AfricaCrypt 2022 (original) (raw)

Lilya Budaghyan - University of Bergen, Norway

Lilya Budaghyan is a professor and the head of the Selmer Center in Secure Communication, Department of Informatics, University of Bergen, Norway. She received her Ph.D. degree from the University of Magdeburg, Germany, in 2005, and the habilitation degree from the University of Paris 8, France, in 2013. Her main research interests include cryptographic Boolean functions and discrete structures and their applications. She also conducted her research at Yerevan State University (Armenia), the University of Trento (Italy) and Telecom ParisTech (France). She was a recipient of the Trond Mohn Foundation Award in 2016, the Young Research Talent Grant from the Norwegian Research Council in 2014, a Postdoctoral Fellowship Award from the Foundation of Mathematical Sciences of Paris in 2012, and the Emil Artin Junior Prize in Mathematics in 2011. Since 2018, she has been a member of the Norwegian Academy of Technological Sciences (NTVA).

Talk title: In search of equivalence relations for cryptographic Boolean functions ( slides )

Talk abstract: Boolean functions are among the most fundamental objects in pure and applied mathematics and computer science. In particular, in cryptography block ciphers are designed by appropriate composition of Boolean functions, and the security of a block cipher depends on special Boolean functions called S-boxes.
The two main cryptographic properties of S-boxes, differential uniformity and nonlinearity, measure the resistance of S-boxes to the two most powerful classical attacks, differential and linear cryptanalyses, respectively. Equivalence relations preserving differential uniformity and nonlinearity divide the set of all functions into classes. Among such equivalence relations are affine, extended affine and CCZ-equivalences. Studying these equivalence relations and finding new ones is important for the following two reasons: first, they can be powerful construction methods providing for each function a huge class of functions with the same properties, and, second, instead of checking invariant properties for all functions, it is enough to check only one in each class.
In the present talk we discuss known equivalence relations of cryptographic functions and possible ways for finding new such equivalence relations.