Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
On Pollard's rho method for solving the elliptic curve discrete logarithm problem
Linnaeus University, Faculty of Technology, Department of Mathematics.
2019 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

    Cryptosystems based on elliptic curves are in wide-spread use, they are considered secure because of the difficulty to solve the elliptic curve discrete logarithm problem. Pollard's rho method is regarded as the best method for attacking the logarithm problem to date, yet it is still not efficient enough to break an elliptic curve cryptosystem. This is because its time complexity is O(√n) and for uses in cryptography the value of n will be very large. The objective of this thesis is to see if there are ways to improve Pollard's rho method. To do this, we study some modifications of the original functions used in the method. We also investigate some different functions proposed by other researchers to see if we can find a version that will improve the performance. From the experiments conducted on these modifications and functions, we can conclude that we get an improvement in the performance for some of them.

Place, publisher, year, edition, pages
2019. , p. 41
Keywords [en]
elliptic curves, Pollard's rho method, elliptic curve discrete logarithm problem, cryptography, adding walk, mixed walk, cycle-detecting algorithm, iterating function, random walk
National Category
Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-85516OAI: oai:DiVA.org:lnu-85516DiVA, id: diva2:1326270
Educational program
Applied Mahtematics Programme, 180 credits
Supervisors
Examiners
Available from: 2019-06-18 Created: 2019-06-17 Last updated: 2019-06-18Bibliographically approved

Open Access in DiVA

fulltext(1357 kB)50 downloads
File information
File name FULLTEXT01.pdfFile size 1357 kBChecksum SHA-512
d9fe016a9971108ece241e5886a30b85db553a9fe4eb75cd4bc6b62d97a46308628abab43627f2871265d3538457d8528be3de1c296ed9c18fbb5ecf4e2dc93e
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Falk, Jenny
By organisation
Department of Mathematics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 50 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

urn-nbn

Altmetric score

urn-nbn
Total: 173 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf