An Algorithm Based Fault Tolerant Scheme for Elliptic Curve Public-Key Cryptography

2009 ◽  
Author(s):  
Chang N. Zhang ◽  
Xiao Wei Liu
Keyword(s):  
Elliptic Curve ◽  
Fault Tolerant ◽  
Public Key Cryptography ◽  
Public Key

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.

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.

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.

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 Twisted Edwards Elliptic Curves for Zero-Knowledge Circuits

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3022
Author(s):  
Marta Bellés-Muñoz ◽  
Barry Whitehat ◽  
Jordi Baylina ◽  
Vanesa Daza ◽  
Jose Luis Muñoz-Tapia
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Elliptic Curve Cryptography ◽  
Public Key Cryptography ◽  
Deterministic Algorithm ◽  
Public Key ◽  
Security Attacks ◽  
Zero Knowledge ◽  
Prime Field ◽  
Encryption Schemes

Circuit-based zero-knowledge proofs have arose as a solution to the implementation of privacy in blockchain applications, and to current scalability problems that blockchains suffer from. The most efficient circuit-based zero-knowledge proofs use a pairing-friendly elliptic curve to generate and validate proofs. In particular, the circuits are built connecting wires that carry elements from a large prime field, whose order is determined by the number of elements of the pairing-friendly elliptic curve. In this context, it is important to generate an inner curve using this field, because it allows to create circuits that can verify public-key cryptography primitives, such as digital signatures and encryption schemes. To this purpose, in this article, we present a deterministic algorithm for generating twisted Edwards elliptic curves defined over a given prime field. We also provide an algorithm for checking the resilience of this type of curve against most common security attacks. Additionally, we use our algorithms to generate Baby Jubjub, a curve that can be used to implement elliptic-curve cryptography in circuits that can be validated in the Ethereum blockchain.

scholarly journals SPDH - A Secure Plain Diffie-Hellman Algorithm

2012 ◽  
Author(s):  
Henrik Tange ◽  
Birger Andersen
Keyword(s):  
Elliptic Curve ◽  
Secure Communication ◽  
Public Key Cryptography ◽  
Public Key ◽  
Wireless System ◽  
Eavesdropping Attack ◽  
Replay Attacks ◽  
Diffie Hellman ◽  
Man In The Middle ◽  
Shared Secret

Secure communication in a wireless system or end-to-end communication requires setup of a shared secret. This shared secret can be obtained by the use of a public key cryptography system. The most widely used algorithm to obtain a shared secret is the Diffie–Hellman algorithm. However, this algorithm suffers from the Man-in-the-Middle problem; an attacker can perform an eavesdropping attack listen to the communication between participants A and B. Other algorithms as for instance ECMQV (Elliptic Curve Menezes Qo Vanstone) can handle this problem but is far more complex and slower because the algorithm is a three-pass algorithm whereas the Diffie–Hellman algorithm is a simple two-pass algorithm. Using standard cryptographic modules as AES and HMAC the purposed algorithm, Secure Plain Diffie–Hellman Algorithm, solves the Man-in-the-Middle problem and maintain its advantage from the plain Diffie–Hellman algorithm. Also the possibilities of replay attacks are solved by use of a timestamp.

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