scholarly journals Elliptic curve point counting over finite fields with Gaussian normal basis

2003 ◽  
Vol 79 (1) ◽  
pp. 5-8
Author(s):  
Je Hong Park ◽  
Jung Youl Park ◽  
Sang Geun Hahn
Keyword(s):  
Elliptic Curve ◽  
Finite Fields ◽  
Normal Basis ◽  
Point Counting ◽  
Gaussian Normal Basis

Fast Elliptic Curve Point Counting Using Gaussian Normal Basis

2002 ◽  
pp. 292-307 ◽  
Author(s):  
Hae Young Kim ◽  
Jung Youl Park ◽  
Jung Hee Cheon ◽  
Je Hong Park ◽  
Jae Heon Kim ◽  
...  
Keyword(s):  
Elliptic Curve ◽  
Normal Basis ◽  
Point Counting ◽  
Gaussian Normal Basis

scholarly journals Computing cardinalities of -curve reductions over finite fields

2016 ◽  
Vol 19 (A) ◽  
pp. 115-129
Author(s):  
François Morain ◽  
Charlotte Scribot ◽  
Benjamin Smith
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Finite Fields ◽  
Lower Degree ◽  
Point Counting ◽  
Low Degree ◽  
Asymptotic Complexity ◽  
Specialized Point ◽  
Counting Algorithm

We present a specialized point-counting algorithm for a class of elliptic curves over $\mathbb{F}_{p^{2}}$ that includes reductions of quadratic $\mathbb{Q}$-curves modulo inert primes and, more generally, any elliptic curve over $\mathbb{F}_{p^{2}}$ with a low-degree isogeny to its Galois conjugate curve. These curves have interesting cryptographic applications. Our algorithm is a variant of the Schoof–Elkies–Atkin (SEA) algorithm, but with a new, lower-degree endomorphism in place of Frobenius. While it has the same asymptotic asymptotic complexity as SEA, our algorithm is much faster in practice.

Gaussian normal basis multiplier over GF(2 m ) using hybrid subquadratic‐and‐quadratic TMVP approach for elliptic curve cryptography

2017 ◽  
Vol 11 (6) ◽  
pp. 579-588 ◽  
Author(s):  
Che Wun Chiou ◽  
Yuh‐Sien Sun ◽  
Cheng‐Min Lee ◽  
Jim‐Min Lin ◽  
Tai‐Pao Chuang ◽  
...  
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Normal Basis ◽  
Gaussian Normal Basis

scholarly journals Design of elliptic curve cryptoprocessors over GF(2^163) using the Gaussian normal basis

2014 ◽  
Vol 34 (2) ◽  
pp. 55-65 ◽  
Author(s):  
Paulo Cesar Realpe ◽  
Vladimir Trujillo-Olaya ◽  
Jaime Velasco-Medina
Keyword(s):  
Elliptic Curve ◽  
Normal Basis ◽  
Gaussian Normal Basis

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.

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