Algebraic Attack on Filter-Combiner Model Keystream Generators

Algebraic attack was applied to attack Filter-Combintr model keystreamgenerators. We proposed the technique of function composition to improve the model, and the improvedmodel can resist the algebraic attack. A new criterion for designing Filter-Combiner model was alsoproposed: the total length I. of Linear Finite State Machines used in the model should be largeenough and the degree d of Filter-Combiner function should be approximate [L/2].

Algebraic-Differential Attacks on a Family of Arithmetization-Oriented Symmetric Ciphers

Motivated by applications in advanced cryptographic protocols,research on arithmetizationoriented symmetric primitives has been rising in the field of symmetric cryptography in recent years.In this paper,the authors focus on on the collision attacks for a family of arithmetization-oriented symmetric ciphers GMiMCHash.The authors firstly enhance the algebraically controlled differential attacks proposed by introducing more variables.Then,combining algebraic attacks and differential attacks,the authors propose algebraic-differential attacks on GMi MCHash.This attack method is shown to be effective by experiments on toy versions of GMi MCHash.The authors further introduce some tricks to reduce the complexities of algebraic-differential attacks and improve the success probability of finding collisions.

On the 2~m-variable symmetric Boolean functions with maximum algebraic immunity

The properties of the 2m-variable symmetric Boolean functions with maximum al- gebraic immunity are studied in this paper. Their value vectors, algebraic normal forms, and algebraic degrees and weights are all obtained. At last, some necessary conditions for a symmetric Boolean function on even number variables to have maximum algebraic immunity are introduced.

Construction and enumeration of Boolean functions with maximum algebraic immunity

Algebraic immunity is a new cryptographic criterion proposed against algebraic attacks. In order to resist algebraic attacks, Boolean functions used in many stream ciphers should possess high algebraic immunity. This paper presents two main results to find balanced Boolean functions with maximum algebraic immunity. Through swapping the values of two bits, and then generalizing the result to swap some pairs of bits of the symmetric Boolean function constructed by Dalai, a new class of Boolean functions with maximum algebraic immunity are constructed. Enumeration of such functions is also n given. For a given function p（x） with deg（p（x）） 〈 [n/2], we give a method to construct functions in the form p（x）＋q（x） which achieve the maximum algebraic immunity, where every term with nonzero coefficient in the ANF of q（x） has degree no less than [n/2].

Some results on the algebraic immunity of Boolean functions

From the motivation of algebraic attacks on stream and block ciphers,the concept of algebraic immunity（AI） of a Boolean function was introduced and studied extensively.High algebraic immunity is a necessary condition for resisting algebraic attacks.In this paper,we give some lower bounds on the algebraic immunity of Boolean functions.The results are applied to give lower bounds on the AI of symmetric Boolean functions and rotation symmetric Boolean functions.Some balanced rotation symmetric Boolean functions with their AI near the maximum possible value「n/2」are constructed.

Construction of Balanced Rotation Symmetric Boolean Functions with Optimal Algebraic Immunity

Algebraic immunity is a new cryptographic criterion proposed against algebraic attacks. In order to resist algebraic attacks, Boolean functions used in many stream ciphers should possess high algebraic immunity. This paper presents one main result to find balanced rotation symmetric Boolean functions with maximum algebraic immunity. Through swapping the values of two orbits of rotation class of the majority function, a class of 4k＋l variable Boolean functions with maximum algebraic immu- nity is constructed. The function f（x） we construct always has terms of degree n-2 independence of what ever n is. And the nonlinearity off（x） is relatively good for large n.

On the construction of odd-variable boolean functions with optimal algebraic immunity

Algebraic immunity is an important cryptographic property of Boolean functions. In this paper, odd-variable balanced Boolean functions with optimal algebraic immunity are obtained by m-sequence and consequently, we get bases with special constructions of vector space. Furthermore, through swapping some vectors of these two bases, we establish all kinds of odd-variable balanced Boolean functions with optimal algebraic immunity.