Cryptology ePrint Archive: Report 2021/405

Revisiting some results on APN and algebraic immune functions

Claude Carlet

Abstract: We push a little further the study of two characterizations of almost perfect nonlinear (APN) functions introduced in our recent monograph. We state open problems about them, and we revisit in their perspective a well-known result from Dobbertin on APN exponents. This leads us to new results about APN power functions and more general APN polynomials with coefficients in a subfield F_{2^k} , which ease the research of such functions and of differentially uniform functions, and simplifies the related proofs by avoiding tedious calculations. In a second part, we give slightly simpler proofs than in the same monograph, of two known results on Boolean functions, one of which deserves to be better known but needed clarification, and the other needed correction.

Category / Keywords: secret-key cryptography / Boolean function, Almost perfect nonlinear, correlation immune

Date: received 26 Mar 2021, last revised 29 Mar 2021

Contact author: claude carlet at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20210329:130223 (All versions of this report)

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