Abstract:

(n,m) functions (or S-boxes) are the most basic components in symmetric cryptography,and its cryptographic properties determine some security of symmetric cryptography.Therefore,how to design and analyze (n,m) functions which satisfy various cryptographic properties is an important problem in the research on symmetric cryptography.With the development of the research on the side channel of symmetric cipher algorithms,there are some indicators in the aspect of (n,m) functions resisting differential power attack:the signal-to-noise ratio,transparency order and confusion coefficient.These indicators have gradually become the main indicators to measure the cryptographic properties of (n,m) functions cryptography,and have been applied to the design and analysis of block cipher S-boxes.In this paper,the research results of the signal-to-noise ratio (SNR),transparency order (TO) and confusion coefficient (CC) of (n,m) functions are summarized,including:(1) some relationships between the signal-to-noise ratio of (n,m) functions and the traditional cryptographic indicators;(2) some relationships between the transparency order of (n,m) functions and the traditional cryptographic property;some relationships between the transparency order of a Boolean function and its decomposition functions;few distributions of the transparency order of small variable balance functions;(3) the confusion coefficient of (n,m) function(s);(4)a comprehensive analysis of three indicators of a S-box in some public algorithms.Finally,the research prospect of these three indicators is given.

Key words: (n,m)functions, boolean functions, differential power analysis, transparency order, signal-to-noise ratio, confusion coefficient