Change search
ReferencesLink to record
Permanent link

Direct link
On the Properties of S-boxes: A Study of Differentially 6-Uniform Monomials over Finite Fields of Characteristic 2
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2013 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

S-boxes are key components of many symmetric cryptographic primitives. Among them, some block ciphers and hash functions are vulnerable to attacks based on differential cryptanalysis, a technique introduced by Biham and Shamir in the early 90’s. Resistance against attacks from this family depends on the so-called differential properties of the S-boxes used.

When we consider S-boxes as functions over finite fields of characteristic 2, monomials turn out to be good candidates. In this Master’s Thesis, we study the differential properties of a particular family of monomials, namely those with exponent 2ͭᵗ-1 In particular, conjectures from Blondeau’s PhD Thesis are proved.

More specifically, we derive the differential spectrum of monomials with exponent 2ͭᵗ-1 for several values of t using a method similar to the proof Blondeau et al. made of the spectrum of x - x⁷. The first two chapters of this Thesis provide the mathematical and cryptographic background necessary while the third and fourth chapters contain the proofs of the spectra we extracted and some observations which, among other things, connect this problem with the study of particular Dickson polynomials.

Place, publisher, year, edition, pages
2013. , 75 p.
TRITA-MAT-E, 2013:13
Keyword [en]
Symmetric cryptography, Differential uniformity, Differential spectrum, Kloosterman sum, Power function, Roots of trinomial, x⟶x^(2t-1), Dickson polynomial, Differential Cryptanalysis
National Category
URN: urn:nbn:se:kth:diva-121342OAI: diva2:618670
Subject / course
Educational program
Master of Science in Engineering -Engineering Physics
Physics, Chemistry, Mathematics
Available from: 2013-04-29 Created: 2013-04-29 Last updated: 2013-04-29Bibliographically approved

Open Access in DiVA

fulltext(752 kB)713 downloads
File information
File name FULLTEXT01.pdfFile size 752 kBChecksum SHA-512
Type fulltextMimetype application/pdf

By organisation
Mathematics (Div.)

Search outside of DiVA

GoogleGoogle Scholar
Total: 713 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 106 hits
ReferencesLink to record
Permanent link

Direct link