
Birger Andersen
Keyword(s):  
Elliptic Curve ◽  
Secure Communication ◽  
Public Key Cryptography ◽  
Public Key ◽  
Wireless System ◽  
Eavesdropping Attack ◽  
Replay Attacks ◽  
Diffie Hellman ◽  
Man In The Middle ◽  
Shared Secret

Secure communication in a wireless system or end-to-end communication requires setup of a shared secret. This shared secret can be obtained by the use of a public key cryptography system. The most widely used algorithm to obtain a shared secret is the Diffie–Hellman algorithm. However, this algorithm suffers from the Man-in-the-Middle problem; an attacker can perform an eavesdropping attack listen to the communication between participants A and B. Other algorithms as for instance ECMQV (Elliptic Curve Menezes Qo Vanstone) can handle this problem but is far more complex and slower because the algorithm is a three-pass algorithm whereas the Diffie–Hellman algorithm is a simple two-pass algorithm. Using standard cryptographic modules as AES and HMAC the purposed algorithm, Secure Plain Diffie–Hellman Algorithm, solves the Man-in-the-Middle problem and maintain its advantage from the plain Diffie–Hellman algorithm. Also the possibilities of replay attacks are solved by use of a timestamp.

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