Component Design And Security Analysis Of Cryptographic Algorithms

As a hot topic in the cryptology, component design and security analysis of crypto-graphicalgorithmsplay significantroles inthedesign andanalysis ofsteamciphers, blockciphers and Hash functions. This thesis firstly investigates the design theory of Booleanfunctions,whichisanimportantcomponentofcryptographicalgorithms. Asamainstudy,the constructions and counts of rotation symmetric Boolean functions(RSBFs) with somecryptographic criteria are investigated. Then we discuss the analysis methods of crypto-graphic algorithms. Furthermore, the security of some familiar block ciphers includingsome block cipher components of Hash functions is evaluated.In the domain of the design theory of Boolean functions, the main contents and fruitsof this thesis are outlined as follows:(1) The constructions of even-variable RSBFs with maximum algebraic immunity(MAI) are studied. Firstly, we present a new construction class of even-variable RSBFswith MAI, which has totally n/2 ? 1 different constructions. And then an improved con-struction which achieves both MAI and high nonlinearity is proposed.(2)Someconstructionsofeven-variablebalancedRSBFswithMAIaregiven. Firstly,we present a new general construction of even-variable balanced RSBFs with MAI. Thenas an example, an improved construction of 2m-variable balanced RSBFs with both MAIand high nonlinearity is proposed.(3) The enumeration of the balanced RSBFs is discussed. Based on some improve-ment and analysis of the solutions of the correlative equation system, the lower bound onthe number of pr-variable balanced RSBFs is improved, where p is a prime. And then fora general odd n, a lower bound on the number of n-variable balanced RSBFs is providedfor the first time.In the domain of the security analysis of cryptographic algorithms, the main contentsand fruits of this thesis are outlined as follows:(1) The security of the full round ARIRANG encryption mode against related-keyrectangle attack is evaluated. Based on a linear transformation of the master key andthe all-one differential of the round function, a related-key rectangle attack of the full40-round ARIRANG encryption mode is presented. The result shows that the ARIRANG encryption mode as a block cipher is not safe, it is not immune to the related-key rectangleattack.(2)ThesecurityofthefullroundHAS-Vencryptionmodeagainstrelated-keyrectan-gle attack is evaluated. Through the analysis of the two parallel-line encryption structureandthekeyscheduleoftheHAS-Vencryptionmode, arelated-keyrectangledistinguisherof the full 100-round HAS-V encryption mode is presented. The result shows that theHAS-V encryption mode is not immune to the related-key rectangle attack.(3) The resistance of HIGHT against integral attack is discussed. Through the the-oretic deducibility and computer simulation, we point out and correct an error in the 12-round integral distinguishers given by the HIGHT proposers. And then two new 17-roundhigher order integral distinguishers are described. Based on which, we present an integralattack on 22-round HIGHT in detail.(4) The resistance of Zodiac against integral attack is investigated deeply. Knownresults show that there are two 8-round integral distinguishers of Zodiac. Firstly, by theanalysis of the equivalent structures and truncated differential with probability being 1,two new 9-round integral distinguishers which are accordant formally are proposed. Thenthe integral attacks are applied to Zodiac with different rounds. Particularly, an integralattack on the full 16-round Zodiac-192 is presented. Additionally, the 9-round integraldistinguishers of Zodiac are extended to the higher order integral distinguishers. Espe-cially, a full 16-round higher order integral distinguisher of Zodiac is obtained. Based onthe 15-round higher order integral distinguishers, the higher order integral attacks on thefull round Zodiac are presented.