Page 135 - Ellingham, Mark, Mariusz Meszka, Primož Moravec, Enes Pasalic, 2014. 2014 PhD Summer School in Discrete Mathematics. Koper: University of Primorska Press. Famnit Lectures, 3.
P. 135
pter 4
Symmetric Key Cryptography and its
Relation to Graph Theory
Enes Pasalic
University of Primorska, Slovenia
SUMMARY
Modern cryptology relies on many scientific disciplines such as information theory, prob-
ability theory, discrete mathematics among others. In addition, many public cryptosys-
tems are based on some hard graph theoretic problems such as graph coloring for in-
stance. While not directly derived from the concepts related to graphs, the most im-
portant cryptographic properties of certain discrete structures may be defined and an-
alyzed in the graph theoretic framework which might give at least different insight at
these structures. We will give a short survey of cryptography with the emphasis on these
discrete structures being basic primitives in the so-called symmetric key cryptography.
Booolean functions, vectorial mappings over finite structures and permutations over fi-
nite fields, as the most important representatives of these structures, will be considered
in real-life encryption schemes. Their cryptographic properties will be stated both in a
classical way using some suitable tools in cryptology and these will be then translated
in the graph theoretic language. The students will also get a brief insight in the state-of-
the-art research in this direction.
123
Symmetric Key Cryptography and its
Relation to Graph Theory
Enes Pasalic
University of Primorska, Slovenia
SUMMARY
Modern cryptology relies on many scientific disciplines such as information theory, prob-
ability theory, discrete mathematics among others. In addition, many public cryptosys-
tems are based on some hard graph theoretic problems such as graph coloring for in-
stance. While not directly derived from the concepts related to graphs, the most im-
portant cryptographic properties of certain discrete structures may be defined and an-
alyzed in the graph theoretic framework which might give at least different insight at
these structures. We will give a short survey of cryptography with the emphasis on these
discrete structures being basic primitives in the so-called symmetric key cryptography.
Booolean functions, vectorial mappings over finite structures and permutations over fi-
nite fields, as the most important representatives of these structures, will be considered
in real-life encryption schemes. Their cryptographic properties will be stated both in a
classical way using some suitable tools in cryptology and these will be then translated
in the graph theoretic language. The students will also get a brief insight in the state-of-
the-art research in this direction.
123
