• Information Technology
  • Human Resources
  • Careers
  • Giving
  • Library
  • Bookstore
  • Active Living
  • Continuing Education
  • Go Dinos
  • UCalgary Maps
  • UCalgary Directory
  • Academic Calendar
My UCalgary
Webmail
D2L
ARCHIBUS
IRISS
  • Faculty of Arts
  • Cumming School of Medicine
  • Faculty of Environmental Design
  • Faculty of Graduate Studies
  • Haskayne School of Business
  • Faculty of Kinesiology
  • Faculty of Law
  • Faculty of Nursing
  • Faculty of Nursing (Qatar)
  • Schulich School of Engineering
  • Faculty of Science
  • Faculty of Social Work
  • Faculty of Veterinary Medicine
  • Werklund School of Education
  • Information TechnologiesIT
  • Human ResourcesHR
  • Careers
  • Giving
  • Library
  • Bookstore
  • Active Living
  • Continuing Education
  • Go Dinos
  • UCalgary Maps
  • UCalgary Directory
  • Academic Calendar
  • Libraries and Cultural Resources
View Item 
  •   PRISM Home
  • Science
  • Science Research & Publications
  • View Item
  •   PRISM Home
  • Science
  • Science Research & Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Early Terminiation over Small Fields

Thumbnail
Download
2003-723-26.pdf (307.5Kb)
2003-723-26.ps (437.4Kb)
Download Record
Download to EndNote/RefMan (RIS)
Download to BibTex
Author
Eberly, Wayne
Accessioned
2008-02-26T20:31:10Z
Available
2008-02-26T20:31:10Z
Computerscience
2003-06-12
Issued
2003-06-12
Subject
Computer Science
Type
unknown
Metadata
Show full item record

Abstract
Krylov-based algorithms have recently been used (alone, or in combination with other methods) in order to solve systems of linear equations that arise during integer factorization and discrete logarithm computations. Since these include systems over small finite fields, the behavior of these algorithms in this setting is of interest. Unfortunately, the application of these methods is complicated by the possibility of several kinds of breakdown. Orthogonal vectors can arise when a variant of the Lanczos algorithm is used to generate a basis, and zero-discrepancies can arise during the computation of minimal polynomials of linearly recurrent sequences when Wiedemann's algorithm is applied. Several years ago, Austin Lobo reported experimental evidence that zero-discrepancies are extremely unlikely when a randomized version of Wiedemann's algorithm is applied to solve systems over large fields. With high probability, results are correct if a computation is terminated as soon as such a sequence is detected. "Early termination" has consequently been included in recent implementations. In this paper, we analyze the probability of long sequences of zero-discrepancies during computations of minimal polynomials of the linearly recurrent sequences that arise when simple Krylov-based algorithms are used to solve systems over very small finite fields. Variations of these algorithms that incorporate early termination are briefly presented and analyzed in the small field case.
Notes
We are currently acquiring citations for the work deposited into this collection. We recognize the distribution rights of this item may have been assigned to another entity, other than the author(s) of the work.If you can provide the citation for this work or you think you own the distribution rights to this work please contact the Institutional Repository Administrator at digitize@ucalgary.ca
Corporate
University of Calgary
Faculty
Science
Doi
http://dx.doi.org/10.11575/PRISM/30588
Uri
http://hdl.handle.net/1880/45468
Collections
  • Science Research & Publications

Browse

All of PRISMCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

LoginRegister

Download Results

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors

  • Email
  • SMS
  • 403.220.8895
  • Live Chat

Energize: The Campaign for Eyes High

Privacy Policy
Website feedback

University of Calgary
2500 University Drive NW
Calgary, AB T2N 1N4
CANADA

Copyright © 2017