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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.

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  • [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

  • [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.

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