Authentication Based Elliptic Curves Digital Signature for ZigBee Networks

2017 ◽  
pp. 63-73 ◽  
Author(s):  
Ouassila Hoceini ◽  
Hossam Afifi ◽  
Rachida Aoudjit
Keyword(s):  
Elliptic Curves ◽  
Digital Signature ◽  
Zigbee Networks

PERSPECTIVES OF ELLIPTICAL CRYPTOGRAPHY TO ENSURE THE INTEGRITY AND CONFIDENTIALITY OF INFORMATION

2019 ◽  
Author(s):  
Anna ILYENKO ◽  
Sergii ILYENKO ◽  
Yana MASUR
Keyword(s):  
Information Systems ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Finite Fields ◽  
Computational Efficiency ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Algebraic Groups ◽  
Schnorr Signature ◽  
Stability Of Algorithms

In this article, the main problems underlying the current asymmetric crypto algorithms for the formation and verification of electronic-digital signature are considered: problems of factorization of large integers and problems of discrete logarithm. It is noted that for the second problem, it is possible to use algebraic groups of points other than finite fields. The group of points of the elliptical curve, which satisfies all set requirements, looked attractive on this side. Aspects of the application of elliptic curves in cryptography and the possibilities offered by these algebraic groups in terms of computational efficiency and crypto-stability of algorithms were also considered. Information systems using elliptic curves, the keys have a shorter length than the algorithms above the finite fields. Theoretical directions of improvement of procedure of formation and verification of electronic-digital signature with the possibility of ensuring the integrity and confidentiality of information were considered. The proposed method is based on the Schnorr signature algorithm, which allows data to be recovered directly from the signature itself, similarly to RSA-like signature systems, and the amount of recoverable information is variable depending on the information message. As a result, the length of the signature itself, which is equal to the sum of the length of the end field over which the elliptic curve is determined, and the artificial excess redundancy provided to the hidden message was achieved.

scholarly journals DIGITAL SIGNATURE PROTOCOLS WITH FAST VERIFYING PROCEDURE

2014 ◽  
pp. 100-107
Author(s):  
Anna Nelasa ◽  
Victor Dolgov ◽  
Anatolij Pogorily
Keyword(s):  
Elliptic Curves ◽  
Digital Signature ◽  
Corporate Network ◽  
The Individual

In this paper the modified algorithms of the individual and collective digital signature on elliptic curves with fast verification for a corporate network are offered.

scholarly journals Parallel implementation of algorithm for creating and verifying digital signature based on elliptic curves

2021 ◽  
Vol 1069 (1) ◽  
pp. 012027
Author(s):  
P T Burtseva ◽  
L I Zelenina ◽  
L E Khaymina ◽  
E S Khaymin ◽  
I M Zashikhina
Keyword(s):  
Elliptic Curves ◽  
Digital Signature ◽  
Parallel Implementation

Cryptographic Primitives

2020 ◽  
pp. 57-134
Author(s):  
Andreas Bolfing
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Public Key ◽  
Public Key Encryption ◽  
Cryptographic Primitives ◽  
Digital Signature Algorithm ◽  
Digital Signature Scheme ◽  
Current Standards

This chapter provides a very detailed introduction to cryptography. It first explains the cryptographic basics and introduces the concept of public-key encryption which is based on one-way and trapdoor functions, considering the three major public-key encryption families like integer factorization, discrete logarithm and elliptic curve schemes. This is followed by an introduction to hash functions which are applied to construct Merkle trees and digital signature schemes. As modern cryptoschemes are commonly based on elliptic curves, the chapter then introduces elliptic curve cryptography which is based on the Elliptic Curve Discrete Logarithm Problem (ECDLP). It considers the hardness of the ECDLP and the possible attacks against it, showing how to find suitable domain parameters to construct cryptographically strong elliptic curves. This is followed by the discussion of elliptic curve domain parameters which are recommended by current standards. Finally, it introduces the Elliptic Curve Digital Signature Algorithm (ECDSA), the elliptic curve digital signature scheme.

scholarly journals Delegating a Product of Group Exponentiations with Application to Signature Schemes (Submission to Special NutMiC 2019 Issue of JMC)

2020 ◽  
Vol 14 (1) ◽  
pp. 438-459
Author(s):  
Giovanni Di Crescenzo ◽  
Matluba Khodjaeva ◽  
Delaram Kahrobaei ◽  
Vladimir Shpilrain
Keyword(s):  
Elliptic Curves ◽  
Digital Signature ◽  
Cryptographic Protocols ◽  
Public Key ◽  
Small Probability ◽  
Signature Schemes ◽  
Cyclic Groups ◽  
Public Key Cryptosystems ◽  
Fixed Base

AbstractMany public-key cryptosystems and, more generally, cryptographic protocols, use group exponentiations as important primitive operations. To expand the applicability of these solutions to computationally weaker devices, it has been advocated that a computationally weaker client (i.e., capable of performing a relatively small number of modular multiplications) delegates such primitive operations to a computationally stronger server. Important requirements for such delegation protocols include privacy of the client’s input exponent and security of the client’s output, in the sense of detecting, except for very small probability, any malicious server’s attempt to convince the client of an incorrect exponentiation result. Only recently, efficient protocols for the delegation of a fixed-based exponentiation, over cyclic and RSA-type groups with certain properties, have been presented and proved to satisfy both requirements.In this paper we show that a product of many fixed-base exponentiations, over a cyclic groups with certain properties, can be privately and securely delegated by keeping the client’s online number of modular multiplications only slightly larger than in the delegation of a single exponentiation. We use this result to show the first delegations of entire cryptographic schemes: the well-known digital signature schemes by El-Gamal, Schnorr and Okamoto, over the q-order subgroup in ℤp, for p, q primes, as well as their variants based on elliptic curves. Previous efficient delegation results were limited to the delegation of single algorithms within cryptographic schemes.

Directed Digital Signature on Isogenies of Elliptic Curves

2018 ◽  
Vol 52 (8) ◽  
pp. 1059-1064
Author(s):  
E. B. Aleksandrova ◽  
A. A. Shtyrkina
Keyword(s):  
Elliptic Curves ◽  
Digital Signature
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