As a hot topic in the cryptology, component design and security analysis of cryptographicalgorithmsplay 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 cryptographic 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 evenvariable RSBFs with maximum algebraic immunity(MAI) are studied. Firstly, we present a new construction class of evenvariable RSBFswith MAI, which has totally n/2 ? 1 different constructions. And then an improved construction which achieves both MAI and high nonlinearity is proposed.(2)SomeconstructionsofevenvariablebalancedRSBFswithMAIaregiven. Firstly,we present a new general construction of evenvariable balanced RSBFs with MAI. Thenas an example, an improved construction of 2mvariable balanced RSBFs with both MAIand high nonlinearity is proposed.(3) The enumeration of the balanced RSBFs is discussed. Based on some improvement and analysis of the solutions of the correlative equation system, the lower bound onthe number of prvariable balanced RSBFs is improved, where p is a prime. And then fora general odd n, a lower bound on the number of nvariable 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 relatedkeyrectangle attack is evaluated. Based on a linear transformation of the master key andthe allone differential of the round function, a relatedkey rectangle attack of the full40round 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 relatedkey rectangleattack.(2)ThesecurityofthefullroundHASVencryptionmodeagainstrelatedkeyrectangle attack is evaluated. Through the analysis of the two parallelline encryption structureandthekeyscheduleoftheHASVencryptionmode, arelatedkeyrectangledistinguisherof the full 100round HASV encryption mode is presented. The result shows that theHASV encryption mode is not immune to the relatedkey rectangle attack.(3) The resistance of HIGHT against integral attack is discussed. Through the theoretic deducibility and computer simulation, we point out and correct an error in the 12round integral distinguishers given by the HIGHT proposers. And then two new 17roundhigher order integral distinguishers are described. Based on which, we present an integralattack on 22round HIGHT in detail.(4) The resistance of Zodiac against integral attack is investigated deeply. Knownresults show that there are two 8round integral distinguishers of Zodiac. Firstly, by theanalysis of the equivalent structures and truncated differential with probability being 1,two new 9round integral distinguishers which are accordant formally are proposed. Thenthe integral attacks are applied to Zodiac with different rounds. Particularly, an integralattack on the full 16round Zodiac192 is presented. Additionally, the 9round integraldistinguishers of Zodiac are extended to the higher order integral distinguishers. Especially, a full 16round higher order integral distinguisher of Zodiac is obtained. Based onthe 15round higher order integral distinguishers, the higher order integral attacks on thefull round Zodiac are presented.
