Two New Electronic Cash Schemes Based on Elliptic Curve

2013 ◽  
Vol 694-697 ◽  
pp. 2388-2393 ◽  
Author(s):  
Mei Na Zhang ◽  
Chun Bao Fu ◽  
Wei Fu
Keyword(s):  
Elliptic Curve ◽  
Discrete Logarithm ◽  
Blind Signature ◽  
Discrete Logarithm Problem ◽  
Effective Solution ◽  
Electronic Cash ◽  
Private Key ◽  
Cryptographic Algorithm ◽  
Payment Protocol ◽  
High Efficient

Two secure, high-efficient and feasible e-cash schemes are proposed in this thesis based on elliptic curve by using blind signature system, the schemes are completed by three protocols, namely, withdrawal protocol, payment protocol and deposit protocol. The two schemes make advantage of blind parameter, namely, after cash is received by Bank, cash is also hardly connected with the signature at some times. They are simple and easily realized. The elliptic curve cryptographic algorithm is adopted in the scheme, the length of the private key is short, and its efficiency and strength is significantly higher than e-cash scheme based on RSA signature proposed by D.Chaum. There is no effective solution to the elliptic curve discrete logarithm problem (ECDLP), therefore, the schemes are safe.

scholarly journals Proposed Developments of Blind Signature Scheme based on The Elliptic Curve Discrete Logarithm Problem

2013 ◽  
Vol 2 (1) ◽  
pp. 151-160
Author(s):  
E.H. El Kinani ◽  
Fatima Amounas
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Discrete Logarithm ◽  
Mathematical Structure ◽  
Blind Signature ◽  
Discrete Logarithm Problem ◽  
Signature Scheme

In recent years, Elliptic Curve Cryptography (ECC) has attracted the attention of researchers due to its robust mathematical structure and highest security compared to other existing algorithm like RSA. Our main objective in this work was to provide a novel blind signature scheme based on ECC. The security of the proposed method results from the infeasibility to solve the discrete logarithm over an elliptic curve. In this paper we introduce a proposed to development the blind signature scheme with more complexity as compared to the existing schemes. Keyword: Cryptography, Blind Signature, Elliptic Curve, Blindness, Untraceability.DOI: 10.18495/comengapp.21.151160

scholarly journals Elliptic Curve Pseudorandom Bit Generator with Maximum Period Sequences

2021 ◽  
pp. 494-505
Author(s):  
Alexandr A. Kuznetsov ◽  
Yurii Gorbenko ◽  
Anastasiia Kiian Anastasiia Kiian ◽  
Yuliia V. Ulianovska ◽  
Tetiana Kuznetsova
Keyword(s):  
Elliptic Curve ◽  
Block Diagram ◽  
Discrete Logarithm ◽  
Random Number Generator ◽  
Point Group ◽  
Discrete Logarithm Problem ◽  
Information Protection ◽  
Random Sequences ◽  
Private Key ◽  
Maximum Period

Pseudo-random number generator is an important mechanism for cryptographic information protection. It can be used independently to generate special data or as the most important element of security of other mechanisms for cryptographic information protection. The application of transformations in a group of points of elliptic and hypereliptic curves is an important direction for the designing of cryptographically stable pseudo-random sequences generators. This approach allows us to build  the resistant cryptographic algorithms in which the problem of finding a private key is associated with solving the discrete logarithm problem. This paper proposes a method for generating pseudo-random sequences of the maximum period using transformations on the elliptic curves. The maximum sequence period is provided by the use of recurrent transformations with the sequential formation of the elements of the point group of the elliptic curve. In this case, the problem of finding a private key is reduced to solving a theoretically complex discrete logarithm problem. The article also describes the block diagram of the device for generating pseudo-random sequences and the scheme for generating internal states of the generator.

scholarly journals On the first fall degree of summation polynomials

2019 ◽  
Vol 13 (3-4) ◽  
pp. 229-237
Author(s):  
Stavros Kousidis ◽  
Andreas Wiemers
Keyword(s):  
Elliptic Curve ◽  
Gröbner Basis ◽  
Discrete Logarithm ◽  
Polynomial Systems ◽  
Discrete Logarithm Problem ◽  
Grobner Basis ◽  
Weil Descent ◽  
Degree Bound

Abstract We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.

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