Improved Primality Proving with Eisenstein Pseudocubes

  • Kjell Wooding
  • H. C. Williams
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6197)


In August 2002, Agrawal, Kayal, and Saxena described an unconditional, deterministic algorithm for proving the primality of an integer N. Though of immense theoretical interest, their technique, even incorporating the many improvements that have been proposed since its publication, remains somewhat slow for practical application. This paper describes a new, highly efficient method for certifying the primality of an integer \(N \equiv 1 \pmod 3\), making use of quantities known as Eisenstein pseudocubes. This improves on previous attempts, including the peudosquare-based approach of Lukes et al., and the pseudosquare improvement proposed by Berrizbeitia, et al.


Congruence Condition Distinct Zero Residue Character Unique Factorization Domain Perfect Power 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Kjell Wooding
    • 1
  • H. C. Williams
    • 1
  1. 1.Institute for Security, Privacy and Information AssuranceUniversity of CalgaryCalgaryCanada

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