| On the construction of cryptographically strong Boolean functions with desirable trade-off |
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| 作者姓名： | REN Kui PARK Jaemin KIM Kwangjo |
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| 作者单位： | ECE Department，Worcester Polytechnic Institute，Worcester，MA 01609，USA，International Research Center for Information Security，Information and Communication University，Daejeon 305-714，Republic of Korea，International Research Center for Information Security，Information and Communication University，Daejeon 305-714，Republic of Korea |
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| 摘 要： | INTRODUCTION A variety of desirable criteria for functions have been identified: balancedness, local and global ava-lanche characteristics, high nonlinearity, etc. These properties are also very important for cryptographic purpose. Obtaining optimal tradeoffs among so many properties is hard. If we take into account more crite-ria, it is more difficult to generate Boolean functions satisfying those properties purely by constructive algebraic methods. How to construct Boolean func-tions …
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| 关 键 词： | 布尔函数 倾向序列 非线性特性 GAC 平衡性 |
On the construction of cryptographically strong boolean functions with desirable trade-off |
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| REN Kui,PARK Jaemin,KIM Kwangjo.On the construction of cryptographically strong Boolean functions with desirable trade-off[J].Journal of Zhejiang University Science,2005,6(5):358-364. |
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| Authors: | Ren Kui Park Jaemin Kim Kwangjo |
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| Institution: | (1) ECE Department, Worcester Polytechnic Institute, 01609 Worcester, MA, USA;(2) International Research Center for Information Security, Information and Communication University, 305-714 Daejeon, Republic of Korea |
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| Abstract: | This paper proposes a practical algorithm for systematically generating strong Boolean functions (f:GF(2)n→GF(2))with cryptographic meaning. This algorithm takes bent function as input and directly outputs the resulted Boolean function in terms of truth table sequence. This algorithm was used to develop two classes of balanced Boolean functions, one of which has very good cryptographic properties: nl(f)=22k-1-2k 2k-2 (n=2k), with the sum-of-squares avalanche characteristic off satisfying σf=24k 23k 2 23k 23k-2 and the absolute avalanche characteristic of △f satisfying △f=2k 1. This is the best result up to now compared to existing ones. Instead of bent sequences, starting from random Boolean functions was also tested in the algorithm. Experimental results showed that starting from bent sequences is highly superior to starting from random Boolean functions. |
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| Keywords: | Boolean functions Bent sequences Nonlinearity GAC PC Balancedness |
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