Fractional two-dimensional discrete chaotic map and its applications to the information security with elliptic-curve public key cryptography

2017 ◽  
Vol 24 (20) ◽  
pp. 4797-4824 ◽  
Author(s):  
Zeyu Liu ◽  
Tiecheng Xia ◽  
Jinbo Wang
Keyword(s):  
Elliptic Curve ◽  
Color Image ◽  
Chaotic Map ◽  
Public Key Cryptography ◽  
Public Key ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Two Dimensional ◽  
Function Combination ◽  
The Difference

A novel fractional two-dimensional triangle function combination discrete chaotic map is proposed by use of the discrete fractional calculus. The chaos behaviors are then discussed when the difference order is a fractional one. The bifurcation diagrams, the largest Lyapunov exponent and the phase portraits are displayed, especially, the elliptic curve public key cryptosystem is used in color image encryption algorithm.

scholarly journals Image Encryption Technology Based on Fractional Two-Dimensional Triangle Function Combination Discrete Chaotic Map Coupled with Menezes-Vanstone Elliptic Curve Cryptosystem

2018 ◽  
Vol 2018 ◽  
pp. 1-24 ◽  
Author(s):  
Zeyu Liu ◽  
Tiecheng Xia ◽  
Jinbo Wang
Keyword(s):  
Elliptic Curve ◽  
Image Encryption ◽  
Chaotic Map ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Elliptic Curve Cryptosystem ◽  
Two Dimensional ◽  
Triangle Function ◽  
Function Combination ◽  
Secret Keys

A new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM) with the discrete fractional difference is proposed. We observe the bifurcation behaviors and draw the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits of the proposed map, respectively. On the application side, we apply the proposed discrete fractional map into image encryption with the secret keys ciphered by Menezes-Vanstone Elliptic Curve Cryptosystem (MVECC). Finally, the image encryption algorithm is analysed in four main aspects that indicate the proposed algorithm is better than others.

scholarly journals IMAGE ENCRYPTION BASED ON TWO-DIMENSIONAL FRACTIONAL QUADRIC POLYNOMIAL MAP

Fractals ◽  
2021 ◽  
pp. 2140041
Author(s):  
ZE-YU LIU ◽  
TIE-CHENG XIA ◽  
HUA-RONG FENG ◽  
CHANG-YOU MA
Keyword(s):  
Image Encryption ◽  
Color Image ◽  
Chaotic Map ◽  
Encryption Algorithm ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Two Dimensional ◽  
Polynomial Map ◽  
Dynamical Behaviors ◽  
Image Encryption Algorithm

A new fractional two-dimensional quadric polynomial discrete chaotic map (2D-QPDM) with the discrete fractional difference is proposed. Afterwards, the new dynamical behaviors are observed, so that the bifurcation diagrams, the largest Lyapunov exponent plot and the phase portraits of the proposed map are given, respectively. The new discrete fractional map is exploited into color image encryption algorithm and it is illustrated with several examples. The proposed image encryption algorithm is analyzed in six aspects which indicates that the proposed algorithm is superior to other known algorithms as a conclusion.

Public-Key Encryption

2017 ◽  
Author(s):  
Keith M. Martin
Keyword(s):  
Elliptic Curve ◽  
Public Key Cryptography ◽  
Public Key ◽  
Public Key Encryption ◽  
Hybrid Encryption ◽  
Public Key Cryptosystems ◽  
Encryption And Decryption ◽  
Encryption Schemes ◽  
Hard Problems ◽  
Set Up

In this chapter, we introduce public-key encryption. We first consider the motivation behind the concept of public-key cryptography and introduce the hard problems on which popular public-key encryption schemes are based. We then discuss two of the best-known public-key cryptosystems, RSA and ElGamal. For each of these public-key cryptosystems, we discuss how to set up key pairs and perform basic encryption and decryption. We also identify the basis for security for each of these cryptosystems. We then compare RSA, ElGamal, and elliptic-curve variants of ElGamal from the perspectives of performance and security. Finally, we look at how public-key encryption is used in practice, focusing on the popular use of hybrid encryption.

Study on the Safety Application of Public Key Cryptography in Electronic Commerce

2014 ◽  
Vol 1079-1080 ◽  
pp. 856-859
Author(s):  
Yu Zhong Zhang
Keyword(s):  
Electronic Commerce ◽  
Elliptic Curve ◽  
Communication Technology ◽  
Elliptic Curve Cryptography ◽  
Public Key Cryptography ◽  
Public Key ◽  
Electronic Transactions ◽  
Safety Application

With the progress of computer and communication technology, electronic commerce flourished. Security is a key problem in the development of electronic commerce. This paper discusses the principle of elliptic curve cryptography and its safety application in electronic transactions.

scholarly journals Scalable Normal Basis Arithmetic Unit for Elliptic Curve Cryptography

10.14311/688 ◽  
2005 ◽  
Vol 45 (2) ◽  
Author(s):  
J. Schmidt ◽  
M. Novotný
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Additional Data ◽  
Public Key Cryptography ◽  
Normal Basis ◽  
Public Key ◽  
Arithmetic Unit ◽  
Inversion Algorithm ◽  
Implementation Data ◽  
And Inversion

The design of a scalable arithmetic unit for operations over elements of GF(2m) represented in normal basis is presented. The unit is applicable in public-key cryptography. It comprises a pipelined Massey-Omura multiplier and a shifter. We equipped the multiplier with additional data paths to enable easy implementation of both multiplication and inversion in a single arithmetic unit. We discuss optimum design of the shifter with respect to the inversion algorithm and multiplier performance. The functionality of the multiplier/inverter has been tested by simulation and implemented in Xilinx Virtex FPGA.We present implementation data for various digit widths which exhibit a time minimum for digit width D = 15.

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