Fast Algebraic Attacks and Decomposition of Symmetric Boolean Functions

Algebraic and fast algebraic attacks are power tools to analyze stream ciphers. A class of symmetric Boolean functions with maximum algebraic immunity were found vulnerable to fast algebraic attacks at EUROCRYPT'06. Recently, the notion of AAR (algebraic attack resistant) functions was introduced as a unified measure of protection against both classical algebraic and fast algebraic attacks. In this correspondence, we first give a decomposition of symmetric Boolean functions, then we show that almost all symmetric Boolean functions, including these functions with good algebraic immunity, behave badly against fast algebraic attacks, and we also prove that no symmetric Boolean functions are AAR functions. Besides, we improve the relations between algebraic degree and algebraic immunity of symmetric Boolean functions.Comment: 13 pages, submitted to IEEE Transactions on Information Theor

Constructing a Ternary FCSR with a Given Connection Integer

FCSRs have been proposed as an alternative to LFSRs for the design of stream ciphers. In 2009, a new ring representation of FCSRs was presented. This new representation preserves the statistical properties and circumvents the weaknesses of the Fibonacci and the Galois FCSRs. Moreover an extension of the ring FCSRs called ternary FCSRs has been proposed. They are suitable for hardware and software implementations of FCSRs. In this paper, we show a method of constructing a ternary FCSR with a given connection integer for hardware implementation. The construction is simple and convenient. And the ternary FCSRs we get are able to meet the hardware criteria

Non-Interactive and Information-Theoretic Secure Publicly Verifiable Secret Sharing

A publicly verifiable secret sharing scheme is more applicable than a verifiable secret sharing because of the property that the validity of the shares distributed by the dealer can be verified by any party. In this paper, we construct a non-interactive and information-theoretic publicly verifiable secret sharing by a computationally binding and unconditionally hiding commitment scheme and zero-knowledge proof of knowledge

Perfectly Hiding Commitment Scheme with Two-Round from Any One-Way Permutation

Commitment schemes are arguably among the most important and useful primitives in cryptography. According to the computational power of receivers, commitments can be classified into three possible types: {\it computational hiding commitments, statistically hiding commitments} and {\it perfect computational commitments}. The fist commitment with constant rounds had been constructed from any one-way functions in last centuries, and the second with non-constant rounds were constructed from any one-way functions in FOCS2006, STOC2006 and STOC2007 respectively, furthermore, the lower bound of round complexity of statistically hiding commitments has been proven to be $\frac{n}{logn}$ rounds under the existence of one-way function. Perfectly hiding commitments implies statistically hiding, hence, it is also infeasible to construct a practically perfectly hiding commitments with constant rounds under the existence of one-way function. In order to construct a perfectly hiding commitments with constant rounds, we have to relax the assumption that one-way functions exist. In this paper, we will construct a practically perfectly hiding commitment with two-round from any one-way permutation. To the best of our knowledge, these are the best results so far