Probability Distribution and Recursive Formula of Difference between mod2n Sum and XOR over F2

doi:10.13190/jbupt.200701.85.zhangl

JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM ›› 2007, Vol. 30 ›› Issue (1): 85-89.doi: 10.13190/jbupt.200701.85.zhangl

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Probability Distribution and Recursive Formula of Difference between mod2n Sum and XOR over F2

ZHANG Long1, 2, WU Wen-ling3, WEN Qiao-yan1

1. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China;
2. College of Mathematics Science, Heilongjiang University, Harbin 150080, China; 3. State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing 100080, China

Received:2006-01-04 Revised:1900-01-01 Online:2007-03-30 Published:2007-03-30
Contact: ZHANG Long

Abstract

Abstract:

An efficient algorithm to calculate the probability distribution of XOR difference between single mod2n sum and XOR is presented. The complexity of this algorithm is O((n-1)/2), which is lower than that of Maximov’s result. For the case of multi-mod2n sum, a recursive formula to calculate the XOR difference between multi-mod2n sum and XOR is given.

Key words: cryptology, stream cipher, mod2n sum, XOR, probability distribution

CLC Number:

TN918.1

ZHANG Long1, 2, WU Wen-ling3, WEN Qiao-yan1. Probability Distribution and Recursive Formula of Difference between mod2n Sum and XOR over F2[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2007, 30(1): 85-89.

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Probability Distribution and Recursive Formula of Difference between mod2n Sum and XOR over F2

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