Editorial: Special issue on Boolean functions and their applications
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Editorial: Special issue on Boolean functions and their applications Lilya Budaghyan 1 & Tor Helleseth 1 Published online: 20 August 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Mathematics Subject Classification (2010) 68P30
This is the fourth special issue of Cryptography and Communication dedicated to Boolean functions and their applications (the previous three appeared in 2016 and 2019 and were associated with the events of BFA 2014, BFA 2017 and BFA 2018). In June 2019, specialists from 15 different countries all over the world gathered in Florence, Italy, at the International Workshop on Boolean Functions and Their Applications BFA 2019, the event celebrating the 70th birthday of Claude Carlet. Prof. Carlet (University of Paris 8 and University of Bergen) is a well-known scientist who has made a considerable contribution to the fields of Boolean functions, cryptography, coding theory, finite fields and sequence design. In particular, he is one of the founders of cryptographic Boolean functions theory. BFA 2019 had 15 invited speakers including Marco Calderini, Claude Carlet, Robert Coulter, Ulrich Dempwolff, Daniel Katz, Chunlei Li, Nian Li, Sihem Mesnager, Daniel Panario, Emmanuel Prouff, Chunming Tang, Alev Topuzoglu and Yuyin Yu. Contributed talks were also presented at the workshop. The presented talks highlighted recent results in the field which covered various applications of Boolean functions including coding, cryptography, sequence design, combinatorics, commutative algebra and discrete mathematics. All speakers have been invited to submit a paper (on the subject of their talk or another subject connected to Boolean functions). All received submissions were thoroughly reviewed and 13 papers, described below, have been accepted after revision. This special issue is dedicated to the 70th Birthday of Claude Carlet This article belongs to the Topical Collection: Boolean Functions and Their Applications IV
* Lilya Budaghyan [email protected] Tor Helleseth [email protected]
1
Department of Informatics, University of Bergen, PO Box 7803, 5020 Bergen, Norway
820
Cryptography and Communications (2020) 12:819–820
Boolean functions are used in cryptography, in particular in block and stream ciphers. An important condition on these functions is a high resistance to the differential and linear cryptanalyses, which are measured by differential uniformity and nonlinearity of functions, respectively. Bent, almost bent, perfect nonlinear and almost perfect nonlinear (APN) functions are those which show optimality in respect to one or both of the above mentioned properties. ‘On the EA-classes of known APN functions in small dimensions’ (Calderini), ‘The multivariate method strikes again: New power functions with low differential uniformity in odd characteristic’ (Felke) and ‘On the linear structures of balanced functions and quadratic APN functions’ (Musukwa and Sala) are dedicated to functions with optimal or near optimal differential uniformity. Results on functions with o
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