Elliptic curve cryptosystem — The answer to strong, fast public-key cryptography for securing constrained environments

1997 ◽  
Vol 2 (2) ◽  
pp. 78-87 ◽  
Author(s):  
Scott A Vanstone
Keyword(s):  
Elliptic Curve ◽  
Public Key Cryptography ◽  
Public Key ◽  
Elliptic Curve Cryptosystem ◽  
Constrained Environments

Public Key Cryptosystem Research Based on Discrete Group

2014 ◽  
Vol 687-691 ◽  
pp. 2984-2988
Author(s):  
Lan Bai ◽  
Jian Zhang ◽  
Li Zhu
Keyword(s):  
Information System ◽  
Elliptic Curve ◽  
Rapid Development ◽  
Discrete Logarithm ◽  
Modern Society ◽  
Public Key Cryptography ◽  
Public Key ◽  
Elliptic Curve Cryptosystem ◽  
Digital Form ◽  
Defensive Measures

In modern society with Internet rapid development, information system takes digital form of 0 and 1, this information system and public channel are very fragile in the case of without defensive measures, and they are easily attacked and destructed by hackers and intruders. This article is mainly based on the knowledge of discrete logarithm, studies public key cipher algorithm, especially elliptic curve cryptosystem. First this paper introduces the basic concepts and knowledge of cryptography, and discusses the relation between discrete logarithm and public key cryptography algorithms. Finally in detail it discusses elliptic curve cryptosystem, and presents the realization and running effect of encryption system.

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.

A General Threshold Signature Scheme Based on Elliptic Curve

2013 ◽  
Vol 756-759 ◽  
pp. 1339-1343
Author(s):  
Yu Lian Shang ◽  
Xiu Juan Wang ◽  
Yu Juan Li ◽  
Yu Fei Zhang
Keyword(s):  
Elliptic Curve ◽  
Communication System ◽  
Public Key ◽  
Threshold Scheme ◽  
Elliptic Curve Cryptosystem ◽  
Signature Scheme ◽  
Threshold Signature ◽  
Private Key ◽  
Generating Polynomial ◽  
Directional Transmission

Based on Elliptic Curve cryptosystem, a threshold signature scheme characterized by (k,l) joint verification for (t,n) signature is put forward. After being signed by a signer company employing (t, n) threshold signature scheme, the informationmis transmitted to a particular verifier company, and then the signature is verified through the cooperation ofkones from the verifier company withlmembers, so as to realize a directional transmission between different companies. Finally, the application examples of the company encryption communication system, the generating polynomial of company private key and public key were given. The security of this scheme is based on Shamir threshold scheme and Elliptic Curve system, and due to the advantages of Elliptic Curve, the scheme enjoys wider application in practice.

Design of Digital Signature Scheme Based on Elliptic Curve Cryptosystem

2014 ◽  
Vol 685 ◽  
pp. 579-582
Author(s):  
Shi Guo Jin ◽  
Guang Jiang Wang
Keyword(s):  
Elliptic Curve ◽  
Digital Signature ◽  
Public Key Cryptography ◽  
Elliptic Curve Cryptosystem ◽  
Generation Process ◽  
Signature Scheme ◽  
Technical Performance ◽  
Elliptic Curve Cryptosystems ◽  
Process System ◽  
Digital Signature Scheme

Digital signature is electronically password technique for electronic document signature. Elliptic curve cryptography is a method of public key cryptography based on elliptic curve mathematical. Digital signature scheme consists of three processes: initialization process, the signature generation process and signature verification process system. This paper analyzes the elliptic curve cryptosystems mathematical principle and technical performance. The paper proposes design of digital signature scheme based on elliptic curve cryptosystem.

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.

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.

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