References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt145",{id:"formSmash:upper:j_idt145",widgetVar:"widget_formSmash_upper_j_idt145",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt146_j_idt148",{id:"formSmash:upper:j_idt146:j_idt148",widgetVar:"widget_formSmash_upper_j_idt146_j_idt148",target:"formSmash:upper:j_idt146:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

On the Properties of S-boxes: A Study of Differentially 6-Uniform Monomials over Finite Fields of Characteristic 2PrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2013 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
##### Abstract [en]

##### Place, publisher, year, edition, pages

2013. , 75 p.
##### Series

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

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-121342OAI: oai:DiVA.org:kth-121342DiVA: diva2:618670
##### Subject / course

Mathematics
##### Educational program

Master of Science in Engineering -Engineering Physics
##### Uppsok

Physics, Chemistry, Mathematics

#####

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##### Examiners

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Available from: 2013-04-29 Created: 2013-04-29 Last updated: 2013-04-29Bibliographically approved

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.

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