Generalized Correlation Analysis of Vectorial Boolean Functions

We investigate the security of n-bit to m-bit vectorial Boolean functions in stream ciphers. Such stream ciphers have higher throughput than those using single-bit output Boolean functions. However, as shown by Zhang and Chan at Crypto 2000, linear approximations based on composing the vector output with any Boolean functions have higher bias than those based on the usual correlation attack. In this paper, we introduce a new approach for analyzing vector Boolean functions called generalized correlation analysis. It is based on approximate equations which are linear in the input x but of free degree in the output z = F(x). Based on experimental results, we observe that the new generalized correlation attack gives linear approximation with much higher bias than the Zhang-Chan and usual correlation attacks. Thus it can be more effective than previous methods. First, the complexity for computing the generalized nonlinearity for this new attack is reduced from 22m ×n+n to 22n . Second, we ...

• Type: Conference
• Year: 2007
• Where: FSE
• Authors: Claude Carlet, Khoongming Khoo, Chu-Wee Lim, Chuan-Wen Loe
• Keywords: Boolean Functions, Correlation Attack, Cryptography, FSE 2007, Generalized Correlation