Change search
ReferencesLink to record
Permanent link

Direct link
Points of High Order on Elliptic Curves: ECDSA
Linnaeus University, Faculty of Technology, Department of Mathematics.
2016 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

This master thesis is about Elliptic Curve Digital Signature Algorithm or ECDSA and two of the known attacks on this security system. The purpose of this thesis is to find points that are likely to be points of high order on an elliptic curve. If we have a point P of high order and if Q = mP, then we have a large set of possible values of m. Therefore it is hard to solve the Elliptic Curve Discrete Logarithm Problem or ECDLP. We have investigated on the time of finding the solution of ECDLP for a certain amount of elliptic curves based on the order of the point which is used to create the digital signatures by those elliptic curves. Method: Algebraic Structure of elliptic curves over finite fields and Discrete logarithms. This has been done by two types of attacks namely Baby Step, Giant Step and Pollard’s Rho and all of the programming parts has been done by means of Mathematica. Conclusion: We have come into a conclusion of having the probable good points which are the points of high order on elliptic curves through the mentioned attacks in which solving the ECDLP is harder if these points have been used in generating the digital signature. These probable good points can be estimated by means of a function we have come up with. The input of this function is the order of the point and the output is the time of finding the answer of ECDLP.

Place, publisher, year, edition, pages
2016. , 57 p.
Keyword [en]
Digital signature (DS.), Elliptic Curve Digital Signature Algorithm (ECDSA), Elliptic Curve Discrete Logarithm Problem (ECDLP), Baby Step, Giant Step (Bs.Gs.), Pollard’s Rho
National Category
Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-58449OAI: oai:DiVA.org:lnu-58449DiVA: diva2:1050671
Subject / course
Mathematics
Educational program
Mathematics and Modelling, Master Programme, 120 credits
Supervisors
Examiners
Available from: 2016-11-30 Created: 2016-11-29 Last updated: 2016-11-30Bibliographically approved

Open Access in DiVA

Behnaz.Barzi.M.S.Thesis.LNU(1409 kB)2 downloads
File information
File name FULLTEXT01.pdfFile size 1409 kBChecksum SHA-512
b0ae493a3200e833c2ee23dcab681b90bd0d509a39e580f42b88b7259895cbd87e8fc8ee5f3260851fb851be09b91c882c89559b80c037af4fe8be028f0a493b
Type fulltextMimetype application/pdf

By organisation
Department of Mathematics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 2 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 2 hits
ReferencesLink to record
Permanent link

Direct link