Cryptology ePrint Archive: Report 2021/574

Constructing More Quadratic APN Functions with the QAM Method

Yuyin Yu and Leo Perrin

Abstract: We found 5412 new quadartic APN on F28 with the QAM method, thus bringing the number of known CCZ-inequivalent APN functions on F28 to 26525. Unfortunately, none of these new functions are CCZ-equivalent to permutations. A (to the best of our knowledge) complete list of known quadratic APN functions, including our new ones, has been pushed to sboxU for ease of study by others.

In this paper, we recall how to construct new QAMs from a known one, and present how used the ortho-derivative method to figure out which of our new functions fall into different CCZ-classes. Based on these results and on others on smaller fields, we make to conjectures: that the full list of quadratic APN functions on F28 could be obtained using the QAM approached (provided enormous computing power), and that the total number of CCZ-inequivalent APN functions may overcome 50000.

Category / Keywords: foundations / APN, quadratic functions

Date: received 30 Apr 2021

Contact author: yuyuyin at 163 com

Available format(s): PDF | BibTeX Citation

Version: 20210503:202056 (All versions of this report)

Short URL:

[ Cryptology ePrint archive ]