A formula for point addition in elliptic curves using affine representation and its implementation in FPGA is presented. The use of this new formula in hardware implementations of scalar multiplications for ell
In this paper we propose a new approach to point scalar multiplication on elliptic curves defined over fields of characteristic greater than 3. It is based on new point addition formulae that suit very well to exponentiation algorithms based on Euclidean addition chains. However finding small chains...
EC Cryptography Tutorials - Herong's Tutorial Examples∟Geometric Introduction to Elliptic Curves∟Addition Operation on an Elliptic Curve This section describes the addition operation on an elliptic curve geometrically. The addition of points P and Q on an elliptic curve is a point R on the curve...
This section describes how to perform the addition operation of a point P to the same point P on an elliptic curve. In this case, we will draw a straight line that passes P and tangent to the curve to find -R.
An efficient computation of scalar multiplication in elliptic curve cryptography can be achieved by reducing the original problem into a chain of additions and doublings. Finding the shortest addition chain is an NP-problem. To produce the nearest possible shortest chain, various methods were ...
Today various cryptographic algorithms like RSA, Elliptic Curve Cryptography (ECC), etc., can be used to protect the information in mobile devices. But, they have some limitations viz., energy, battery power, processing speed, operating systems, screen size, resolution, memory size, etc. ...
As is well known, the unified point addition formula is useful for resisting side channel attacks in elliptic curve cryptography. Furthermore, if the unified formula is complete, which means it is valid for any two points, then there are no exceptional cases to be described particularly. This ...
public key cryptographyrational functions/ elliptic curve cryptosystemdiscrete logarithmalgebraic curvespublic key cryptosystemelliptic curveshyperelliptic curvessuperelliptic curvesJacobian group/ B6120D Cryptography B0290F Interpolation and function approximation (numerical analysis) B0210 Algebra C1260C Cryptography...
Registers,Elliptic curves,Clocks,Elliptic curve cryptography,CoprocessorsIn this paper we report on the results of selected horizontal SCA attacks against two open-source designs that implement hardware accelerators for elliptic curve cryptography. Both designs use the complete addition formula to make the...
The successful application to elliptic curve cryptography of side-channel attacks, in which information about the secret key can be recovered from the observation of side channels like power consumptidoi:10.1007/11894063_28Douglas StebilaUniversity of WaterlooNicolas Thériault...