Please use this identifier to cite or link to this item:
Title: On a class of quadratic polynomials with no zeros and its application to APN functions
Authors: Bracken, C.
Tan, C.H. 
Tan, Y. 
Keywords: APN functions
Irreducible polynomials
Zeros of polynomials
Issue Date: 2014
Citation: Bracken, C., Tan, C.H., Tan, Y. (2014). On a class of quadratic polynomials with no zeros and its application to APN functions. Finite Fields and their Applications 25 : 26-36. ScholarBank@NUS Repository.
Abstract: In [6], Lilya Budaghyan and Claude Carlet introduced a family of APN functions on F22k of the form F(x)=x(x2i+x2k+cx2k+i) +x2i(c2kx2k+δx2k+i)+x2k+i+2k. They showed that this infinite family exists provided the existence of the quadratic polynomial G(y)=y2i +1+cy2i+c2ky+1, which has no zeros such that y2k+1=1, or in particular has no zeros in F22k. However, up to now, no construction of such polynomials is known. In this paper, we show that, when k is an odd integer, the APN function F is CCZ-equivalent to the one in [2, Theorem 1]; and when k is even with 3â̂, we explicitly construct the polynomial G, and hence demonstrate the existence of F. More generally, it is well known that G relates to the polynomial ;bsupesupbsup. © 2013 Elsevier Inc. All rights reserved.
Source Title: Finite Fields and their Applications
ISSN: 10715797
DOI: 10.1016/j.ffa.2013.08.006
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.


checked on Apr 7, 2021


checked on Apr 7, 2021

Page view(s)

checked on Apr 10, 2021

Google ScholarTM



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.