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ПРИКЛАДНАЯ ДИСКРЕТНАЯ МАТЕМАТИКА

ПРИЛОЖЕНИЕ Сентябрь 2012

АННОТАЦИИ ДОКЛАДОВ НА АНГЛИЙСКОМ ЯЗЫКЕ

SECTION 1

Glusko K.L.,Titov S.S.ON THE SOLUTION OF QUADRATIC EQUATIONS

IN BINARY FIELDS.The article presents a fast method to nd the roots of quadratic

equations in nite elds of characteristic two.The generalized formula of semitrace is

obtained based on the construction of normal bases using a symmetric quadratic extension.

Edemskiy V.A.,Antonova O.V.LINEAR COMPLEXITY OF GENERALIZED

CYCLOTOMIC SEQUENCES WITH PERIOD 2

m

p

n

.A method for analyzing

the linear complexity of generalized cyclotomic sequences with period 2

m

p

n

is proposed.

It allows to pick out sequences with the high linear complexity.The linear complexity of

some sequences is computed on the base of classes of quadratic and biquadratic residues.

Zubkov A.M.,Kruglov V.I.ON DISTRIBUTIONS OF WEIGHT SPECTRA FOR

RANDOM LINEAR BINARY CODES.Weight spectra of random binary codes are

considered.Formulas for their means and variances are derived.

Zubkov A.M.,Serov A.A.ESTIMATES FOR THE NUMBER OF BOOLEAN

FUNCTIONS HAVING AFFINE OR QUADRATIC APPROXIMATIONS

WITH A GIVEN ACCURACY.Boolean functions having ane or quadratic ap-

proximations with a given accuracy are considered.Two-sided inequalities for the number

of such functions are obtained by means of inclusion-exclusion formula and estimates of

binomial distribution tails.

Kolomeec N.A.ON NONLINEARITY OF SOME BOOLEAN FUNCTIONS

WITH MAXIMAL ALGEBRAIC IMMUNITY.An estimation for nonlinearity of

Dalai's Boolean functions with maximal possible algebraic immunity in even number of

variables is given.It is proved that the estimation is achieved.

Kolcheva O.L.,Pankratova I.A.STATISTICAL INDEPENDENCE OF THE

BOOLEAN FUNCTION SUPERPOSITION.II.Let x,y,z be sets of dierent

Boolean variables,f(x;y),f

1

(x;y),f

2

(x;y),f

1

(x;y) f

2

(x;y) are Boolean functions being

statistically independent on the variables in x,and h(x

1

;x

2

;z),g(x) are any Boolean func-

tions.Then the function h(f

1

(x;y);f

2

(x;y);z) is statistically independent on the variables

in x;and the same is true for the function f(x;y) g(x) i f is balanced or g = const.

Kuznetsova A.S.,Safonov K.V.ON A COMBINATORIAL OPTIMIZATION

PROBLEM.A combinatorial optimization problem reduced to the building a symmetric

group in a format of minimal words is considered.There are solutions for some cases of the

problem.

Kjazhin S.N.,Fomichev V.M.STRUCTURAL PROPERTIES OF PRIMITIVE

SYSTEMS OF NATURAL NUMBERS.The primitive systems of natural numbers

are considered.The structure of their set is described,and the main properties of them

are installed.An algorithm for enumerating primitive systems of natural numbers not

exceeding a given number m is given.

Murin D.M.ABOUT THE NUMBERS OF THE INJECTIVE AND OF THE

SUPER-INCREASING VECTORS AND SOME PARTICULARITIES OF

128 Прикладная дискретная математика.Приложение

THE STRONG MODULAR MULTIPLICATION.The numbers of injective and

of super-increasing vectors appeared in knapsack cryptosystems are estimated.Besides,

it is shown that the set of increasing injective vectors is uniformly covered by the vectors

received from the super-increasing vectors through the strong modular multiplication and

the ascending ordering the vector elements.

Pichkur A.B.DESCRIPTION OF THE CLASS OF PERMUTATIONS REP-

RESENTED AS A PRODUCT OF TWO PERMUTATIONS WITH FIXED

NUMBER OF MOBILE POINTS.II.The complete description for the structure of

the class of permutations represented as the product of two permutations with q and q +t

mobile points is given in the case 1 6 t < N 2,2 6 q < (N t)=2 +1.

Pogorelov B.A.,Pudovkina M.A.ON COMBINATORIAL PROPERTIES OF THE

GROUP GENERATEDBYXL LAYERS.XSL block ciphers are based on Shannon's

principles of confusion and diusion.Round functions of these ciphers consist of round key

addition,a substitution and a linear transformation.In this paper,the combinatorial

properties of the group generated by the linear transformation and all round keys XOR-

addition are described.

Potapov V.N.ON ALMOST BALANCED BOOLEAN FUNCTIONS.A Boolean

function is called correlation-immune of degree n m if it takes the value 1 the same

number of times for each m-dimensional face of the hypercube.Balanced correlation-

immune function is called resilient.The almost balanced (or almost resilient) Boolean

function is dened as a function taking values 1 in a half or in a half plus or minus one of

vertices in each face.Here,some constructions of almost balanced functions are proposed,

some properties and a low bound for the number of these functions are established.

Pudovkina M.A.PROPERTIES OF X;S-LAYERS.Round functions of XSL block

ciphers consist of round key addition,a substitution and a linear transformation.In this

paper,the properties of the group generated by the substitution and all round keys XOR-

addition are described.

Smyshlyaev S.V.PERFECT BALANCEDNESS OF k-VALUED FUNCTIONS

AND GOLI

C CONDITION.Problems of k-valued logic generalizations of Golic Con-

jecture are considered.In the case of prime k,a number of results on correctness of k-valued

analogue of Golic Conjecture are obtained in certain subcases.Here,the full proof of in-

correctness of Golic Conjecture k-valued analogue in the case of composite k is presented.

Tokareva N.N.ON DECOMPOSITION OF A BOOLEAN FUNCTION INTO

SUM OF BENT FUNCTIONS.In the paper,some new results on bent sum decom-

position problem are discussed.It is proved that any Boolean function in n variables of

degree d 6 n=2 can be represented as the sum of not more than 2

2b

b

bent functions,

where b > d and b is the least integer such that 2bjn.

Tuzhilin M.E.LATIN SQUARES AND THEIR APPLICATIONS IN CRYP-

TOGRAPHY.This survey contains examples of applications of Latin squares in crypto-

graphy.

Frolova A.A.PROPERTY OF KASAMI BENT FUNCTIONS MULTIPLE

DERIVATIVES.It is proved that every bent function Kasami of degree t > 4 has (t 3)-

multiple non-zero derivative in the direction of any linearly independent vectors.

Аннотации докладов на английском языке 129

Sholomov L.A.DECOMPOSITION AND APPROXIMATION OF UNDERDE-

TERMINED DATA.For any underdetermined source,we consider its decomposition as

product of sources generating symbols 0,1,and the indenite symbol .Also,we learn best

approximate (in a prescribed sense) decomposition if correct decomposition is impossible.

We prove that the best approximate decomposition always exists (for the decomposable

source,it coincides with its decomposition),and it may be constructed by a polynomial

algorithm.For some problems relating to simplications and equivalent transformations of

decompositions,polynomial algorithms are oered.In closing,we state that any underde-

termined source has a decomposition in some more general form.

SECTION 2

Borisenko B.B.ON SIMILAR IMAGES SEARCH FOR DIGITAL WATER-

MARK DETECTION.An approach to similar images search is discussed.These images

have to satisfy some conditions and should be involved into education sample for the digital

watermark detection method based on the modied Hotelling's control chart.For searching

similar images,the author suggests to dene an image I to be more similar to an image I

1

than to an image I

2

if the hash of I is being nearer to the hash of I

1

than to the hash of I

2

according to a special metric.

Volgin A.V.,Ivanov A.V.A METHOD FOR SEED RECOVERINGIN THE LIN-

EAR GENERATOR OVER THE FINITE FIELD COMPLICATED BY MASK

ADDING.In the paper,a method for recovering the initial state of a linear generator com-

plicated by mask adding over the nite eld is oered.It is supposed that the additive

constant is unknown.

Glukhov M.M.-jr.ABOUT McEliece CRYPTOSYSTEM WITH ALGEBRAIC-

GEOMETRIC CODES.A new idea for designing the generator matrix of algebraic-

geometric codes in McEliece public-key cryptosystem is described.

Kamaeva A.A.TRUNCATED DIFFERENTIAL CHARACTERISTICS WITH

MINIMUMNUMBEROF ACTIVE BYTES FORSIMPLIFIEDWHIRLPOOL.

In this paper,a truncated dierential characteristics with minimum number of active bytes

is built to produce a collision for two reduced variants of the hash function Whirlpool:

with 1 and 2 rounds in the underlying block-cypher instead of 14.For the rst variant this

number equals 23,for the second one | 45.The probabilities of these characteristics are

maximal and equal 2

115

and 2

225

respectively.

Karpunin G.A.,Ermolaeva E.Z.ESTIMATES OF COLLISION RESISTANCE

COMPLEXITY FOR THE HASH FUNCTION RIPEMD.In 2005,Wang et al.

developed practical collision attacks on MD4 and RIPEMD hash functions.For RIPEMD

however,description of the attack has been presented only at ideological level,raising con-

cerns about the attack complexity claimed by the authors.X.Wang et al.stated that the

attack complexity is about 2

18

calls of compression function.In this paper,the omitted

details of the Wang attack on RIPEMD hash function are recovered and the single-step

message modication being the rst stage of this attack is implemented.The experiments

showed that the lower bound of the average complexity of the Wang's attack is greater

than 2

32;49

compression function calls.This estimation is signicantly higher than the one

stated in the Wang's paper.

Kovalev D.S.FPGA IMPLEMENTATION OF FAPKC-4.The paper presents

FPGA implementation of the latest version of Finite Automata Public Key Cryptosystem

130 Прикладная дискретная математика.Приложение

(FAPKC-4).The change of the throughput/hardware resources in comparison with the

basic cryptosystem (FAPKC) is investigated.These parameters for encryption/decryption

and digital signature is compared.A comparison of software and hardware implementations

of FAPKC-4 is given too.

Kogos K.G.,Fomichev V.M.CRYPTOGRAPHIC PROPERTIES OF BRANCH-

ING OF FUNCTIONS OF VECTOR SPACES.The report is devoted to branchings

of vector functions by the transformations having a given sign.Two approaches for using

them for the solution of systems of the nonlinear equations are discussed.

Koreneva A.M.,Fomichev V.M.CRYPTOGRAPHIC PROPERTIES OF BLOCK

CIPHERS BASED ON SHIFT REGISTERS.Cryptographic properties of register-

type block ciphers are studied.A way for designing a block encryption algorithm which

is based on shift register with length 4 over the set of binary 16-dimensional vectors is

investigated.

Loshkaryov S.D.DIFFERENTIAL EQUATIONS FOR HASH FUNCTIONS

FROM MDx-FAMILY.Creating a hash function cryptographers almost never prove

the selection of algorithmic blocks,the order of blocks.The hash-function HAVAL pro-

posed in 1992 is probably the only exception from this rule.This hash-function is con-

structed of blocks with specic properties such as strong independence of output bits,strong

avalanche eect,0-1 balance and others for Boolean functions,and the result hash func-

tion was proposed to be cryptographically strong.But time had shown that it is not true.

The papers,proposing other popular hash-functions such as MD4,MD5,SHA-0,SHA-1,

SHA-2,RIPEMD,GOST 34.11-94 and others,do not contain any proof for choice of ele-

ments.The algorithms used in construction of the hash-family of MDx contain constant

values,addition modulo 2

32

,rotations and primitive Boolean functions,chosen by the au-

thor.The cryptanalytics almost had not undertaken yet any attempts to prove the choice

of elements and if it is possible to change them to improve the cryptographic properties

of the algorithm.The main target of this paper is an analysis of how primitive Boolean

functions and rotations in uence the resistance of MD5 to dierential attacks.

Medvedev N.V.,Titov S.S.PROBLEMS OF ALMOST THRESHOLD SECRET

SHARING SCHEMES.The article deals with questions of information security,secret

sharing schemes.The problem of structure access realization by elliptic curves is discussed.

It is shown that one can realize secret sharing schemes with innite set of participants,

and the everywhere density of rational points is an analogue of perfectness.The problem

of unreplacible participants is considered.It is proved that the binary almost threshold

matroids without unreplacible participants are only matroids on Reed | Muller codes of

rst order.

Stolov E.L.MATHEMATICAL MODEL OF RANDOMGENERATOR BASED

ON TERNARY LOGIC.A mathematical model of physical generator that is based on

ternary logic is suggested.A few combinational units form a ring circuit.Each unit realizes

the same ternary logical function,and the circuit works as a chaotic generator.It is proved

that signal on output of any unit has uniform distribution.

Chikishev G.O.ONE-TIME RINGSIGNATURE INE-CASH.Ring signature allows

to specify a set of potential message signers instead of the actual signer.In this paper,a

new signature type is introduced | the one-time ring signature which allows to sign only

Аннотации докладов на английском языке 131

one message.The use of the same secret key twice reveals signer's identity.A protocol for

untraceable payments in Bitcoin e-cash system is also oered.

Shushuev G.I.OPTIMAL LINEAR APPROXIMATIONS FOR FEISTEL NET-

WORKS.ESTIMATION FOR THE RESISTANCE OF THE CIPHER SMS4

TO LINEAR CRYPTANALYSIS.An approach to obtain the best linear approxi-

mations for Feistel networks is proposed.The resistance of the cipher SMS4 to linear

cryptanalysis is investigated.

SECTION 3

Bernstein A.Yu.,Shilov N.V.\ROBOTS INSPACE"MULTIAGENT PROBLEM:

INFORMATION AND CRYPTOGRAPHIC ASPECTS.The multiagent problem

RinS (Robot in Space) considered here is formulated as follows:there are n > 2 autonomous

robots that need to agree without outside on distribution of shelters so that the straight

paths to the shelters will not intersect.The problemis closely related to geometry problems,

to the assignment problem in Graph Theory,to the convex hull problem in Combinatorial

Geometry,and to the path-planning problem in Articial Intelligence.This paper studies

two aspects of the problem|the informational and cryptographic ones:we prove that there

is no protocol that solves the RinS transferring a bounded number of bits,and we suggest

a protocol that allows robots to check whether their paths intersect,without revealing

additional information about their positions.

Brechka D.M.THE SEARCH FOR BRIDGES IN TAKE-GRANT SECURITY

MODEL.An algorithmfor searching bridges in protection graph for Take-Grant protection

model is described.The proof of its correctness is given.

Devyanin P.N.RESULTS OF REALIZATION CONDITIONS ANALYSIS FOR

INFORMATION FLOWS BY MEMORY IN ROSL DP-MODEL.The role DP-

model of Linux operating systems is considered.Conditions for realization in it of informa-

tion ows by memory are analysed.Some results of the analysis are presented.

Dolgikh A.N.MITIGATIONMETHODS FORILLEGAL INFORMATIONTIM-

INGFLOWS ONTHE SOCKET PROGRAMINTERFACE.Some ways for creat-

ing and implementing information timing ows based on sockets in GNU/Linux operating

systemare considered.Methods for mitigating thembased on the subjects blocking accesses

are proposed.

Kolegov D.N.HIERARCHICAL ROLE-BASED ACCESS CONTROL.A new ac-

cess control model is proposed.It is obtained by adding a hierarchy and type attributes to

elements of the RBAC model family.The allowed access rights of subjects to entities in it

are specied dependent on the values of the subject and entity attributes.

Kolegov D.N.,Hasanov B.S.\NETWORKSECURITYARCHITECTURES FUN-

DAMENTALS"LABORATORY PRACTICE IN CISCO PACKET TRACER.

The laboratory practice named in the title includes a number of dierent network security

labs (secure routing,secure switching,Internet perimeter protection,etc.),studying games

and network security projects.All practical studies are performed in Cisco Packet Tracer

emulator.

Sviridov P.Y.RESEARCH OF MANDATORY AND ROLE BASED ACCESS

CONTROL IN RSBAC SYSTEM.The main properties of the access management

132 Прикладная дискретная математика.Приложение

system RSBAC are described,and,for the realization of them in DP-model,an adequate

extension of the last is proposed.

Smolyaninov V.Y.SUFFICIENT CONDITIONS FOR ACCESS RIGHTS

STEALING IN DP-MODEL OF DATABASE MANAGEMENT SYSTEMS.

For a security theoretical analysis of database management systems,a DP-model of them

is suggested.Sucient conditions for stealing access rights in it are formulated.

Tkachenko N.O.BASED ON SELinux MANDATORY ACCESS CONTROL IN

DATABASE MANAGEMENT SYSTEM MySQL.The main steps for addition of

mandatory access control to relational database management system(RDBMS) MySQL are

proposed on the base of SELinux.These steps are the following:to set security contexts for

all entities of the RDBMS MySQL,to create the security policy module,to implement the

interaction of SELinux system and RDBMS MySQL hook functions,and to replace (fully

or partly) functions realizing discretionary access control in RDBMS with hook functions.

Chernov D.V.ATTRIBUTE BASED ACCESS CONTROL MODELS.The paper

presents reasons for necessity of more exible access control systems,like attribute based

access control (ABAC) system.General properties of ABAC are described.Several articles

which discuss how ABAC principles may be combined with other access control models and

how this models can be used are shown.

SECTION 4

Abrosimov M.B.,Komarov D.D.ON A COUNTEREXAMPLE TO A MINIMAL

VERTEX 1-EXTENSION OF STARLIKE TREES.For a given graph G with n

nodes,we say that graph G

is its vertex extension if for each vertex v of G

the subgraph

G

v contains graph G up to isomorphism.A graph G

is a minimal vertex extension of

the graph G if G

has n +1 nodes and there is no vertex extension with n +1 nodes of G

having fewer edges than G

.A tree is called starlike if it has exactly one node of degree

greater than two.We give a lower and upper bounds of the edge number of a minimal

vertex extension of a starlike tree and present trees for which these bounds are achieved.

Abrosimov M.B.,Kuznetsov N.A.ON THE NUMBER OF MINIMAL VERTEX

AND EDGE 1-EXTENSIONS OF CYCLES.For a given graph G with n nodes,we

say that graph G

is its vertex extension if for each vertex v of G

the subgraph G

v

contains graph G up to isomorphism.A graph G

is a minimal vertex extension of the

graph G if G

has n+1 nodes and there is no vertex extension with n+1 nodes of G having

fewer edges than G

.A graph G

is edge extension of graph G with n nodes if every graph

obtained by removing any edge from G

contains G.Edge extension of graph G with n

vertices is called minimal if among all edge extensions of graph G with n vertices it has the

minimum possible number of edges.We present the results of computational experiment

in which all minimal vertex and edge extensions of cycles up to 17 vertices were found.

Abrosimov M.B.,Modenova O.V.ON DIGRAPHS WITH A SMALL NUMBER

OF ARCS IN A MINIMAL 1-VERTEX EXTENSION.A graph G

nodes is vertex

extension of graph G with n nodes if every graph obtained by removing any vertex fromG

contains G.Vertex extension of graph G with n + 1 vertices is called minimal if among

all vertex extensions of graph G with n +1 vertices it has the minimum possible number

of edges.We study digraphs,whose minimal vertex extensions have a specied number

of additional arcs.A solution is given when the number of additional arcs is equal to one

or two.

Аннотации докладов на английском языке 133

Bondarenko P.P.ON MINIMAL EXTENSIONS OF SPECIAL TYPE BLACK-

WHITE PATHS.The circles and circuits with two vertices of one type and with other

vertices of another type are considered.Their minimal vertex and edge extensions are

studied.A connection between vertex extensions of some of such circuits and circles are

described.

Grunsky I.S.,Sapunov S.V.DETERMINISTIC LABELLING OF GRAPH VER-

TICES BY WALKING AGENT.This paper is devoted to the problem of on-line

labelling of graph vertices by walking agent so that all vertices in the neighbourhood of the

current vertex have dierent labels (i.e.deterministic labelling).This problem arises in

the navigation of mobile robots using topological maps of an environment.Here,a method

for deterministic labelling is proposed for an agent of two types diering by the size of the

observed neighbourhood of the current vertex.

Zharkova A.V.ON INDICES IN DYNAMIC SYSTEMOF BINARY VECTORS

ASSOCIATED WITH CYCLES ORIENTATIONS.An algorithm is proposed for

computation of indices in dynamic system of binary vectors associated with cycles orien-

tations.Evolutionary function of the system transforms vectors according to the following

rules:if both the initial component is 0 and the nal one is 1 they are replaced by 1 and 0

respectively,and all digrams 10 are replaced simultaneously by 01.Maximal index of a

subsystem formed by vectors of a given dimension is found.

Karmanova E.O.GRAPH CONGRUENCES:SOME COMBINATORIAL PRO-

PERTIES.A congruence relation of a path is an equivalence relation on the set of its

vertices all of whose classes are independent subsets.It is proved (theorem 1) that the

number of all congruence relations of a path with m edges equals to the number of all

equivalence relations on a m-element set.For a given connected graph G theorem 2 deter-

mines the length of the shortest path whose quotient-graph is G.

Magomedov A.M.ONINTERVAL EDGE -COLOURING.It is shown that there is a

(6,3)-biregular graph G = (X;Y;E),such that jXj +jY j = 33,with no interval 6-colourings,

and it is proved that the -colouring problem for bipartite multigraph G = (X;Y;E) is

NP-complete even if jXj = 2.

Magomedov T.A.MATCHINGS CONSTRUCTIONPROCEDURE.Conditions for

the existence of consecutive matchings in a bipartite graph are considered.

Sennikova L.I.,Kochkarov A.A.A PARALLEL ALGORITHMFOR SEARCHING

THE MINIMUMWEIGHT SPANNING TREE ON PREFRACTAL GRAPH.

Prefractal (fractal) graphs are models of complex self-similar structures.Hence,there is

a need in theoretical studies related to processing prefractal graph models.In view of a

large dimension of prefractal graphs,it is advisable to analyze these models on parallel

computational systems.In this paper,a parallel algorithm for searching the minimum

weight spanning tree of a prefractal graph is suggested.The parallelization of the algorithm

is based on the use of self-similarity properties of prefractal graphs.

Tatarinov E.A.GRAPHRECONSTRUCTIONBYAUTOMATATEAM.The pa-

per is devoted to analysis and modication of the Basic Algorithm for graph reconstruction

by agent,moving through graph edges,reading and modifying marks on the elements of

the graph.The algorithm uses an implicit enumeration of graph vertices.The modication

of the Basic Algorithm implements the reconstruction by automata team.In this case,the

134 Прикладная дискретная математика.Приложение

upper bound on the time complexity of the algorithm depends on the number of agents in

the automata team that perform the reconstruction.

SECTION 5

Bannykh A.G.MASS UPDATES ON MULTIDIMENSIONAL DATA.A problem

of ecient implementation of mass updates on multidimensional data is studied.For a

specic range of operations,a exible solution is proposed.The solution is applicable if

the data elements form an abelian group with some operator +.In that case,the proposed

method allows eective sum calculation and addition of the same value to the rectangular

areas.

Burlakov A.S.ANALYSIS OF ALGORITHMS OF EXECUTABLE FILES IN A

COMPUTER EMULATOR WITH A CHANGEABLE SPECIFICATION.The

report addresses to issues related to the description of the semantics of machine instructions.

This includes the analysis of expressions.It also discusses the methods for dynamic analysis

of applications executed within the built-in environment,such as tracing the progress of

the program and the construction of the graph of conditional transitions.

Bykova V.V.METHODS FORDESIGNINGFPT-ALGORITHMS ONGRAPHS

OF LIMITED TREEWIDTH.A method for designing FPT-algorithms by means of

dynamic programming based on the tree decomposition is investigated.Some problems

limiting the application of this method in practice are pointed.The problem of memory is

solved by using a binary tree decomposition of the separator,which reduces the theoretical

and the actual size of the dynamic programming tables.The technique of tables in the

language of relational algebra is described.

Glotov I.N.,Ovsyannikov S.V.,Trenkaev V.N.ABOUTDISTRIBUTEDDATABASE

MANAGEMENT SYSTEMBASED ON MariaDB SERVER.The paper presents

a distributed database management system (DDBMS) based on MariaDB server.The dis-

tinguishing feature of the DDBMS is a partition of MariaDB server.The MariaDB server

core and remote storage engine are placed on dierent machines and interact through a

network.

Zaikin O.S.,Posypkin M.A.,Semenov A.A.USING VOLUNTEER COMPUTA-

TION TO SOLVE CRYPTOGRAPHIC PROBLEMS.In the paper a technology

for solving cryptographic problems in volunteer computing projects is described.Authors

have implemented volunteer project SAT@home in which a successful cryptanalysis of the

keystream generator A5/1 was performed.

Mikhailov A.A.DELPHI OBJECT FILES ANALYSIS USINGSPECIFICATION

OF MACHINE COMMANDS SEMANTICS.The object Delphi les decompilation

problemis considered.The DCU format specication in Flext and disassembler DCU32INT

of the DCU format specication are made use for the Delphi compiled les analysis.Mech-

anism of the code semantics description for Intel x86 processors is developed.Using this

gives much of opportunities and makes the decompilation process more eective.

Saukh A.M.ANALYSIS OF SOME PROGRAM SOURCES SEMANTIC AS-

PECTS BASED ON FORMAL SYNTAX AND SEMANTICS SPECIFICA-

TIONS.In this work,the problem of syntax and semantic analysis of program sources

written in dierent languages is considered.The programming language is considered to

be specied by describing the lexis as a set of regular expressions and the syntax as a

Аннотации докладов на английском языке 135

context-free grammar with a set of controlling structures matching grammar rules.These

controlling structures manage abstract syntax tree building and other analysis tasks.All

these allow performing some sort of semantic analysis against the source written in the

specied language.

SECTION 6

Andreeva L.N.,Poteryaeva V.A.INVOLUTIONS NUMERATION.Two algorithms

for involutions numeration are proposed in this paper:an algorithm nding index of the

given involution and an algorithm constructing involution by means of the given index.

Zachesov Y.L.,Grishin A.M.ABSENCE OF DYNAMISM AT METHOD NFS.

At present,the number eld sieve (NFS) and a software package GGNFS are the primary

tools for solving the factorization problem.Extrapolation of the data complexity of the

algorithm NFS shows that it is impossible to apply this algorithm for factoring 768-bit or

more modules.This work compares the evaluation of labor-intensiveness of sub-exponential

algorithms of whole number factorization and evaluation of productivity of supercomputers

fromthe Top 500 list.The conclusion following fromthe comparison is that these algorithms

are now non-dynamic.

Filina M.V.,Zubkov A.M.EXACT COMPUTATION OF DISTRIBUTIONS BY

MEANS OF MARKOV CHAINS.The machinery of Markov chains may be used for

the exact computation of distributions of some statistics.Numerical results reveal some

unexpected dierences between exact and asymptotic distributions.

Medvedev A.V.BOOLEAN FUNCTION ABSOLUTE NONLINEARITY CAL-

CULATION ON GPU.The algorithm for calculating the absolute nonlinearity of

Boolean function on CUDA-enabled GPUs is proposed.Experiments showed that com-

putation on GPU is 106 times faster than on one core of CPU.

Semenov A.A.,Ignatiev A.S.ABOUT CONVERGENCE OF A HYBRID

SAT+ROBDD-DERIVATION.In the paper,the authors consider a new property of a

hybrid SAT+ROBDD-derivation.This property consists in a convergence with respect to

the number of paths to a terminal vertex"1"in a ROBDD which represents database of

con icts accumulated during the process of non-chronological DPLL.

Usatyuk V.S.THE IMPLEMENTATION OF THE PARALLEL ORTHOGO-

NALIZATION ALGORITHMS IN THE SHORTEST INTEGER LATTICES

BASIS PROBLEM.This article presents a way to signicantly increase the performance

of lattice basis reduction algorithms (hundredfold to three hundred times) by replacing re-

cursive orthogonalization Gram|Schmidt algorithmby parallel QRalgorithms.The paper

contains a comparison between implementation of serial column-major Gram | Schmidt

and parallel algorithms on NVIDIA CUDA GPU framework using Givens rotation,multi-

core CPU Intel Math Kernel library,and Householder transformation.

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