At Asiacrypt'2001, Courtois, Finiasz and Sendrier proposed the first coding-based signature scheme which is also known as the CFS signature. The CFS signature is seen as one of the candidates of quantum immune signatures. In this letter, we show that the CFS signature is susceptible to both strong-key substitution attacks and weak-key substitution attacks. We also discuss potential countermeasures.

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Based on Tu-Deng's conjecture and the Tu-Deng function, in 2010, X. Tang et al. proposed a class of Boolean functions in even variables with optimal algebraic degree, very high nonlinearity and optimal algebraic immunity. In this corresponding, we consider the concatenation of Tang's function and another Boolean function, and study its cryptographic properties. With this idea, we propose a class of 1-resilient Boolean functions in odd variables with optimal algebraic degree, good nonlinearity and suboptimal algebraic immunity based on Tu-Deng's conjecture.

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Permutation polynomial based interleavers over integer rings have recently received attention for their excellent channel coding performance, elegant algebraic properties and simplicity of implementation. In this letter, it is shown that permutation polynomial based interleavers of practical interest is decomposed into linear permutation polynomials. Based on this observation, it is shown that permutation polynomial based interleavers as well as their inverses can be efficiently implemented.

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