scholarly journals On Multi-Scalar Multiplication Algorithms for Register-Constrained Environments

Electronics ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 605
Author(s):  
Da-Zhi Sun ◽  
Ji-Dong Zhong ◽  
Hong-De Zhang ◽  
Xiang-Yu Guo
Keyword(s):  
Electronic Devices ◽  
Additive Group ◽  
Fixed Number ◽  
Scalar Multiplication ◽  
Computation Cost ◽  
Public Key Cryptosystems ◽  
Adaptive Window ◽  
Computation Efficiency ◽  
Window Method ◽  
Constrained Environments

A basic but expensive operation in the implementations of several famous public-key cryptosystems is the computation of the multi-scalar multiplication in a certain finite additive group defined by an elliptic curve. We propose an adaptive window method for the multi-scalar multiplication, which aims to balance the computation cost and the memory cost under register-constrained environments. That is, our method can maximize the computation efficiency of multi-scalar multiplication according to any small, fixed number of registers provided by electronic devices. We further demonstrate that our method is efficient when five registers are available. Our method is further studied in detail in the case where it is combined with the non-adjacent form (NAF) representation and the joint sparse form (JSF) representation. One efficiency result is that our method with the proposed improved NAF n-bit representation on average requires 209n/432 point additions. To the best of our knowledge, this efficiency result is optimal compared with those of similar methods using five registers. Unlike the previous window methods, which store all possible values in the window, our method stores those with comparatively high probabilities to reduce the number of required registers.

scholarly journals Estimation of Various Scalar Multiplication Algorithms in ECC

2019 ◽  
Vol 8 (6S4) ◽  
pp. 183-186
Keyword(s):  
High Performance ◽  
Additive Group ◽  
Public Key Cryptography ◽  
Scalar Multiplication ◽  
Public Key ◽  
Integer Multiple ◽  
Public Key Cryptosystems ◽  
Fast Processing ◽  
Implementation Costs ◽  
Modern Era

this modern era of security, public key cryptography is quite popular and holds a great significance. Various public key cryptosystems are available in today’s environment such as RSA and ECC. Elliptic Curve cryptography is beneficial in a lot of aspects which includes shorter key as compared to other cryptosystems, high security, fast processing speed, low storage, low bandwidth, small software print, low hardware implementation costs, high performance. The main and the costliest step in ECC is the Scalar Multiplication. In scalar multiplication, integer multiple of an element in additive group of elliptic curves is calculated. In this paper, we compare various available algorithms for the scalar multiplication used in ECC.

scholarly journals Iterative sliding window method for shorter number of operations in modular exponentiation and scalar multiplication

2017 ◽  
Vol 4 (1) ◽  
pp. 1304499 ◽  
Author(s):  
Adamu Muhammad Noma ◽  
Abdullah Muhammed ◽  
Zuriati Ahmad Zukarnain ◽  
Muhammad Afendee Mohamed ◽  
Duc Pham
Keyword(s):  
Sliding Window ◽  
Scalar Multiplication ◽  
Modular Exponentiation ◽  
Window Method ◽  
Sliding Window Method

Secure and Robust Telemedicine using ECC on Radix-8 with Formal Verification

2021 ◽  
pp. 573-590
Author(s):  
Gautam Kumar ◽  
Hemraj Saini
Keyword(s):  
Computational Complexity ◽  
Elliptic Curve ◽  
Formal Verification ◽  
Elliptic Curve Cryptography ◽  
Clock Cycle ◽  
Scalar Multiplication ◽  
Efficient Technique ◽  
Computation Efficiency ◽  
Research Gap ◽  
Hardware Performance

The scalar multiplication techniques used in Elliptic curve cryptography (ECC) are having the scope for gaining the computation efficiency. This is possible through the reduction of precomputed operations. Finding the more efficient technique compares to the most recent or efficient one is a research gap for all schemes. The manuscript presents an application oriented work for Telemedicine using ECC. It is based on robust application on reduced computational complexity. The methodology we apply for the same is Scalar Multiplication without precomputation on Radix-8. Introduced software and the hardware performance are reporting a big advantage over all the related proposed techniques. The reason to cover this problem is to provide a path on a fascinating area of ECC on a smaller key size be applicable for all applications on a same level of security strengths. The smaller length key gives the higher speed and shorter clock cycle to initiate the operation.

7. Introduction to matrices

2015 ◽  
pp. 87-100
Author(s):  
Peter M. Higgins
Keyword(s):  
Social Sciences ◽  
Linear Algebra ◽  
Network Theory ◽  
Fixed Number ◽  
Scalar Multiplication ◽  
The Subject ◽  
Rectangular Arrays

Matrices represent the central algebraic vehicle for advanced computation throughout mathematics as well as the physical and social sciences. ‘Introduction to matrices’ explains that matrices are simply rectangular arrays of numbers. There are some natural, simple operations that can be performed on matrices. Scalar multiplication is where all entries in a matrix are multiplied by a fixed number. Network theory is one of the major applications of linear algebra, which is the branch of the subject that is largely represented by matrices and matrix calculations. Another application of matrices is to the geometry of transformations.

Fast Prediction of Temperature Evolution in Electronic Devices for Run-Time Thermal Management Applications

2010 ◽  
Author(s):  
Yizhang Yang ◽  
Sridhar Sundaram ◽  
Gamal Refai-Ahmed ◽  
Maxat Touzelbaev
Keyword(s):  
Thermal Management ◽  
Electronic Devices ◽  
Temperature Response ◽  
Temperature Evolution ◽  
Computational Time ◽  
Infinite Impulse Response ◽  
Switching Frequency ◽  
Computation Efficiency ◽  
High Switching Frequency ◽  
Run Time

Increase of non-uniform power density and high switching frequency has presented new challenges in predicting transient temperature response to fast-changing power inputs in advanced electronic devices. While the computational effort with direct calculation through the finite element model (FEM) is expensive, various methods of model reduction with drastically improved computing speed have been developed for calculation of dynamic thermal responses of the electronic systems. However, those methods’ still-considerable computational time consumption inhibits their practices in real-time temperature prediction and dynamic thermal management (DTM) applications. This work presents a fast algorithm for predicting temperature evolution in electronic devices subjected to multiple heat source excitations. It utilizes the equivalent thermal RC network for model reductions, and adopts recursive infinite impulse response (IIR) digital filters for accelerated computation in discrete time-domain. The algorithm is validated by comparison to existing convolution integral methods, yielding excellent agreement with several orders of magnitude improvement in computation efficiency. Due to its simplicity in implementation, the algorithm is very suitable for run-time evaluation of temperature response for dynamic power management applications.

Secure and Robust Telemedicine using ECC on Radix-8 with Formal Verification

2021 ◽  
pp. 1733-1748
Author(s):  
Gautam Kumar ◽  
Hemraj Saini
Keyword(s):  
Computational Complexity ◽  
Elliptic Curve ◽  
Formal Verification ◽  
Elliptic Curve Cryptography ◽  
Clock Cycle ◽  
Scalar Multiplication ◽  
Efficient Technique ◽  
Computation Efficiency ◽  
Research Gap ◽  
Hardware Performance

The scalar multiplication techniques used in Elliptic curve cryptography (ECC) are having the scope for gaining the computation efficiency. This is possible through the reduction of precomputed operations. Finding the more efficient technique compares to the most recent or efficient one is a research gap for all schemes. The manuscript presents an application oriented work for Telemedicine using ECC. It is based on robust application on reduced computational complexity. The methodology we apply for the same is Scalar Multiplication without precomputation on Radix-8. Introduced software and the hardware performance are reporting a big advantage over all the related proposed techniques. The reason to cover this problem is to provide a path on a fascinating area of ECC on a smaller key size be applicable for all applications on a same level of security strengths. The smaller length key gives the higher speed and shorter clock cycle to initiate the operation.

Sign in / Sign up

Export Citation Format

Share Document