The analysis of the number of fixed points in the key extending algorithm of RC4  

作　　者：XU KeJian HE Liang DAI ZhaoPeng FAN XiuBin 

机构地区：[1]College of Mathematics,Qingdao University,Qingdao 266071,China [2]State Key Laboratory of Information Security,Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Science China Mathematics》2008年第3期407-415,共9页中国科学：数学（英文版）

基　　金：the National Natural Science Foundation of China (Grant No. 10371061)

摘　　要：The probabilities of the state transitions of the initial value S 0 in the S table of RC4 are described by a kind of bistochastic matrices, and then a computational formula for such bistochastic matrices is given, by which the mathematical expectation of the number of fixed points in the key extending algorithm of RC4 is obtained. As a result, a statistical weakness of the key extending algorithm of RC4 is presented.The probabilities of the state transitions of the initial value So in the S table of RC4 are described by a kind of bistochastic matrices, and then a computational formula for such bistochastic matrices is given, by which the mathematical expectation of the number of fixed points in the key extending algorithm of RC4 is obtained. As a result, a statistical weakness of the key extending algorithm of RC4 is presented.

关 键 词：bistochastic matrix fixed point key extending algorithm RC4 state transition probability matrix 94A60 37C25 60J10 11A05 

分 类 号：O211[理学—概率论与数理统计]