JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (11): 89-94.doi: 10.6040/j.issn.1671-9352.2.2014.212

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Matrix description and properties of global avalanche characteristics

YUAN Hong-bo, YANG Xiao-yuan, WEI Yue-chuan, LIU Long-fei, FAN Cun-yang   

  1. Key Laboratory of Network & Information Security of APF, Engineering University of APF, Xi'an 710086, Shaanxi, China
  • Received:2014-06-24 Revised:2014-10-17 Online:2014-11-20 Published:2014-11-25

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Abstract: The global avalanche characteristics matrix representation method was proposed by starting from the expression of global avalanche characteristics.And the same absolute value indicator of Boolean functions f(x) and f(x+α) were proved.The relationship between global avalanche characteristics (GAC) and Walsh spectrum was studied by matrix representation and the GAC absolute indicator's limits between a Boolean function and an affine functions. At last, the influence on GAC indicator by modifying sequence of a Boolean function was analyzed. In combination with hill-climbing algorithm, a large number of Boolean functions with good absolute value indicator were achieved via M-MF Bent functions.

Key words: hill-climbing algorithm, nonlinearity, global avalanche characteristics, matrix, Boolean functions

CLC Number: 

  • TP309
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