Thesis (MSc)--Stellenbosch University, 2015 / ENGLISH ABSTRACT: Steganography is the art of hiding information inside a data host called the
cover. The amount of distortion caused by that embedding can influence the security of the steganographic system. By secrecy we mean the detectability of the existence of the secret in the cover, by parties other than the sender and the intended recipient. Crandall (1998) proposed that coding theory (in
particular the notion of covering radius) might be used to minimize embedding distortion in steganography. This thesis provides a study of that suggestion.
Firstly a method of constructing a steganographic schemes with small embedding radius is proposed by using a partition of the set of all covers into subsets indexed by the set of embeddable secrets, where embedding a secret s is a maximum likelihood decoding problem on the subset indexed by s. This converts the problem of finding a stego-scheme with small embedding radius to a coding theoretic problem. Bounds are given on the maximum amount of information that can be embedded. That raises the question of the relationship
between perfect codes and perfect steganographic schemes. We define a translation from perfect linear codes to steganographic schemes; the latter belong to the family of matrix embedding schemes, which arise from random linear codes. Finally, the capacity of a steganographic scheme with embedding constraint is investigated, as is the embedding efficiency to evaluate the performance of steganographic schemes. / AFRIKAANSE OPSOMMING: Steganografie is die kuns van die wegsteek van geheime inligting in 'n data gasheer genoem die dekking. Die hoeveelheid distorsie veroorsaak deur die inbedding kan die veiligheid van die steganografiese stelsel beïnvloed. Deur geheimhouding bedoel ons die opspoorbaarheid van die bestaan van die geheim in die dekking, deur ander as die sender en die bedoelde ontvanger partye. Crandall (1998) het voorgestel dat kodeerteorie (in besonder die idee
van dekking radius) kan gebruik word om inbedding distorsie te verminder in steganografie. Hierdie tesis bied 'n studie van daardie voorstel. Eerstens 'n metode van die bou van 'n steganografiese skema met 'n klein
inbedding radius word voorgestel deur die gebruik van 'n partisie van die versameling van alle dekkings in deelversamelings geïndekseer deur die versameling
van inbedbare geheime, waar inbedding 'n geheime s is 'n maksimum waarskynlikheid dekodering probleem op die deelversameling geïndekseer deur s. Dit vat die probleem van die vind van 'n stego-skema met klein inbedding radius na 'n kodering teoretiese probleem. Grense word gegee op die maksimum hoeveelheid inligting wat ingebed kan word. Dit bring op die vraag van die verhouding tussen perfekte kodes en perfekte steganographic skemas. Ons definieer 'n vertaling van perfekte lineêre kodes na steganographic skemas; laasgenoemde behoort aan die familie van matriks inbedding skemas, wat ontstaan as gevolg van ewekansige lineêre kodes. Laasten, die kapasiteit van 'n steganografiese skema met inbedding beperking word ondersoek, asook die inbedding doeltreffendheid om die prestasie van steganografiese skemas te evalueer.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/96997 |
| Date | 03 1900 |
| Creators | Ralaivaosaona, Tanjona Fiononana |
| Contributors | Sanders, J. W., Stellenbosch University. Faculty of Science. Department of Mathematical Sciences |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | x, 61 pages, illustrations |
| Rights | Stellenbosch University |
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