Differential and Linear Distributions of Substitution Boxes for Symmetric-Key Cryptosystems

Peter Roelse ()
Additional contact information
Peter Roelse: Eindhoven University of Technology, Department of Mathematics and Computer Science

A chapter in Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, 2002, pp 270-285 from Springer

Abstract: Abstract In many secret-key cryptosystems substitution boxes are the only nonlinear component, and provide resistance against both differential and linear cryptanalyis. In this paper the notions of differential and linear distribution of the mapping defined by a substitution box are introduced. These distributions contain considerable information about its resistance against linear and differential cryptanalysis. With a computer search the differential and linear distribution of four-bit permutations with an optimal resistance against the attacks mentioned above were determined. In particular, this shows that Almost Perfect Nonlinear (APN) permutations on four bits do not exist. The substitution-boxes used in the AES finalist Serpent and the construction used for the S-box of AES are compared with these optimal four-bit permutations. In addition, identities on the elements of the differential and linear distribution of a mapping are presented. These relations are used to explain the close connection between the optimal distributions of four-bit permutations that were found by the computer search.

Keywords: Linear Distribution; Dual Code; Weight Enumerator; Round Function; Almost Perfect Nonlinear (search for similar items in EconPapers)
Date: 2002
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-59435-9_22

Ordering information: This item can be ordered from
http://www.springer.com/9783642594359

DOI: 10.1007/978-3-642-59435-9_22

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().