Hardware realization of fast elliptic curve point multiplication using balanced ternary representation and pre-computation overGF(p)

2016 ◽  
Vol 19 (1) ◽  
pp. 141-161
Author(s):  
N. Shylashree ◽  
V. Sridhar
Keyword(s):  
Elliptic Curve ◽  
Point Multiplication ◽  
Hardware Realization

Profiled Attacks Against the Elliptic Curve Scalar Point Multiplication Using Neural Networks

2021 ◽  
pp. 238-257
Author(s):  
Alessandro Barenghi ◽  
Diego Carrera ◽  
Silvia Mella ◽  
Andrea Pace ◽  
Gerardo Pelosi ◽  
...  
Keyword(s):  
Neural Networks ◽  
Elliptic Curve ◽  
Point Multiplication ◽  
Scalar Point Multiplication

scholarly journals A Compact Coprocessor for the Elliptic Curve Point Multiplication over Gaussian Integers

Electronics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 2050
Author(s):  
Malek Safieh ◽  
Johann-Philipp Thiers ◽  
Jürgen Freudenberger
Keyword(s):  
Elliptic Curve ◽  
Modular Arithmetic ◽  
Complex Numbers ◽  
Gaussian Integer ◽  
Gaussian Integers ◽  
Point Multiplication ◽  
Hardware Implementations ◽  
Secure Hardware ◽  
Prime Fields ◽  
High Flexibility

This work presents a new concept to implement the elliptic curve point multiplication (PM). This computation is based on a new modular arithmetic over Gaussian integer fields. Gaussian integers are a subset of the complex numbers such that the real and imaginary parts are integers. Since Gaussian integer fields are isomorphic to prime fields, this arithmetic is suitable for many elliptic curves. Representing the key by a Gaussian integer expansion is beneficial to reduce the computational complexity and the memory requirements of secure hardware implementations, which are robust against attacks. Furthermore, an area-efficient coprocessor design is proposed with an arithmetic unit that enables Montgomery modular arithmetic over Gaussian integers. The proposed architecture and the new arithmetic provide high flexibility, i.e., binary and non-binary key expansions as well as protected and unprotected PM calculations are supported. The proposed coprocessor is a competitive solution for a compact ECC processor suitable for applications in small embedded systems.

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