The spectra of DES S-Boxes
Fukuzawa, Mathew B.
MetadataShow full item record
We typically do not associate the field of graph theory with the field of cryptography. In graph theory, the aim is to model relationships with a graph and examine properties of that graph. The goal of cryptography is to design a communication system over a nonsecure channel. One connection between the two fields can be found with Cayley graphs and Boolean functions (BF). Accordingly, we can represent a cryptographic Boolean function with a Cayley graph and examine its properties. In this thesis, we convert the substitution boxes within the Data Encryption Standard (DES) to Boolean functions and represent them with Cayley graphs. From the Cayley graph, we analyze the graph spectra and attempt to determine a relationship with the cryptographic properties of the corresponding Boolean functions. With the spectra, we also make some inferences about the structure of the Cayley graph.
Approved for public release; distribution is unlimited
Showing items related by title, author, creator and subject.
Stӑnicӑ, Pantelimon (2007);In this paper we consider the Cayley graph Gf associated with a Boolean function f and we use it to investigate some of the cryptographic properties of f. We derive necessary (but not sufficient) conditions for a Boolean ...
Stanica, Pantelimon (2007);In this paper, we consider te Cayley graph Gf associated with a Boolean function f and we use it to investigate some of the cryptographic properties of f. We derive necessary (but not sufficient) conditions for a Boolean ...
Gangopadhyay, Sugata; Gangopadhyay, Aditi Kar; Pollatos, Spyridon; Stănică, Pantelimon (2015-07-15);While performing cryptanalysis, it is of interest to approximate a Boolean function in n variables f : Fn → F2 by affine functions. Usually, it is assumed that all the input vectors to a Boolean function are equiprobable ...