scholarly journals EFFICIENT OPERATIONS IN LARGE FINITE FIELDS FOR ELLIPTIC CURVE CRYPTOGRAPHIC

2020 ◽  
Vol 7 (6) ◽  
pp. 141-151
Author(s):  
Yan-Haw Chen ◽  
Chien-Hsing Huang
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
High Speed ◽  
Lookup Table ◽  
Computation Cost ◽  
Encryption And Decryption ◽  
Software Implementations ◽  
Field Multiplication ◽  
Rule Method ◽  
Elliptic Curve Scalar Multiplication

An efficient method to compute the finite field multiplication for Elliptic Curve point multiplication at high speed encryption of the message is presented. The methods of the operations are based on dynamic lookup table and modified Horner rule method. The modified Horner rule method is not only to finite field operations but also to Elliptic curve scalar multiplication in the encryption and decryption. By comparison with using Russian Peasant method and in the new proposed method, one of the advantages of utilizing the proposed algorithm is that in the Elliptic Curve point addition are reduced by a factor of three in GF (2163). Therefore, using the Algorithm 1 running on Intel CPU, computation cost of the multiplication method is above 70% faster than using standard multiplication by Russian Peasant method. Ultimately, the proposed Algorithm 1 for evaluating multiplication can be made regular, simple and suitable for software implementations.  

scholarly journals FPGA Based High Speed SPA Resistant Elliptic Curve Scalar Multiplier Architecture

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Khalid Javeed ◽  
Xiaojun Wang
Keyword(s):  
Elliptic Curve ◽  
High Speed ◽  
Cryptographic Protocols ◽  
General Purpose ◽  
Good Choice ◽  
Scalar Multiplication ◽  
Computational Time ◽  
Multiplication Operation ◽  
Hardware Architectures ◽  
Elliptic Curve Scalar Multiplication

The higher computational complexity of an elliptic curve scalar point multiplication operation limits its implementation on general purpose processors. Dedicated hardware architectures are essential to reduce the computational time, which results in a substantial increase in the performance of associated cryptographic protocols. This paper presents a unified architecture to compute modular addition, subtraction, and multiplication operations over a finite field of large prime characteristicGF(p). Subsequently, dual instances of the unified architecture are utilized in the design of high speed elliptic curve scalar multiplier architecture. The proposed architecture is synthesized and implemented on several different Xilinx FPGA platforms for different field sizes. The proposed design computes a 192-bit elliptic curve scalar multiplication in 2.3 ms on Virtex-4 FPGA platform. It is 34%faster and requires 40%fewer clock cycles for elliptic curve scalar multiplication and consumes considerable fewer FPGA slices as compared to the other existing designs. The proposed design is also resistant to the timing and simple power analysis (SPA) attacks; therefore it is a good choice in the construction of fast and secure elliptic curve based cryptographic protocols.

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

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.

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