The Single Cycle T-functions

Zhaopeng Dai; Zhuojun Liu

Paper 2011/547 Original: eprint.iacr.org/2011/547 ↗

The Single Cycle T-functions

Zhaopeng Dai

Zhuojun Liu

Abstract

In this paper the single cycle T-functions are studied. Making use of the explicit formulas of sum and product of 2-adic integers, we present the necessary and sufficient conditions on the generalized polynomial $\widetilde{p(x)} = a_{0} \substack {+ \\ \oplus} a_{1}x \substack {+ \\ \oplus} \cdots \substack {+ \\ \oplus} a_{d}x^{d} (\mbox{mod} \, 2^{n} )$ being a single cycle T-function. Furthermore, for any given generalized polynomial, we can deduce some expressions about its coefficients by which we can determine whether it is single cycle or not.

Metadata

Available format(s): PDF
Publication info: Preprint.
History: 2011-10-11: last updated; 2011-10-11: published
Short URL: https://ia.cr/2011/547
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2011/547,
      author = {Zhaopeng Dai and Zhuojun Liu},
      title = {The Single Cycle T-functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2011/547},
      year = {2011},
      url = {https://eprint.iacr.org/2011/547}
}