scholarly journals Fast Algorithms for Elliptic Curve Cryptosystems over Binary Finite Field

1999 ◽  
pp. 75-85 ◽  
Author(s):  
Yongfei Han ◽  
Peng-Chor Leong ◽  
Peng-Chong Tan ◽  
Jiang Zhang
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Fast Algorithms ◽  
Elliptic Curve Cryptosystems

scholarly journals EMBEDDING FINITE FIELDS INTO ELLIPTIC CURVES

2019 ◽  
pp. 889
Author(s):  
Amirmehdi Yazdani Kashani ◽  
Hassan Daghigh
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Finite Fields ◽  
Hyperelliptic Curves ◽  
Rational Points ◽  
Elliptic Curve Cryptosystems ◽  
General Elliptic ◽  
Genus 2

Many elliptic curve cryptosystems require an encoding function from a finite field Fq into Fq-rational points of an elliptic curve. We propose a uniform encoding to general elliptic curves over Fq. We also discuss about an injective case of SWU encoing for hyperelliptic curves of genus 2. Moreover we discuss about an injective encoding for elliptic curves with a point of order two over a finite field and present a description for these elliptic curves.

Power Side-Channel Analysis of RNS GLV ECC Using Machine and Deep Learning Algorithms

2021 ◽  
Vol 21 (3) ◽  
pp. 1-20
Author(s):  
Mohamad Ali Mehrabi ◽  
Naila Mukhtar ◽  
Alireza Jolfaei
Keyword(s):  
Deep Learning ◽  
Elliptic Curve ◽  
Smart Cities ◽  
Information Leakage ◽  
Side Channel ◽  
Side Channel Attacks ◽  
Public Key Cryptosystems ◽  
Elliptic Curve Cryptosystems ◽  
Hardware Implementations ◽  
Substantial Progress

Many Internet of Things applications in smart cities use elliptic-curve cryptosystems due to their efficiency compared to other well-known public-key cryptosystems such as RSA. One of the important components of an elliptic-curve-based cryptosystem is the elliptic-curve point multiplication which has been shown to be vulnerable to various types of side-channel attacks. Recently, substantial progress has been made in applying deep learning to side-channel attacks. Conceptually, the idea is to monitor a core while it is running encryption for information leakage of a certain kind, for example, power consumption. The knowledge of the underlying encryption algorithm can be used to train a model to recognise the key used for encryption. The model is then applied to traces gathered from the crypto core in order to recover the encryption key. In this article, we propose an RNS GLV elliptic curve cryptography core which is immune to machine learning and deep learning based side-channel attacks. The experimental analysis confirms the proposed crypto core does not leak any information about the private key and therefore it is suitable for hardware implementations.

scholarly journals Classification of Elliptic Cubic Curves Over The Finite Field of Order Nineteen

2016 ◽  
Vol 13 (4) ◽  
pp. 846-852
Author(s):  
Baghdad Science Journal
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Maximum Size ◽  
Cubic Curves ◽  
Projective Equivalence

Plane cubics curves may be classified up to isomorphism or projective equivalence. In this paper, the inequivalent elliptic cubic curves which are non-singular plane cubic curves have been classified projectively over the finite field of order nineteen, and determined if they are complete or incomplete as arcs of degree three. Also, the maximum size of a complete elliptic curve that can be constructed from each incomplete elliptic curve are given.

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