Elliptic Curve and Integer Factorization

2021 ◽  
pp. 316-330
Author(s):  
Zhizhong Pan ◽  
Xiao Li
Keyword(s):  
Elliptic Curve ◽  
Integer Factorization

scholarly journals Computing canonical heights on elliptic curves in quasi-linear time

2016 ◽  
Vol 19 (A) ◽  
pp. 391-405 ◽  
Author(s):  
J. Steffen Müller ◽  
Michael Stoll
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Linear Time ◽  
Integer Factorization ◽  
Canonical Height ◽  
The Difference

We introduce an algorithm that can be used to compute the canonical height of a point on an elliptic curve over the rationals in quasi-linear time. As in most previous algorithms, we decompose the difference between the canonical and the naive height into an archimedean and a non-archimedean term. Our main contribution is an algorithm for the computation of the non-archimedean term that requires no integer factorization and runs in quasi-linear time.

scholarly journals Analysis Review on Public Key Cryptography Algorithms

2018 ◽  
Vol 12 (2) ◽  
pp. 447 ◽  
Author(s):  
Jasmin Ilyani Ahmad ◽  
Roshidi Din ◽  
Mazida Ahmad
Keyword(s):  
Elliptic Curve ◽  
Digital Signature ◽  
Coding Theory ◽  
Discrete Logarithm ◽  
Public Key Cryptography ◽  
Hybrid Algorithms ◽  
Public Key ◽  
Integer Factorization

This paper presents several Public Key Cryptography (PKC) algorithms based on the perspective of researchers’ effort since it was invented in the last four decades. The categories of the algorithms had been analyzed which are Discrete Logarithm, Integer Factorization, Coding Theory, Elliptic Curve, Lattices, Digital Signature and Hybrid algorithms. This paper reviewed the previous schemes in different PKC algorithms. The aim of this paper is to present the comparative trends of PKC algorithms based on number of research for each algorithm in last four decades, the roadmap of PKC algorithms since they were invented and the most chosen algorithms among previous researchers. Finally, the strength and drawback of proposed schemes and algorithms also presented in this paper.

Study of Safe Elliptic Curve Cryptography over Gaussian Integer

2020 ◽  
Vol E103.A (12) ◽  
pp. 1624-1628
Author(s):  
Kazuki NAGANUMA ◽  
Takashi SUZUKI ◽  
Hiroyuki TSUJI ◽  
Tomoaki KIMURA
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Gaussian Integer

Enhanced Security Authentication of WiMAX using EC3A

2017 ◽  
Vol 7 (8) ◽  
pp. 219
Author(s):  
Mohd Javed ◽  
Khaleel Ahmad ◽  
Ahmad Talha Siddiqui
Keyword(s):  
Cellular Automata ◽  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Information Rate ◽  
Security Authentication ◽  
Encryption And Decryption ◽  
High Information

WiMAX is the innovation and upgradation of 802.16 benchmarks given by IEEE. It has numerous remarkable qualities, for example, high information rate, the nature of the service, versatility, security and portability putting it heads and shoulder over the current advancements like broadband link, DSL and remote systems. Though like its competitors the concern for security remains mandatory. Since the remote medium is accessible to call, the assailants can undoubtedly get into the system, making the powerless against the client. Many modern confirmations and encryption methods have been installed into WiMAX; however, regardless it opens with up different dangers. In this paper, we proposed Elliptic curve Cryptography based on Cellular Automata (EC3A) for encryption and decryption the message for improving the WiMAX security

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