Low latency flexible FPGA implementation of point multiplication on elliptic curves over GF(p)

2016 ◽  
Vol 45 (2) ◽  
pp. 214-228 ◽  
Author(s):  
Khalid Javeed ◽  
Xiaojun Wang
Keyword(s):  
Elliptic Curves ◽  
Fpga Implementation ◽  
Low Latency ◽  
Point Multiplication

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.

A Low-Latency and Low-Complexity Point-Multiplication in ECC

2018 ◽  
Vol 65 (9) ◽  
pp. 2869-2877 ◽  
Author(s):  
Raziyeh Salarifard ◽  
Siavash Bayat-Sarmadi ◽  
Hatameh Mosanaei-Boorani
Keyword(s):  
Low Complexity ◽  
Low Latency ◽  
Point Multiplication
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