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10 articles for “discrete logarithmic problems”
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Efficient Computation of Point Multiplication in the Implementation of Elliptic Curve Cryptography
Abstract: In recent times, elliptical curves have been used for public-key cryptographic and signature schemes in information security. The security provided by elliptic curve cryptographic protocols, either using signature or public-key encryption, is entirely based on the discrete logarithm problem. The discrete logarithm problem says that for a given a point Q that is a certain multiple k of a fixed point P, how to find the value of k in …
Published in E-Commerce for Future & Trends · Vol. 1, Issue 1, 2014 · pp. 1–5 Read article
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Discrete Logarithm and Cryptosystem
Abstract: We formulate a new DLP and designed a PKC. Our ProposedDiscrete Logarithm Problem (PDLP) is distinct from the Traditional Discrete Logarithm Problem (TDLP), which is proved in this paper. We use this PDLP for design a PKC. Our claim that, this PKC is more secure than the previous PKC’s, because a one reason is enough in support of this statement that, the PDLP is more complex problem because the computation …
Published in Journal of Open Source Developments · Vol. 7, Issue 2, 2020 · pp. 15–17 Read article
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Discrete Cryptography
Abstract: The theory of Public Key Cryptography (PKC) was introduced by Diffie and Hellman [2]. There was the key agreement protocol based on the Discrete Logarithm Problem (DLP) in 1976. In 1985, ElGamal [1] applied the concept of [1] and presented the first real and practical PKC. The security of this PKC interacts with the hardness of DLP. The discrete cryptography is presented in this paper. Cryptography interacts with the hard …
Published in Journal of Multimedia Technology & Recent Advancements · Vol. 7, Issue 2, 2020 · pp. 1–3 Read article
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Crypto-trace Based Open Source Developing Scheme
Abstract: In this paper, we propose a new scheme based on crypto-trace for open source development, It is based on the method of representing the elements of a subgroup of the multiplicative group of the finite field GF (p12) *. The security of this public key cryptosystem is based on difficult mathematical problems i.e., the discrete logarithm problem on the subgroup of a multiplicative group of a finite field GF(p12)* of …
Published in Journal of Open Source Developments · Vol. 8, Issue 2, 2021 · pp. 28–35 Read article
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Artificial Neural Network and Its Application to Diagnosis
Abstract: In this paper, we are giving an excellent idea for the designing of the standard diagnosis key diagnosis systems, which security is based on the well known number theoretic problem, i.e., elliptic curve discrete logarithm problem in multiplicative group of the finite field. But now we are moving in the revolutionary idea, “The Automatic groups G converted into the multiplicative groups G’ of the finite field Zp* of the order …
Published in Journal of Advancements in Robotics · Vol. 7, Issue 2, 2020 · pp. 15–22 Read article
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Medical Applications of Artificial Neural Network
Abstract: The correspondence between the natural neurons and artificial neurons is defined in this paper. Thus, an excellent idea appears to design the standard diagnosis key diagnosis systems, which security is based on the well known number theoretic problem, i.e. elliptic curve discrete logarithm problem in multiplicative group of the finite field. But now we are moving in the revolutionary idea, “The Automatic groups G converted into the multiplicative groups G’ …
Published in Journal of Software Engineering Tools & Technology Trends · Vol. 7, Issue 2, 2020 · pp. 23–30 Read article
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PKC based on DLP
Abstract: We propose a new representation of Discrete Logarithm Problem (DLP) as and use this to design a Public Key Cryptosystem (PKC). The problem to find the index of the primitive element of the cyclic group is referred as the DLP. This paper sets the discrete structure of the finite field for introducing the securer PKC than the existed.Key Words: DLP, PKC, Cyclic Group, Primitive Element, Finite Field.Cite this Article: Sunil …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 7, Issue 2, 2020 · pp. 28–30 Read article
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Extended Cryptosystem
Abstract: In this paper, we propose Discrete Logarithm Problems (DLPs) over finite extension Fields. Consequently we propose Public Key Cryptosystems (PKCs), corresponding to these DLP As we know all the DLPs so designed are based on Galois Field of order p. More emphasis is given on algebraic aspect of the respective Galois Fields for DLPs defined therein.2000 Mathematics Subject Classification Number: 94A60.Keywords and Phrases: DLP, Finite Extension Field, PKCs, Galois Field, …
Published in Journal of Multimedia Technology & Recent Advancements · Vol. 7, Issue 2, 2020 · pp. 9–12 Read article
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Atomic Cryptosystem
Abstract: We propose public key cryptosystem (PKC), which is based on the atomic discrete logarithm problem (DLP). Sometimes, the word atomic referred as logical. This can be found by the logical formulation over the finite field. We study the work of [1-10].Atomic cryptosystem deals with the Galois representation of the elements of the cyclic group over finite field for providing the security against semantic attacks. 2000 Mathematics Subject Classification Number: 94A60.Keywords: …
Published in Journal of Open Source Developments · Vol. 7, Issue 2, 2020 · pp. 1–6 Read article
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Discrete Encryption
Abstract: The present work will be directed the future plan towards the security. This study is presented as the application of the fuzzy set and cryptography both. Zadeh’s contribution was the landmark in the development of real mathematical application but today this has been applied in almost every field of the society. Hard mathematical problem interacts with the security of any cryptography. Such mathematical problems are; factorization, discrete logarithm, lattice, quantum …
Published in Journal of Software Engineering Tools & Technology Trends · Vol. 7, Issue 2, 2020 · pp. 11–12 Read article