New Instances of Quadratic APN Functions in Small Dimension
Description
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 12,921 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], the 10 APN instances presented in [WTG13], and the two APN instances from the Taniguchi family [Tan19], those are all 8-bit APN functions up to CCZ-equivalence known until December 2020 (21,113 in total).
(In May 2021, Yu and Perrin [YP21] found more than 5,400 other new quadratic APN instances by applying the QAM method, bringing up the total number of known 8-bit APN instances to over 26,500.)
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.
Changelog: In this version, we removed the two 8-bit APN instances found in [Tan19] from the list of our new 8-bit APN instances. In Version 2.0, we claimed those two APN instances to be new.
Files
apn_10bit.txt
Additional details
Related works
- Is derived from
- Software: https://github.com/cbe90/quadratic_apn (URL)
- Is documented by
- Preprint: https://arxiv.org/abs/2009.07204 (URL)
References
- [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.
- [Tan19]: H. Taniguchi. On some quadratic APN functions. Des. Codes Cryptogr., 87(9):1973–1983, 2019.
- [YP21]: Y. Yu and L. Perrin. Constructing more quadratic APN functions with the QAM method. Cryptology ePrint Archive, Report 2021/574, 2021. https://eprint.iacr.org/2021/574