Cryptographic Properties Of Unsigned Ones Complement Addition

In this paper, it's studied the cryptographic properties of unsigned ones complement addition, with the aim of affording reliable theory for design and analysis of cipher algorithm. We first study the computation Walsh spectral of addition for real numbers and present the concrete computation formula of Walsh spectral of addition for real numbers. Then we import the conception of half Walsh spectrum and transform the study of unsigned ones complement addition Walsh spectrum computation to the study of the computation of half Walsh spectrum. The computation formula of half Walsh spectrum is given, followed with the computation formula of Walsh spectral for unsigned ones complement addition. Consequently, the problem of computing Walsh spectrum of unsigned ones complement addition is thoroughly solved. After that, according to the proposed formula, we study the properties of Walsh spectrum of unsigned ones complement addition and propose conditions for Walsh spectrum being zero. Then all possible values and typical methods of constructing these values are given. And the recording problem of Walsh spectrum is discussed; the structures and numbers of the greater Walsh spectrum points are proposed. All of the above results will help us in further understanding and applying the unsigned ones complement addition.At last, it's studied the consistency of unsigned ones complement addition with bit-wise exclusive-OR and addition modulo 2". The formula of consistency probability is proposed. It's revealed that the consistency probability of unsigned ones complement addition with bit-wise exclusive-OR is very greater than the ideal value 2~", though it is very small, and the consistency probability of unsigned ones complement addition with addition modulo 2" is 2/3 approximately, hence it is very large.