Classification of quadratic APN functions with coefficients in GF(2) for dimensions up to 9

Yuyin Yu; Nikolay Kaleyski; Lilya Budaghyan; Yongqiang Li

Paper 2019/1491

Classification of quadratic APN functions with coefficients in GF(2) for dimensions up to 9

Yuyin Yu, Nikolay Kaleyski, Lilya Budaghyan, and Yongqiang Li

Abstract

Almost perfect nonlinear (APN) and almost bent (AB) functions are integral components of modern block ciphers and play a fundamental role in symmetric cryptography. In this paper, we describe a procedure for searching for quadratic APN functions with coefficients in GF(2) over the finite fields GF(2^n) and apply this procedure to classify all such functions over GF(2^n) with n up to 9. We discover two new APN functions (which are also AB) over GF(2^9) that are CCZ-inequivalent to any known APN function over this field. We also verify that there are no quadratic APN functions with coefficients in GF(2) over GF(2^n) with n between 6 and 8 other than the currently known ones.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: Boolean functions Almost Perfect Nonlinear Almost Bent Quadratic functions
Contact author(s): nikolay kaleyski @ uib no
History: 2019-12-30: received
Short URL: https://ia.cr/2019/1491
License: CC BY

BibTeX

@misc{cryptoeprint:2019/1491,
      author = {Yuyin Yu and Nikolay Kaleyski and Lilya Budaghyan and Yongqiang Li},
      title = {Classification of quadratic {APN} functions with coefficients in {GF}(2) for dimensions up to 9},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/1491},
      year = {2019},
      url = {https://eprint.iacr.org/2019/1491}
}