An Advanced Signature Scheme Based on Non-abelian Group Over Algebraic Technique
01 Jan 2021-Vol. 700, pp 2855-2864
TL;DR: In this article, an advanced signature scheme constructed over non-abelian group above algebraic technique in this paper is defined. But, the signature scheme is based on nonabelian property of groups.
Abstract: In general, digital signatures are part of cryptosystem. Here, signature scheme is based on non-abelian property of groups. It proposes an advanced signature scheme constructed over non-abelian group above algebraic technique in this paper. It is defined a scheme of signature algorithm through generation and verification signature. Here, algorithm is verified and confirmed by illustrations. To strengthen the algorithm, security analysis is given in this paper.
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Journal Article•
TL;DR: A new public key cryptosystem built on finite non abelian groups is proposed in this paper, which is convertible to a scheme in which the encryption and decryption are much faster than other well-known public key Cryptosystems, even without no message expansion.
Abstract: Most public key cryptosystems have been constructed based on abelian groups up to now. We propose a new public key cryptosystem built on finite non abelian groups in this paper. It is convertible to a scheme in which the encryption and decryption are much faster than other well-known public key cryptosystems, even without no message expansion. Furthermore a signature scheme can be easily derived from it, while it is difficult to find a signature scheme using a non abelian group.
70 citations
References
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Book•
01 Jan 1996TL;DR: A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols.
Abstract: From the Publisher:
A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper.
13,597 citations
23 Aug 1985
TL;DR: A new signature scheme is proposed, together with an implementation of the Diffie-Hellman key distribution scheme that achieves a public key cryptosystem that relies on the difficulty of computing discrete logarithms over finite fields.
Abstract: A new signature scheme is proposed, together with an implementation of the Diffie-Hellman key distribution scheme that achieves a public key cryptosystem. The security of both systems relies on the difficulty of computing discrete logarithms over finite fields.
7,514 citations
01 Jun 1986
TL;DR: An introduction to the theory of finite fields, with emphasis on those aspects that are relevant for applications, especially information theory, algebraic coding theory and cryptology and a chapter on applications within mathematics, such as finite geometries.
Abstract: The first part of this book presents an introduction to the theory of finite fields, with emphasis on those aspects that are relevant for applications. The second part is devoted to a discussion of the most important applications of finite fields especially information theory, algebraic coding theory and cryptology (including some very recent material that has never before appeared in book form). There is also a chapter on applications within mathematics, such as finite geometries. combinatorics. and pseudorandom sequences. Worked-out examples and list of exercises found throughout the book make it useful as a textbook.
1,819 citations
TL;DR: Algebraic key establishment protocols based on the difficulty of solving equations over algebraic structures are described as a theoretical basis for constructing public–key cryptosystems.
Abstract: Algebraic key establishment protocols based on the difficulty of solving equations over algebraic structures are described as a theoretical basis for constructing public–key cryptosystems.
431 citations
TL;DR: Several related algorithms are presented for computing logarithms in fieldsGF(p),p a prime, with novel ingredients are new ways of obtaining linear equations and new methods of solving these linear equations by adaptations of sparse matrix methods from numerical analysis to the case of finite rings.
Abstract: Several related algorithms are presented for computing logarithms in fieldsGF(p),p a prime. Heuristic arguments predict a running time of exp((1+o(1))
$$\sqrt {\log p \log \log p} $$
) for the initial precomputation phase that is needed for eachp, and much shorter running times for computing individual logarithms once the precomputation is done. The running time of the precomputation is roughly the same as that of the fastest known algorithms for factoring integers of size aboutp. The algorithms use the well known basic scheme of obtaining linear equations for logarithms of small primes and then solving them to obtain a database to be used for the computation of individual logarithms. The novel ingredients are new ways of obtaining linear equations and new methods of solving these linear equations by adaptations of sparse matrix methods from numerical analysis to the case of finite rings. While some of the new logarithm algorithms are adaptations of known integer factorization algorithms, others are new and can be adapted to yield integer factorization algorithms.
266 citations