Security

On the Immunity of Boolean Functions Against Fast Algebraic Attacks Using Bivariate Polynomial Representation

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Executive Summary

Boolean functions are frequently used in the design of stream ciphers, block ciphers and hash functions. One of the most vital roles in cryptography of Boolean functions is to be used as filter and combination generators of stream ciphers based on Linear Feedback Shift Registers (LFSR). In the last decade, algebraic and fast algebraic attacks are regarded as the most successful attacks on LFSR-based stream ciphers. Since the notion of algebraic immunity was introduced, the properties and constructions of Boolean functions with maximum algebraic immunity have been researched in a large number of papers. However, it is unclear whether these functions behave well against fast algebraic attacks. In this paper, the authors study the immunity of Boolean functions against fast algebraic attacks using bivariate polynomial representation.

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