scholarly journals Speed-Oriented Architecture for Binary Field Point Multiplication on Elliptic Curves

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 32048-32060 ◽  
Author(s):  
Jiakun Li ◽  
Shun'an Zhong ◽  
Zhe Li ◽  
Shan Cao ◽  
Jingqi Zhang ◽  
...  
Keyword(s):  
Elliptic Curves ◽  
Field Point ◽  
Binary Field ◽  
Point Multiplication

Efficient 3-dimensional GLV method for faster point multiplication on some GLS elliptic curves

2010 ◽  
Vol 110 (22) ◽  
pp. 1003-1006 ◽  
Author(s):  
Zhenghua Zhou ◽  
Zhi Hu ◽  
Maozhi Xu ◽  
Wangan Song
Keyword(s):  
Elliptic Curves ◽  
3 Dimensional ◽  
Point Multiplication ◽  
Glv Method

The Construction of ElGamal over Koblitz Curve

2014 ◽  
Vol 931-932 ◽  
pp. 1441-1446 ◽  
Author(s):  
Krissanee Kamthawee ◽  
Bhichate Chiewthanakul
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Discrete Logarithm ◽  
Scalar Multiplication ◽  
Computer Hardware ◽  
Point Multiplication ◽  
Koblitz Curves ◽  
Elliptic Curve Cryptosystems ◽  
Elgamal Cryptosystem ◽  
Primary Advantage

Recently elliptic curve cryptosystems are widely accepted for security applications key generation, signature and verification. Cryptographic mechanisms based on elliptic curves depend on arithmetic involving the points of the curve. it is possible to use smaller primes, or smaller finite fields, with elliptic curves and achieve a level of security comparable to that for much larger integers. Koblitz curves, also known as anomalous binary curves, are elliptic curves defined over F2. The primary advantage of these curves is that point multiplication algorithms can be devised that do not use any point doublings. The ElGamal cryptosystem, which is based on the Discrete Logarithm problem can be implemented in any group. In this paper, we propose the ElGamal over Koblitz Curve Scheme by applying the arithmetic on Koblitz curve to the ElGamal cryptosystem. The advantage of this scheme is that point multiplication algorithms can be speeded up the scalar multiplication in the affine coodinate of the curves using Frobenius map. It has characteristic two, therefore it’s arithmetic can be designed in any computer hardware. Moreover, it has more efficient to employ the TNAF method for scalar multiplication on Koblitz curves to decrease the number of nonzero digits. It’s security relies on the inability of a forger, who does not know a private key, to compute elliptic curve discrete logarithm.

scholarly journals Performance Evaluation of Scalar Multiplication in Elliptic Curve Cryptography Implementation using Different Multipliers Over Binary Field GF (2233)

2020 ◽  
Vol 26 (9) ◽  
pp. 45-64
Author(s):  
Alaa Mohammed Abdul-Hadi ◽  
Yousraa Abdul-sahib Saif-aldeen ◽  
Firas Ghanim Tawfeeq
Keyword(s):  
Elliptic Curve Cryptography ◽  
Performance Index ◽  
High Frequency ◽  
Low Frequency ◽  
Scalar Multiplication ◽  
Maximum Frequency ◽  
Binary Field ◽  
Point Multiplication ◽  
Additional Layer ◽  
Different Types

This paper presents a point multiplication processor over the binary field GF (2233) with internal registers integrated within the point-addition architecture to enhance the Performance Index (PI) of scalar multiplication. The proposed design uses one of two types of finite field multipliers, either the Montgomery multiplier or the interleaved multiplier supported by the additional layer of internal registers. Lopez Dahab coordinates are used for the computation of point multiplication on Koblitz Curve (K-233bit). In contrast, the metric used for comparison of the implementations of the design on different types of FPGA platforms is the Performance Index. The first approach attains a performance index of approximately 0.217610202 when its realization is over Virtex-6 (6vlx130tff1156-3). It uses an interleaved multiplier with 3077 register slices, 4064 lookup tables (LUTs), 2837 flip-flops (FFs) at a maximum frequency of 221.6Mhz. This makes it more suitable for high-frequency applications. The second approach, which uses the Montgomery multiplier, produces a PI of approximately 0.2228157 when its implementation is on Virtex-4 (6vlx130tff1156-3). This approach utilizes 3543 slices, 2985 LUTs, 3691 FFs at a maximum frequency of 190.47MHz. Thus, it is found that the implementation of the second approach on Virtex-4 is more suitable for applications with a low frequency of about 86.4Mhz and a total number of slices of about 12305.

A reconfigurable processor for high speed point multiplication in elliptic curves

2005 ◽  
Vol 1 (3/4) ◽  
pp. 237 ◽  
Author(s):  
Nazar A. Saqib ◽  
Francisco Rodriguez Henriquez ◽  
Arturo Diaz Perez
Keyword(s):  
Elliptic Curves ◽  
High Speed ◽  
Reconfigurable Processor ◽  
Point Multiplication
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