Lai-Massey結(jié)構(gòu)平均差分概率和平均線性鏈概率的上界估計
doi: 10.11999/JEIT180196
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解放軍戰(zhàn)略支援部隊信息工程大學(xué) ??鄭州 ??450001
基金項目: 國家自然科學(xué)基金(61402523, 61572516, 61502532)
Upper Bound Estimation of Average Differential Probability and Average Linear Chains Probability of Lai-Massey Structure
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The Information Engineering University of PLA, Zhengzhou 450001, China
Funds: The National Natural Science Foundation of China (61402523, 61572516, 61502532)
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摘要: Lai-Massey結(jié)構(gòu)是由IDEA算法發(fā)展而來的一個分組密碼結(jié)構(gòu)，F(xiàn)OX系列密碼算法是該密碼結(jié)構(gòu)的代表。該文從差分概率關(guān)于獨立等概輪密鑰的平均概率上界和給定起點和終點的線性鏈的平均概率上界兩個角度出發(fā)，研究Lai-Massey 結(jié)構(gòu)的差分和線性可證明安全性。該文證明了2輪Lai-Massey結(jié)構(gòu)的非平凡差分對應(yīng)關(guān)于獨立等概的輪密鑰的平均概率
$ \le p{}_{\max }$ ；證明了當(dāng)Lai-Massey 結(jié)構(gòu)的F函數(shù)是正型置換時，輪數(shù)$r \ge 3$ 的非平凡差分對應(yīng)關(guān)于獨立等概的輪密鑰的平均概率$ \le p_{\max }^2$ 。針對給定起點和終點的線性鏈的平均概率上界，該文也獲得了類似的結(jié)論。Abstract: Lai-Massey structure is a block cipher structure developed from IDEA algorithm. FOX is the representative of this cipher structure. In this paper, the keys are assumed to be generated independently and uniform randomly, and then the provable security against differential and linear cryptanalysis of Lai-Massey structure is studied from two aspects: the upper bound of the average differential probability and the upper bound of the average linear chains probability with the given starting and ending points. This paper proves that when$r{\rm{ = }}2$ , the average differential probability$ \le p{}_{\max }$ . With the F function of the Lai-Massey structure is orthomorphism, this paper proves that when$r \ge 3$ , the average differential probability$ \le p_{\max }^2$ . A similar conclusion is obtained for the linear chains with a given starting and ending point. -
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