Speeding Up the GVW Algorithm via a Substituting Method

Journal of Systems Science and Complexity - The GVW algorithm is an efficient signature-based algorithm for computing Gröbner bases. In this paper, the authors consider the implementation of...     

On implementing the symbolic preprocessing function over Boolean polynomial rings in Gröbner basis algorithms using linear algebra

Some techniques using linear algebra was introduced by Faugère in F4 to speed up the reduction process during Gr?bner basis computations.These techniques can also be used in fast implementations of F5 and some other signature-based Gr?bner basis algorithms.When these techniques are applied,a very important step is constructing matrices from critical pairs and existing polynomials by the Symbolic Preprocessing function(given in F4).Since multiplications of monomials and polynomials are involved in the Symbolic Preprocessing function,this step can be very costly when the number of involved polynomials/monomials is huge.In this paper,multiplications of monomials and polynomials for a Boolean polynomial ring are investigated and a specific method of implementing the Symbolic Preprocessing function over Boolean polynomial rings is reported.Many examples have been tested by using this method,and the experimental data shows that the new method is very efficient.     

A New Upper Bound on the Order of Affine Sub-families of NFSRs

Journal of Systems Science and Complexity - Nonlinear feedback shift registers (NFSRs) are widely used as building blocks in the design of stream ciphers. Let NFSR(f) be an NFSR with the...     

Linearization of multi-valued nonlinear feedback shift registers

Nonlinear feedback shift registers (NFSRs) have been used in many stream ciphers for cryptographic security. The linearization of NFSRs is to describe their state transitions using some matrices. Such matrices are called their state transition matrices. Compared to extensive work on binary NFSRs, much less work has been done on multi-valued NFSRs. This paper uses a semi-tensor product approach to investigate the linearization of multi-valued NFSRs, by viewing them as logical networks. A new state transition matrix is found for a multi-valued NFSR, which can be simply computed from the truth table of its feedback function. The new state transition matrix is easier to compute and is more explicit than the existing results. Some properties of the state transition matrix are provided as well, which are helpful to theoretically analyze multi-valued NFSRs.     

THE CHARACTERISTIC PAIR AND TRACE EXPRESSION OF LR ARRAYS

In this paper, the concept of characteristic pair of linear recurring (or LR inshort) arrays is introduced. A decomposition of the linear space consisting of LR arraysand trace expressions of LR arrays is showed.     

AN APPROACH TOWARDS THE IMPLEMENTATION OF CHARACTERISTIC SET METHOD

1.IntroductionInthiscentury,theinventionofcomputerhasbroughtustoanewrevolutionera:weevencouldnotimaginewhattheworldwouldlooklikewithoutcomputer.Nowadays,wehavegottenusedtolettingcomputerhelpustodoinformationsearching,wordprocessing,complicatedcomputationsandsoon.Buthowaboutthementalworkmechanization,i.e.askingcomputertodomelltalworkforussuchasreasoning?MathematicsmechanizationisanewresearchfieldinitiatedbyProfessorWuWentsUnll]taChinesemathematician.Itisanalgebraicapproachratherthanalogicapp…     

A Note on Rotation Symmetric S-boxes

This paper is twofold. The first is devoted to study a class of quadratic rotation symmetric S-boxes(RSSBs) which was presented by Gao G, et al., Constructions of quadratic and cubic rotation symmetric bent functions, IEEE Transactions on Information Theory, vol. 58, no. 7, pp. 4908 –4913, 2012, by decomposing a class of cubic rotation symmetric bent functions. The authors obtain its nonlinearity and differential uniformity of such class of S-boxes. In particular, the compositional inversion of the class of rotation symmetric S-boxes is also presented. Then the authors introduce a steepest-descent-like search algorithm for the generation of RSSBs. The algorithm finds 5,6,7,8-bit RSSBs with very good cryptographic properties which can be applied in designing cryptographical algorithms.     

DCCS： A General-Purpose Distributed Cryptographic Computing System

0 Introduction Ageneral-purpose cryptographic computing system plays an important role in cryptography and becomes a hot topic step by step. In 1987, Lenstra[1] developed a distributed factoring system which made use of elec- tronic mail for the distribut…     

ENUMERATION OF LINEAR RECURRING m-ARRAYS

In this paper we prove that the number of translation equivalence classes of linearrecurring m-arrays over F_q with period(r,s)is(φ(rs))/(log_q(rs+1)),where φ is Euler function.     

SYNTHESES OF ARRAYS

In this paper,we present an algorithm to find a shortest linear recurringrelation generating a given finite array.