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Thesis
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Design and analysis of chaos based enciphering methods using information theory and statistics
Ilyas, Azeem
2012-07-15
Abstract: Abstract In ultimul deceniu criptografia bazata pe sisteme haotice s-a bucurat tot mai mult de atentia cercetatorilor. Teza a pornit cu reconsiderarea sistemelor haotice din punctul de vedere al criptografiei si aduce noi modalitati de generare si evaluare a secventelor de cifrare pentru criptografia cu chei secrete. Prima prate a tezei prezinta si evalueaza doua propuneri originale de generatoare binare pseudoaleatoare obtinute folosind functia cort. Secventele binare propuse sunt obtinute fie considerand toate iteratiile successive ale functiei cort si alegand un prag de binarizare egal cu parametrul functiei cort, fie aplicand o esantionare periodica a functiei cort ( care sa asigure independenta statistica intre valorile extrase) si alegand un prag de binarizare egal cu 0,5. Ambele generatore sunt sustinute atat teoretic cat si experimental. De aseamnea, este analizata si valoarea/folosinta acestor propuneri prin ilustrarea unor aplicatii de criptare de imagini; sunt discutate si elementele specifice care pot face parte sau nu din componenta cheii secrete. S-au aplicat teste statistice NIST pentru evaluarea aleatorismului secventelor binare pseudoaleatoare propuse si s-au obtinut bune rezultate din punct de vedere statistic pentru ambele generatoare. Partea doua a tezei prezinta a noua modalitate de a genera secvente de cifrare pornind de la metoda foarte provocatoare ca gandire in criptografie, “running-key”; sunt aduse in discutie si dezvoltate idei privind semnificatia si importanta redundantei si ergodicitatii in criptografie. Teza aduce o noua abordare a metodei running-key care permite reluarea si extinderea ei pentru alte surse ergodice decat limbajul natural, conducand la obtinerea de bune generatore de chei de cifrare . Metoda a fost intai aplicata si evaluata pe limbajul natural (limba ROMANA) si apoi extinsa pentru sisteme haotice. Demonstrarea valorii/ utilitatii metodei propuse este ilustrata pe functia logistica, dar teza contine toate elementele necesare astfel incat intreaga procedura sa poata fi aplicata pentru alte sisteme haotice (examplu pentru functia cort ). Secventele de cifrare obtinute folosind noua abordare a metodei “running-key” sunt conforme din punct de vedere statistic cu modelul aruncarii cu zarul corect, iar conditiile initiale care specifica secventa haotica de cifrare pot fi considerate ca elemente in cheia secreta. During the last decade, chaos based cryptography is getting more and more attention. Thesis begins with a cryptographic view of the chaotic maps and comes with new ways to design and to evaluate pseudorandom enciphering sequences for applications in secret key cryptography. The first part of thesis presents and evaluates two advanced pseudorandom binary generators starting from tent map. The proposed binary sequences are obtained either by considering all the successive iterations of the tent map and choosing a threshold equal to the tent map parameter or by applying a periodical sampling on the tent map values and by choosing a threshold equal to 0.5. Both generators are supported theoretically as well as experimental. Additionally, thesis provides a discussion concerning the utilization based on image enciphering and on elements that could be considered as part of the secret key. NIST statistical test suite is applied on the pseudorandom enciphering sequences. Based upon the result from the NIST test suite, both generators are good from statistical point of view. Second part of the thesis presents a new approach to generating enciphering sequences using a very thought provoking enciphering method, running-key cipher and brings into discussion a debate concerning the meaning and the importance of redundancy and ergodicity in cryptography. Thesis comes with a new view of running-key method which permits to resume and extend it for ergodic sources other than Natural Languages in order to provide good quality key generators for cryptography. The method is elaborated first on NL and then extended to other ergodic sources i.e. on chaotic maps. The demonstration of this method is mainly based upon logistic map but thesis contains all the necessary elements so that the overall procedure can be applied to other chaotic maps (e.g. tent map). The new enciphering sequences obtained by means of the new running-key approach comply with fair dice model and the randomly chosen initial conditions of the logistic map (defining the enciphering sequence) can be part of the secret key.
Keyword(s): Criptografie -- Teză de doctorat ; Teoria informaţiei, Aplicaţii -- Teză de doctorat ; Haos (teoria sistemelor) -- Teză de doctorat
OPAC: See record in BC-UPB Web OPAC
Full Text: see files
Record created 2017-02-14, last modified 2017-02-14
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