Security Analysis Of S Box Constructed By Linear Fractional Transformation

Analyzing from the mathematical point of view, an S-box is a multi-output Boolean func-tion, that is, a mapping from GF(2)nto GF(2)m. As the Substitution box(S-box) is generallythe only non-linear component of a block cipher, the security of a cipher is centralized on thecharacteristics of the S-box. The most important step of the encryption process is how to de-sign and construct the high performance S-box. The main factors for designing an S-box arenonlinearity, algebraic degree and distribution of number of terms, balance, orthogonality, andso on.In this paper, we ?rst refer to the related de?nitions and properties of multi-output Booleanfunctions. Moreover, from the theory of multi-output Boolean functions, we study the crypto-graphic properties of S-boxes of symmetric cryptographic algorithms. Finally, we represent alinear fractional transformation on a ?nite ?eld as a multi-output Boolean function, and use itto construct a new S-box. Also, we analyse the cryptographic properties of the S-box by thetheory of multi-output Boolean functions and programming methods, and compare the S-boxwith the S-boxes of current mainstream symmetric cryptographic algorithms.In Chapter 1, we recall some backgrounds of this paper.In Chapter 2, we recall the theory of multi-output Boolean functions.In Chapter 3, we recall the design criteria of an S-box in a block cipher.In Chapter 4, we represent a linear fractional transformation on a ?nite ?eld as a multi-output Boolean function, use it to construct a new S-box, analyse the cryptographic propertiesof the S-box by code programming, and compare it with the S-boxes of current mainstreamsymmetric cryptographic algorithms.