Generating certain quintic irreducible polynomials over finite fields
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In the paper [1], an explicit correspondence between certain cubic irreducible polynomials over F_q and cubic irreducible polynomials of special type over 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.
Abstract
In the paper [1], an explicit correspondence between certain cubic irreducible polynomials over F_q and cubic irreducible polynomials of special type over 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.
참고문헌 (3)
- 김형돈, "Certain cubic polynomials over finite fields", 대한수학회지, 46(1), pp.1~12 (2009), 대한수학회
- A.K. Lenstra, "The XTR public key system, Advances in Cryptology (CRYPTO 2000)", pp.1~19 (1880), LNCS
- A.K. Lenstra, "Fast Irreducibility and subgroup membership testing in XTR, Advances in Cryptology (PKC 2001)", pp.73~86 (1992), LNCS