scholarly journals Speeding Up the Fixed-Base Comb Method for Faster Scalar Multiplication on Koblitz Curves

2013 ◽  
pp. 168-179 ◽  
Author(s):  
Christian Hanser ◽  
Christian Wagner
Keyword(s):  
Scalar Multiplication ◽  
Koblitz Curves ◽  
Fixed Base ◽  
Comb Method

Improved Fixed-Base Comb Method for Fast Scalar Multiplication

2012 ◽  
pp. 342-359 ◽  
Author(s):  
Nashwa A. F. Mohamed ◽  
Mohsin H. A. Hashim ◽  
Michael Hutter
Keyword(s):  
Scalar Multiplication ◽  
Fixed Base ◽  
Comb 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 Efficient Fixed-base exponentiation and scalar multiplication based on a multiplicative splitting exponent recoding

2018 ◽  
Vol 9 (2) ◽  
pp. 115-136
Author(s):  
Jean-Marc Robert ◽  
Christophe Negre ◽  
Thomas Plantard
Keyword(s):  
Scalar Multiplication ◽  
Fixed Base

Short-Memory Scalar Multiplication for Koblitz Curves

2008 ◽  
Vol 57 (4) ◽  
pp. 481-489 ◽  
Author(s):  
C. Vuillaume ◽  
K. Okeya ◽  
T. Takagi
Keyword(s):  
Scalar Multiplication ◽  
Koblitz Curves ◽  
Short Memory
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