A New Double Point Multiplication Algorithm and Its Application to Binary Elliptic Curves with Endomorphisms

2014 ◽  
Vol 63 (10) ◽  
pp. 2614-2619 ◽  
Author(s):  
Reza Azarderakhsh ◽  
Koray Karabina
Keyword(s):  
Elliptic Curves ◽  
Double Point ◽  
Point Multiplication ◽  
Multiplication Algorithm

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 Floating Point Multiplication Based on Schonhage Strassen Algorithm

2018 ◽  
Vol 7 (2.20) ◽  
pp. 14
Author(s):  
B Srikanth ◽  
M Siva Kumar ◽  
K Hari Kishore
Keyword(s):  
Fixed Point ◽  
Real Time ◽  
Floating Point ◽  
Single Precision ◽  
Point Multiplication ◽  
Multiplication Algorithm ◽  
Integer Multiplication

In this paper, the single precision float point multiplication is performed using the Schonhage Strassen Algorithm. There are several types of floating point multiplications like Karatsubha and Toom cook. The Schonhage Strassen algorithm is conventionally a fixed point integer multiplication algorithm. The main advantage of the Schonhage Strassen multiplication is that, the multiplication of integer values greater than 5 digits ranging from 2215 to 2217 bit values proves to be efficient. The validation of the proposed floating point multiplication is done using FPGA real time implementation. The analysis of parameters like area and power are evaluated.  

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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