There is a newer version of this record available.

Dataset Open Access

New Instances of Quadratic APN Functions in Small Dimension

Beierle, Christof; Leander, Gregor

This dataset contains the look-up tables of the new quadratic APN instances found by utilizing linear self-equivalences and/or applying the switching construction of [EP09]. A preprint of our paper is available at arxiv: C. Beierle and G. Leander. New instances of quadratic APN functions. 2020.

The file apn_8bit.txt contains the look-up tables of the 12,923 new quadratic APN instances in dimension eight found by this approach. Together with the 23 APN instances listed in [EP09], the 8,157 APN instances constructed by the QAM method [YWL14], and the 10 APN instances presented in [WTG13], those are all 8-bit APN functions up to CCZ-equivalence known so far (21,113 in total).

The file apn_9bit.txt contains the look-up tables of the 35 new quadratic APN instances in dimension nine found by this approach. The last two functions in this list are APN permutations which have not been known before.

The file apn_10bit.txt contains the look-up tables of the five new quadratic APN instances in dimension ten found by this approach.

Files (15.3 MB)
Name Size
apn_10bit.txt
md5:fb764bf66658ab1076bd1a5498034ef1
25.1 kB Download
apn_8bit.txt
md5:cd4e99ff5fcdd6c5fc6e8161ca571a9b
15.1 MB Download
apn_9bit.txt
md5:e9c986e70ae1135486bb13f54aec806f
85.9 kB Download
  • [EP09]: Y. Edel and A. Pott. A new almost perfect nonlinear function which is not quadratic. Adv. Math. Commun., 3(1):59-81, 2009.

  • [YWL14]: Y. Yu, M. Wang, and Y. Li. A matrix approach for constructing quadratic APN functions. Des. Codes Cryptogr., 73(2):587-600, 2014. Updated version available via https://eprint.iacr.org/2013/007.pdf

  • [WTG13]: G. Weng, Y. Tan, and G. Gong. On quadratic almost perfect nonlinear functions and their related algebraic object. Workshop on Coding and Cryptography, WCC 2013.

299
95
views
downloads
All versions This version
Views 29992
Downloads 9540
Data volume 789.6 MB168.2 MB
Unique views 23687
Unique downloads 7326

Share

Cite as