Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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GENERATING CERTAIN QUINTIC IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS

  • Received : 2011.05.31
  • Accepted : 2011.08.31
  • Published : 2011.09.30
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Abstract

In the paper [1], an explicit correspondence between certain cubic irreducible polynomials over $\mathbb{F}_q$ and cubic irreducible polynomials of special type over $\mathbb{F}_{q^2}$ was established. In this paper, we show that we can mimic such a correspondence for quintic polynomials. Our transformations are rather constructive so that it can be used to generate irreducible polynomials in one of the finite fields, by using certain irreducible polynomials given in the other field.

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References

  1. H. Kim, J. Kim, and I. Yie, Certain Cubic Polynomials over Finite Fields, J. Korean Math. Soc. 46 (2009), no. 1, 1-12. https://doi.org/10.4134/JKMS.2009.46.1.001
  2. A.K. Lenstra and E. Verheul, The XTR public key system, Advances in Cryp- tology (CRYPTO 2000), LNCS 1880, 1-19.
  3. A.K. Lenstra and E. Verheul, Fast Irreducibility and subgroup membership test- ing in XTR, Advances in Cryptology (PKC 2001), LNCS 1992, 73-86.