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The review on elliptic curves as cryptographic pairing groups [PDF]
Mathematics and Computational Sciences, 2021 Elliptic curve is a set of two variable points on polynomials of degree 3 over a field acted by an addition operation that forms a group structure. The motivation of this study is the mathematics behind that elliptic curve to the applicability within a ...
E Khamseh
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Fully distributed certificate authority based on polynomial over elliptic curve for MANET [PDF]
International Journal of Networked and Distributed Computing (IJNDC), 2014 A mobile ad hoc network (MANET) is a wireless communication network, which does not rely on any centralized management or a pre-existing infrastructure. Various certificate authorities (CAs) distributed over the network, each with a periodically updated ...
Ahmad Alomari
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THEORETICAL ASSUMPTIONS FOR AN INTRODUCTION TO ELLIPTIC CURVE CRYPTOGRAPHY
STED Journal, 2023 Understanding elliptic curves contributed to solving mathematical problems in number theory that had been unsolved for centuries. Elliptic curves were also used in solving one of the millennial problems, which is Fermat's last theorem.
Ognjen Milivojević, Boris Damjanović
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Twisted Edwards Elliptic Curves for Zero-Knowledge Circuits
Mathematics, 2021 Circuit-based zero-knowledge proofs have arose as a solution to the implementation of privacy in blockchain applications, and to current scalability problems that blockchains suffer from.
Marta Bellés-Muñoz +4 more
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Attribute-Based Blind Signature Scheme Based on Elliptic Curve Cryptography
IEEE Access, 2022 Blind signature is a special digital signature that allows the signer to sign a document without knowing its content. However, in many situations, multiple people need to blindly sign messages.
Rui Ma, Linyue Du
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SYMMETRIC BILINEAR CRYPTOGRAPHY ON ELLIPTIC CURVE AND LIE ALGEBRA [PDF]
, 2023 Elliptic Curve Cryptography (ECC) has gained widespread adoption in the field of cryptography due to its efficiency and security properties. Symmetric bilinear pairings on elliptic curves have emerged as a powerful tool in cryptographic protocols ...
John, Michael Nsikan +2 more
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Generalized Fibonacci Sequences for Elliptic Curve Cryptography
Mathematics, 2023 The Fibonacci sequence is a well-known sequence of numbers with numerous applications in mathematics, computer science, and other fields. In recent years, there has been growing interest in studying Fibonacci-like sequences on elliptic curves.
Zakariae Cheddour +2 more
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Efficient Unified Arithmetic for Hardware Cryptography [PDF]
, 2008 The basic arithmetic operations (i.e. addition, multiplication, and inversion) in finite fields, GF(q), where q = pk and p is a prime integer, have several applications in cryptography, such as RSA algorithm, Diffie-Hellman key exchange algorithm [1 ...
Koc, Cetin Kaya +3 more
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Methods for using elliptic curves in cryptography [PDF]
E3S Web of ConferencesElliptic Curve Cryptography (ECC), a significant modern cryptography, is more secure and robust than most others due to its construction using an elliptic curve and the application of mathematical operations for encryption and key generation. Furthermore,
Obukhov Vadim +4 more
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Hyper-and-elliptic-curve cryptography [PDF]
LMS Journal of Computation and Mathematics, 2014 AbstractThis paper introduces ‘hyper-and-elliptic-curve cryptography’, in which a single high-security group supports fast genus-2-hyperelliptic-curve formulas for variable-base-point single-scalar multiplication (for example, Diffie–Hellman shared-secret computation) and at the same time supports fast elliptic-curve formulas for fixed-base-point ...
Tanja Lange, Daniel J. Bernstein
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