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Cyclotomy primality proving — Recent developments
1998Primality proving by cyclotomy is an extension of the Jacobi sum primality test, initially proposed by Adleman, Rumely and Pomerance [3] and implemented by H. Cohen and A. Lenstra [7]. In his presentation of the algorithm of Adleman, Rumely and Pomerance at the Bourbaki Seminar 1981 [14], H. W. Lenstra Jr. proposed under the name of “Galois theory test”
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2004
Summary: First, an explicit expression for \((1-\zeta^{k})^{-1}\), where \(\zeta =\exp (2\pi i/n)\), is given, in the form of a polynomial in \(\zeta\), with rational coefficients. Then a new primality criterion is obtained, which involves the greatest integer function. Further, using a result due to \textit{Yu. I.
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Summary: First, an explicit expression for \((1-\zeta^{k})^{-1}\), where \(\zeta =\exp (2\pi i/n)\), is given, in the form of a polynomial in \(\zeta\), with rational coefficients. Then a new primality criterion is obtained, which involves the greatest integer function. Further, using a result due to \textit{Yu. I.
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A Unified Approach to Whiteman's and Ding-Helleseth's Generalized Cyclotomy Over Residue Class Rings
IEEE Transactions on Information Theory, 2014Gennian Ge
exaly
A new frequency-hopping sequence set based upon generalized cyclotomy
Designs, Codes, and Cryptography, 2012Zhengchun Zhou, Daiyuan Peng
exaly