International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Chu-Wee Lim

Publications

Year
Venue
Title
2011
JOFC
2009
EPRINT
Extensions of the Cube Attack
At Crypto 2008, Shamir introduced a new algebraic attack called the cube attack, which allows us to solve black-box polynomials if we are able to tweak the inputs by varying an initialization vector. We offer a few extensions of this attack by applying it to Boolean functions for which we can find low-degree multiples. We then extend this to vectorial Boolean functions by finding relations with low-degree polynomials.
2007
FSE
2007
FSE
2007
EPRINT
On an Improved Correlation Analysis of Stream Ciphers Using Muti-Output Boolean Functions and the Related Generalized Notion of Nonlinearity
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 $z=F(x)$. The complexity for computing the generalized nonlinearity for this new attack is reduced from $2^{2^m \times n+n}$ to $2^{2n}$. Based on experimental results, we show that the new generalized correlation attack gives linear approximation with much higher bias than the Zhang-Chan and usual correlation attack. We confirm this with a theoretical upper bound for generalized nonlinearity, which is much lower than for the unrestricted nonlinearity (for Zhang-Chan's attack) and {\em a fortiori} for usual nonlinearity. We also prove a lower bound for generalized nonlinearity which allows us to construct vector Boolean functions with high generalized nonlinearity from bent and almost bent functions. We derive the generalized nonlinearity of some known secondary constructions for secure vector Boolean functions. Finally, we prove that if a vector Boolean function has high nonlinearity or even a high unrestricted nonlinearity, it cannot ensure that it will have high generalized nonlinearity.