Using Montgomery curve arithmetic over F2p for point scalar multiplication on short Weierstrass curve over Fp with exactly one 2-torsion point and order not divisible by 4
Journal Title: Computer Science and Mathematical Modelling - Year 2016, Vol 0, Issue 4
Abstract
Montgomery curves are well known because of their efficiency and side channel attacks vulnerability. In this article it is showed how Montgomery curve arithmetic may be used for point scalar multiplication on short Weierstrass curve ESW over Fp with exactly one 2-torsion point and #ESW (Fp) not divisible by 4. If P ∈ ESW (Fp) then also P ∈ ESW (Fp2). Because ESW (Fp2) has three 2-torsion points (because ESW (Fp) has one 2-torsion point) it is possible to use 2-isogenous Montgomery curve EM (Fp2) to the curve ESW (Fp2) for counting point scalar multiplication on ESW (Fp). However arithmetic in (Fp2) is much more complicated than arithmetic in Fp, in hardware implementations this method may be much more useful than standard methods, because it may be nearly 45% faster.
Authors and Affiliations
Michał Wroński
Keywords
Related Articles
- EP ID EP188132
- DOI -
- Views 77
- Downloads 0
Early exit from a function as method of code optimization in the component environments
This paper presents the use of code optimization method in the component environments (Java VM, MS .NET, Mono). In the proposed solution implemented for component environments there are occurrences when manual code optim...
Evaluation of the expert system as a stage of the life cycle model ESDLC on the example of WIKex
The use of electroencephalography as a future-oriented brain-computer interface. Current concepts, solutions, technologies that allow communication through thoughts
Nowadays, brain-computer interfaces are gaining more and more popularity. Research centers develop new methods of human communication with devices through thoughts. There are many methods used for this kind of interfaces...
The analysis of selected properties of medical patterns cobweb models in the medical diagnosis support process
W pracy przedstawiono możliwość zastosowania mechanizmów wnioskowania diagnostycznego wykorzystujących modele pajęczynowe zdefiniowane w wielokryterialnej przestrzeni danych medycznych pacjenta. Istotą rozpatrywanego pro...
Requirements Engineering in Agile Software Development
Agile Software Development approaches have become increasingly popular during the last few years. Agile practises have been developed with the aim to deliver software faster and to ensure that the software meets changing...