Efficient Arithmetic in Finite Field Extensions with Application in Elliptic Curve Cryptography

2001 ◽  
Vol 14 (3) ◽  
pp. 153-176 ◽  
Author(s):  
Daniel V. Bailey ◽  
Christof Paar
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Field Extensions

scholarly journals Implementation of Double Fold Text Encryption Based on Elliptic Curve Cryptography (ECC) with Digital Signature

2020 ◽  
Vol 8 (5) ◽  
pp. 3840-3846
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Digital Signature ◽  
Elliptic Curve Cryptography ◽  
Public Key ◽  
The Internet ◽  
Public Key Cryptosystems ◽  
The World ◽  
Recent Attention ◽  
Cryptographic Scheme

As the internet provides access to millions of communications in every second around the world, security implications are tremendously increasing. Transfer of important files like banking transactions, tenders, and e commerce require special security and authenticated mechanism in its journey from the sender to the receiver. Recent attention of cryptography is mainly focused on use of elliptic curves in public key cryptosystems. The present paper explains an innovative public key cryptographic scheme for protecting sensitive of critical information using elliptic curve over finite field. This mechanism besides providing the robustness of the cipher contributes the authentication of the message with digital signature.

scholarly journals Generating pairing-friendly elliptic curve parameters using sparse families

2018 ◽  
Vol 12 (2) ◽  
pp. 83-99
Author(s):  
Georgios Fotiadis ◽  
Elisavet Konstantinou
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Number Field ◽  
Recent Progress ◽  
Discrete Logarithm ◽  
Numerical Examples ◽  
Field Extensions ◽  
Number Field Sieve ◽  
First Time

Abstract The majority of methods for constructing pairing-friendly elliptic curves are based on representing the curve parameters as polynomial families. There are three such types, namely complete, complete with variable discriminant and sparse families. In this paper, we present a method for constructing sparse families and produce examples of this type that have not previously appeared in the literature, for various embedding degrees. We provide numerical examples obtained by these sparse families, considering for the first time the effect of the recent progress on the tower number field sieve (TNFS) method for solving the discrete logarithm problem (DLP) in finite field extensions of composite degree.

Sign in / Sign up

Export Citation Format

Share Document