Finite-dimensional and dynamic optimization in a distributed computing

environment

A.P. Afanasyev, Vladimir Voloshinov, M.A. Posypkin, A.S. Tarasov, Kurochkin I.I.

Center of Grid-technologies & Distributed Computing Institute for System Analysis RAS

5th International Conference"Distributed Computing and Grid-technologies in Science

and Education"

JINR, Dubna, 2012

General lines of our team researchesSoftware & distributed computing algorithms for scientific researches ✔ Software toolkit for distributed computing systems

(MathCloud, REST-services)✔ Toolkit for high-performance (parallel) global

optimization (BNB-solver, *-grid, DesktopGrid)✔ Decomposable optimization problems (e.g. with

block structure)✔ Unified optimization modeling REST-services (for

description, solving and processing of results) based on existing standards (AMPL)

✔ Problem-specific distributed applications #2

Decomposition of computing process

Mathematics, physics, chemistry, biology, ...Everywhere researches require integration of various existing domain-specific software

#3

Optimization Differential equations Statistical datamanipulation

Data processing Other

4

●Problems that we dealt with Optimization control problems with mixed constraints

Quasi-analytic solution of polynomial differential equations Global & discrete optimization:

knapsack problems, molecules clusters conformation (with Lennard-Jones & Morse potential models), charge distribution in DNA molecules, cryptanalysis of binary keys generator (A5/1)

Combinatorial geometry problems Modeling of telecommunication networks Physical experiments data processing:

Fine structure of carbon films deposited in thermonuclear reactor TOKAMAK T-10 by results of synchrotron X-ray scattering diffraction (in collaboration with National Research Centre, NRC "Kurchatov Institute")

Geodesic data processing (in collab. with "Vernadsky Institute of Geochemistry and Analytical Chemistry RAS")

Roots of algebraic equations Solution of mathematical programming problems (LP,

NLP, ...) Differential equation solution as explicit function of initial

values (for polynomial equations via distributed symbolic computing of Taylor series)

Symbolic computing resources Effective distributed compute of multivariate polynomial

(by generalized "Horner rule")

#5

Dynamic optimization. Optimal control problem: Required software resources

Search solution of ODE as Taylor series

#6

Quasi analytical solution of Cauchy problem

))((=)( txfdt

tdx00 )( xtx =

!

)()())((=)( 00

)(00

(1)0 s

tttxtttxxtxs

s −++−+

Symbolic equation for ODE solution derivatives

) )(()( txftx =

)()()(

))(()(

)()()())(()(

)()(

01

1)(

20)2(

00

0

0

xfxfx

xfxfdtdtx

xfxfxxfxf

dtdtx

xftx

sx

ss

s

x

=⋅∂

∂==

=⋅∂

∂==

=

−−

Polynomial approximation of solution as a finite segment of Taylor series with "controllable" error bound (depending of radius of convergence R)

#7

Effective for polynomial ODE

P1,i(x) - n-multivariate polynomial of m-order

))(()(

))(()(

))(()(

,1

2,12

1,11

txPdt

tdx

txPdt

tdx

txPdt

tdx

nn =

=

=

00 )( xtx =

n

RttCH

−< 0

2

0 0 2 1 0 3 2 0 ( 1) 0

( 1) 0 0

0

( , ) ( ) ( ) ( , , )2! !

( ) multvariate polynomial of of power ( 1)

( , , ) residual memberlength of seriessegment

i

m m i m i

i m i

t tx x t x T x t T x T H x T ki

T x n x i m iR x T kk

− − + −

+ −

= + + + + + +

− − + −

−−

#8

●A number of important results for quasi-periodical solutions of ODE

Classical Lorenz system

3213

31212

121

,),(

bxxxxxxxrxx

xxx

−=−−=

−=

σ

σ=10, r=28,b =8/3

Live demo in PPT

The approach was verified via distributed computing based on Maxima computing algebra system. A generalized Horner rule for multivariate polynomial has been implemented

#9

List of publicationshttp://dcs.isa.ru/drupal/ru/staff/apa/publicationsАфанасьев А.П., Дзюба С.М. О типичном поведении систем дифференциальных уравнений с периодической правой частью Дифференциальные уравнения, т.41, №11, 2005

Афанасьев А.П., Дзюба С.М., Репина Ю.Е. Об обобщенно-периодических решениях автономных дифференциальных включений Дифференциальные уравнения. 2009. Т. 45. №1 с.3-7

Афанасьев А.П., Тарасов А.С. Квазианалитическое решение систем дифференциальных уравнений с полиномиальными правыми частями Сб. трудов ИСА РАН «Проблемы вычислений в распределенной среде: распределенные приложения, коммуникационные системы, математические модели и оптимизация», / Под ред. С.В. Емельянова, А.П. Афанасьева – Т.14 - М.: КомКнига, 2006г

Афанасьев А.П., Продолжение траекторий в оптимальном управлении М.: Эдиториал УРСС, 2005. 263 с.

Афанасьев А.П., Дзюба С.М. Устойчивость по Пуассону в динамических и непрерывных периодических системах М.: Издательство ЛКИ, 2007.

●Distributed computing software/hardware layers

Computing resources

Middleware Globus Toolkit, Condor, gLite, MPI ...

REST-services, Zeroc Ice…

High level services and toolkits

Applications

#10

MathCloudREST-

servicesDesktop

Grid

BNB(Solver,

Grid,DG)

jLite

Middleware Globus Toolkit, Condor, gLite, MPI ...

REST-services, Zeroc Ice…

Computing resources

High level services and toolkits

Applications

jLite

MathCloudREST-

services

#11

●Software Toolkits (BnB-global & discrete opt.)

Desktop Grid

BNB(Solver,

Grid,DG)

BNB-Solver

#12

BNB-Solver provides a collection of C ++ classes for generic optimization algorithm schemes: branch-and-bound, heuristic methods, hybrid approaches.

Currently the following solvers are implemented using BNB-Solver framework: Branch-and-Bound for Knapsack problem Branch-and-Bound for Traveling Salesman Problem Interval and Lipschitzian optimization for NLP and MINLP Basin-Hopping method for unconstrained global optimization Deterministic multiobjective optimization

Supported platforms: Serial platform Shared memory platforms (POSIX threads) Distributed memory parallel clusters (MPI library)

BNB-Grid

#13

BNB-Grid framework organizes efficient cooperative work of different BNB-Solver library instances available via BNB-Service interfaceSupported platforms: Standalone computers Public supercomputers with batch

systems Service grid CEs Desktop grids

BNB-Grid Applications

#14

Molecular clusters

3-4 supercomputers (MVS-100 K from JSCC, SKIF-MGU and some less powerful clusters) were consolidated

Results showed that general purposed optimization algorithm can efficiently cope with hard optimization problems providing the sufficient computational resources are employed.

Deciphering of A5/1by reducing it to SAT problem (ISDCT of SB-RAS Semenov A.A. Zaikin O.S.) More than 1 week continuous computing with the number of

cores from 1000 to 6000 (MVS-100K, SKIF-MGU, BlueGene from MSU etc.)

3 test A5/1 problems were successfully deciphered

( ) min→−= ∑ ∑= +=

n

i

n

ij

ji xxvxF1 1

)()()(

Computing resources

MiddlewareDesktopGridServiceGrid (EDGeS 3G Bridge)

gLite, BOINC, XTremWeb

High level services and toolkits

Приложения

jLite

MathCloudREST-

services

#15

Software Toolkits (DesktopGrids)

BNB(Solver,

Grid,DG)

Desktop Grid

ISA RAS participates in DEGISCO (FP7 project) and is a coordinator of http://desktopgridfederation.org in Russia

http://desktopgridfederation.org/

16

DesktopGrid at Grid'2012 from our team18 July 2012Section Desktop grids (LIT conference hall)14.45-15.00 Using virtualization technology for the study of principles of operation of combined computing infrastructuresN.P. Khrapov

16.30-16.45 Implementation of the distributed evolutionary algorithms for BOINC platformM.A. Posypkin, T.E. Vlasov

16.45-17.00 A distributed branch and bound method for BOINC desktop gridsBo Tian, M.A. Posypkin

20 July 2012Plenary (LIT conference hall)

14.30-19.00 Tutorial (r. 407 LIT)Desktop grid computing (Eng/Rus)M.A. Posypkin, et al...

Optimization on Desktop Grids

#17

OPTIMA@home - a research project that uses Internet-connected computers to solve challenging large-scale optimization problems http://boinc.isa.ru/dcsdg/ More than 700 hosts connected Challenging 150-atomic Morse cluster was minimized

Project SAT@home – another research project aimed at solving hard combinatorial problems reduced to SAT problemshttp://sat.isa.ru/pdsat/ (ISDCT of SB-RAS Semenov A.A. Zaikin O.S.) More than 5500 hosts connected More than 3 Tflops sustainable performance Deciphered several hard A5/1 instances

Desktop Grid session – July 18, 14:30Plenary Talk July 20, 12.00: Russian chapter of international desktop grid federation: achievements, current state and prospective Desktop Grid Tutorial: July 20 14:30

http://boinc.isa.ru/dcsdg/http://sat.isa.ru/pdsat/

MathCloud software toolkit (RESTful-services)

Software platform for Service-Oriented Science providing tools for building, deployment, discovery

and integration of distributed scientific services

#18

Service AService B

Service CService D

Users

Applications

Services

Computing Resources

MathCloud: from software toolkit to cloud platform for building computing servicesO.V. Sukhoroslov @ Section clouds and grid, 17 July 2012

http://dcs.isa.ru/drupal/ru/mathcloud ● Fast "conversion" existing application (including

cluster and Grid ones) into RESTful-services● Visual programming of workflows available as new

composite RESTful-services● Workflows running system● REST-style, implemented as RESTfull-services

(REST, HTTP, JSON - JavaScript Object Notation)

Open source, http://code.google.com/p/websolve/ Apache License, Version 2.0

MathCloud features

http://dcs.isa.ru/drupal/ru/mathcloud

JAX-RS(Jersey)

Service-B

Service-A

Service-J (Python)

Service-G

Jobs/Results

WAITINGRUNNINGDONEERROR

ServerResource

ServiceResource

JobResource

FileResource

ServiceManager

JobManager

service.conf

Java Adapter

Console Adapter

Grid Adapter

Cluster Adapter

Java App

Console App

gLite (EGGE)

Port. Batch. Sys

Web-сервер(Jetty)

Service-C

MathCloud toolkit. Service container Everest.

MathCloud toolkit. Workflow Management System (WFMS).

Workfloweditor WUI(browser)

WFMSeditor

interfaceWFs as

a services

WF JSONdescriptor WF running

engine

WFMS service / server

RESTService

RESTService

RESTService

Methodology, unification, unified REST-interfaces for solvers and modeling tools for complete "modeling cycle" (input data-> solve problem -> processing solution data -> ...inputs -> more complex opt. algorithms -> processing results) ,REST-services JSON-descriptors "templates" and implementation with MathCloud toolkit

http://dcs.isa.ru/drupal/ru/development/mathcloud/optimizationServices

Supported by Federal special purpose program “Research and development in the priority fields of Russian science and technology complex in 2007-2013" (Agreement # 07.514.11.4024)

Unified optimization modeling REST-services

On development of distributed optimization modeling systems in the REST architectural style V.V. Voloshinov @ Section clouds and grid (LIT, r. 407), 17 July 2012

http://dcs.isa.ru/drupal/ru/development/mathcloud/optimizationServices Support optimization modeling approaches in the practice of scientific researches

● Mathematical programming problems' solvers (LP/MILP, NLP/MINLP) as REST-services

● Translators of optimization modeling languages (AMPL, A Modeling Language for Math. Programming) - as REST-services

● Integration of all above and others utilities (e.g. visualization) into workflows - a new domain-specific distributed applications (available as REST-services)

Support of scientific collaboration in Web2.0 style (e-Science) regarding "publication" of various solvers

REST-services for optimization modeling. General purposes

Urgency of "service-oriented" optimizationSince 2004, project Optimization Services, www.optimizationservices.org, under the aegis of COIN-OR (IBM) www.COIN-OR.org/projects/OS.xml

COIN solvers !!!AMPL, GAMS - !!!XML-RPC, WSDL, BPEL - ???

http://www.optimizationservices.org/http://www.COIN-OR.org/projects/OS.xml

Our approachhttp://dcs.isa.ru/drupal/ru/development/mathcloud/optimizationServices

REST - as an architectural styleRESTful-(web)-services - as a middle-wareHTTP as a transport protocol, JSON (JavaScript Object Notation) as a messages format (plain text), HTML+JavaScript for Web User Interface (WUI)

MathCloud (aka WebSolve, http://code.google.com/p/websolve/) - as a middleware and software toolkit

AMPL and GNU MathProg - optimization modeling and algorithms (high-level) description

AMPL-compatible solvers (LP/MILP, NLP, MINLP), GNU MathProg (LP/MILP, GLPK, GNU LP Kit)

Optimization modeling standards

Finite-dimension mathematical programming problems (LP/MILP, NLP/MINLP)

f o p , x minx

,

f i p , x0 i∈ I ,g j p , x =0 j∈J x∈Mp∈

x - variables,

p - parameters,

I, J - indices,

M - additional variables constraints (positive/negative, boolean, integer, ranges)Π - check constraints on parameters

∇ x f o p , x , ∇ x f i p , x i∈ I ,∇ x g j p , x j∈J ;∇ xx f o p , x ,∇ xx f i p , x i∈ I ,∇ xx g j p , x j∈J .

Numerical methods (solvers) also requires procedures for first and second derivatives (Jacobians & Hessians):

#26

The existing approach - usage of AML-system

AML - Algebraic Model Languages.

Common features:✔ Convenient (symbolic "TeX-like") description of object &

constraints functions ✔ Separation of "symbolic/abstract" models and numerical

data for multivariate computation (parameter sweeping)✔ Automatic differention (Jacobian & Hessian)✔ Support of "Lagrange formalism" - access to variables and

duals found as a result of solution✔ Unified open-source (even for "commercial" AMLs) API for

solvers' developers

#27

There are a number of AMLs

Incomplete list:

AMPL - A Modeling Language for Mathematical Programming, AT&T Bell Laboratories, D.M. Gay, Brian W. Kernighan, since 1980- , http://www.ampl.comхGAMS - General Algebraic Modeling System, International Bank for Reconstruction and Development, since 1980-x, http://www.gams.com

OPL - Optimization Programing Lang., IBM, ILOG CPLEX (LP, QP, ...), CP Optimizer, http://www-01.ibm.com/

GNU MathProg - "subset" of AMPL for GLPK, GNU LP Kit, Andrey Makhorin, MAI, since 2000, http://www.gnu.org/software/glpk/

Zimpl - since 2004, http://zimpl.zib.de/ (LP, MILP, NLP ?) Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)

#28

General scheme of AMLs usage

"Symbolic" opt. model

file *.mod

f o p , xminx

,

f i p , x0 i∈ I ,g j p , x=0 j∈J x∈M

Parameters' values

param p : ...;set I : ...;set J : ...;

file *.dat

AML-scriptmodel *.mod;data *.dat;option solver ipopt;solve;display _var, _dvar;printf ...

AML-translator ampl.exegams.exe.

Problem's data as a stub fileAMPL "stub", *.nl, *.sol

GAMS data exch., *.gdx

AML API

AMPL/Solver interfaceLibrary

GAMS....

SolversCPLEXLpsolveMinosKnitroSnoptGurobiMosek...

COIN-OPIpoptBonmin...

AMPL and GAMS - most popular de-facto standards

#29

GLPK

Set of "atomic" RESTful-optimization services

Atomic REST-services deployed in a single MathCloud Everest container

Prepare input data & processing output (solution):ampl-stub - generate AMPL-stub from model and data ampl-pre-opt - more complex AMPL-stub generation (model, data, AMPL- script)ampl-post-opt - processing solution (model, data, solution AMPL- format, AMPL-script)

Solver services (via LPSOLVE, IPOPT, BONMIN other AMPL-solvers):optimization-service-{command | cluster | grid} - to solve LP/MILP, NLP/MINLP problems presnted by their AMPL-stub, respectively on dedicated server, cluster, grid-node

Set of GLPK services (GLPK includes GNU MathProg translator):glpk-{command | cluster | grid} - full scheme of optimization: model, data, pre opt. GMP script -> solution -> post opt. GMP respectively on dedicated server, cluster, grid-node

#30

Web-interface of RESTful-optimization services

#31

Set of "composite" RESTful-optimization serviceshttp://dcs.isa.ru/drupal/ru/development/mathcloud/optimizationServicesComposite services are implemented as Workflows of atomic ones."Full optimization cycle" services (ampl-pre-opt, optimization-*, ampl-post-opt):ampl-optimization-service-{command | cluster | grid} - full scheme of AMPL-optimization: model, data, pre opt. AMPL script -> solution -> post opt. AMPL respectively by solvers on dedicated server, cluster, grid-nodemcl-control - "enhanced" AMPL-translator, enables running any (!) AMPL-algorithm in distributed mode; all stubs are sent to a pool off optimization-service-* and solutions are brought back to AMPL (and so on); Includes simple task manager (Python) for load balanceIn more details - in our section report On development of distributed optimization modeling systems in the REST architectural style V.V. Voloshinov @ Section clouds and grid (LIT, r. 407), 17 July 2012

http://dcs.isa.ru/drupal/ru/development/mathcloud/optimizationServices

Workflow for ampl-optimization-service-(command). MathCloud WF Editor

#33

Auto generated web-interface for composite ampl-optimization-service-(cluster)

#34

Web-interface "inherits" WUI of atomic services

Running progress (by WFMS)

Optimization in processing of experimental data

#35

Fine structure of carbon films deposited in thermonuclear reactor TOKAMAK T-10 by results of synchrotron X-ray scattering diffraction

Experimental data (on scattering angles)

=

2sin4 xq θ

λπ

Problem formulation (an idea)Modeling of scattering on amorphous uniform carbon structures (films, fullerenes, tubules, toroids, half-fragments etc.) massive parallel computing ==> optimization over every structure parts of weight to minimize discrepancy with experimental data

#36

Optimization identification of parameters

Z j (x , a ,b , A)=S exp(q j)−∑i=1

n

xi⋅S i(q j)−a⋅( f c(q j))2−A ∑

k=1

N impur

αk ( f k (q j))2−b ,( j=1: m)

Minimize error between experimental and model data (n ~ 1000, m ~ 500):

Additional constraints:

S exp q j−a⋅ f c q j2−A ∑

k=1

N impur

k f k q j 2−b−0.5 , j=1: m ,∑

i=1

n

x i+a=A , x i , a0

Three criteria (on variables x, a, b, A):

∑j=1

m

∣Z j(x , a , b , A)∣ →x ,a ,b , A minL1: (for Laplace distribution of experimental error)

maxj=1: m

∣Z j( x , a , b , A)∣ →x , a ,b , A minLinf: (for uniform distribution ...)

∑j=1

m

(Z j(x , a ,b , A))2 →

x ,a ,b , AminL2: (for Gaussian distribution ...)

For L1 и Linf criteria LP_SOLVE, (http://lpsolve.sourceforge.net)

For L2 - IPOPT (http://projects.coin-or.org/Ipopt)

MathCloud application as WF (Grid- & cluster- apps)

#38

Unexpected interesting result

#39

Dominance of toroidal spatial forms of carbon has been revealed (7 toroidal form over ~500 candidates for all criteria !)A. B. Kukushkin, V. S. Neverov, N. L. Marusov, I. B. Semenov, B. N. Kolbasov, V. V. Voloshinov, A. P. Afanasiev, A. S. Tarasov, V. G. Stankevich, Svechnikov "Few-nanometer-wide carbon toroids in the hydrocarbon films deposited in tokamak T-10" // Chemical Physics Letters (14 March 2011) doi:10.1016/j.cplett.2011.03.036

40

Geodesic data processing via convex NLP (QP)Restore earth surface by isolines series given as an input data.In collaboration with "Vernadsky Institute of Geochemistry and Analytical Chemistry RAS"

To find zy,x for the mesh (x,y) (heights for (x,y) coordinates) by "global" spline interpolation, i.e. minimization of

with the following constraints:zy,x = ck for (x,y) ∈ Ik (k=1:K) sets of isolines points with fixed heights Typical mesh dimensions Nx, Ny ~ 1000, 600

41

Geodesic data processing REST-serviceREST-service (secured access) on the base on AMPL translator and Ipopt (NLP) solver

Program toolkit NetMax for modeling of telecommunication networks for the maximization of the general traffic.

The analysis technique of the telecommunication networks, loading of networks revealing direct dependence on routing strategy is implemented.

Primary goals● Check of efficiency of strategy of routing;● Determination of vulnerabilities in a telecommunication network; ● Modeling on a failure for determination of reliability of corporate

networks; ● Execution of an estimation and the comparative analysis of various

strategies of routing;● Visualization of network graph.

NetMax – program toolkit of modeling of telecommunication networks

NetMax – toolkit

Revelation of network bottleneck

Use in high-performance computing (HPC) and desktop-gridThe toolkit is implemented in the addition (toolbox) to

Matlab environment. For hard computing tasks● the version for usage in multiprocessor systems

(MATLAB)● the version for the distributed computing (on BOINC

platform) is implemented.

NetMax – toolkit

Distributed simulation of telecommunication networks – NETMAX projectI.I. Kurochkin, A.I. Prun Section Desktop grids (LIT conference hall), 18 July 2012

45

Combinatorial geometry. Enumeration of irreducible graphsInspired by Tammes problem - optimal placement of N points on a sphere (to max min point-to-point distance)Well known hard global optimization problem (since XVII century, Isaac Newton, James Gregory)Irreducible graph is stable conformation of points on the sphere, i.e. corresponding local minima of energy of a molecule.Live demos http://dcs.isa.ru/taras/irreducible/seven1_int.htmlhttp://dcs.isa.ru/taras/irreducible/

A.S. Tarasov, Enumeration of the irreducible graphsfor the Tammes problem using distributed calculations20 July, 15.15-15.30, r.310, LIT

http://dcs.isa.ru/taras/irreducible/seven1_int.htmlhttp://dcs.isa.ru/taras/irreducible/

46

Scheme of Enumeration

Generation of suitable planar graphs Solving LP problem for each graph Solving NLP problem for each graph by Branch

and Bound method and LP problems.

We use: Own cluster Cluster FUTURO ot UTB (Brownsville, USA)

Thank you for your attention.

Questions?

To apply our experience and available softwarewe are looking for problems requiring optimization modeling.

And we are open for collaboration, http://dcs.isa.ru.

Instead of conclusion

http://dcs.isa.ru/

48

Задача оптимального управления со смешанными ограничениями

- целевая функция, отвечающая за качество управления

- управляемая динамическая система, записанная в форме системы ОДУ с функцией управления в правой части

- краевые условия

- множество допустимых управлений

J [u ]=∫0

T

F 0 x t , u t dt min

ẋ=F x t , u t

x 0 , x T ∈Xu t ∈U t

#48

BNB-Solver

BNB-Solver – объектно-ориентированная библиотека для решения задач оптимизации на многопроцессорных вычислительных комплексах.

Библиотека написана на Си++ и MPI, является переносимой, модульной и расширяемой.

BNB-Grid

Internet

Программный комплекс позволяет:

проводить расчеты на разнородных, географически удаленных вычислительных ресурсах;

решать различные задачи оптимизации точными и эвристическим методами;

проводить расчеты в течение длительного времени с контрольными точками и устойчивостью к сбоям.

АРХИТЕКТУРА

CSM

CEM

CEM

CEM

BNB-Solver

BNB-Solver

BNB-Solver

ICE

TCP/IP

MPI

52

BNB-GRID: ПОИСК КОНФИГУРАЦИИ АТОМОВ С МИНИМАЛЬНОЙ ЭНЕРГИЕЙ ВЗАИМОДЕЙСТВИЯ

( ) min→−= ∑ ∑= +=

n

i

n

ij

ji xxvxF1 1

)()()(

( ) ( )i jx x− - расстояние между частицами i и j;

)(rv - потенциал попарного взаимодействия;

( ) 61221rr

rvLJ −= - Lennard-Jones potential;

( ) ( )2; )1()1( −= −− rrM eerv ρρρ - Morse potential.

53

Потенциал Число атомов

Число начальных приближений

Nmax Общее время расчетов (мин)

Количество«попаданий»

Найденный минимум

Наилучший известный минимум

Леннард- Джонс

98 512 8192 43 8 -543.665361 -543.665361

Морзе 85 512 8192 63 3 -405.246158 -405.246158

Морзе 90 512 8192 91 74 -433.355380 -433.355380

Морзе 100 512 8192 96 98 -488.675685 -488.675685

Морзе 70 1024 8192 174 9 -292.462856 -292.462856

Морзе 75 1024 8192 205 2 -318.407330 -318.407330

Морзе 80 1024 8192 244 3 -340.811371 -340.811371

Морзе 85 1024 8192 188 5 -363.891261 -363.893075

Морзе 90 1024 8192 266 2 -388.401652 -388.401652

Морзе 100 1024 8192 232 8 -439.070547 -439.070547

Дзюгутов 50 1024 8192 175 2 -104.366189 -104.366189

Дзюгутов 100 1024 8192 175 1 -218.678229 -219.523265

Дзюгутов 100 1024 32758 371 1 -218.744395 -219.523265

6=ρ

6=ρ

6=ρ

14=ρ

14=ρ

14=ρ

14=ρ

14=ρ

14=ρ

54

Криптоанализ генераторов Генератор двоичной последовательности

(генератор) – дискретная функция : .

– входная (инициализирующая) последовательность

– выходная последовательность (ключевой поток)

Задача криптоанализа: по известному алгоритму генератора (алгоритму, реализующему ) и фрагменту выходной последовательности требуется найти инициализирующую последовательность.

{ } *}1,0{}1,0{:, →= ∈ nnNnn fff

nf

),...,( 1 nxxx =

),...,( 1 nxxx = ),...,( 1 myyy =

),...,( 1 myyy =

nf

55

BNB-GRID: КРИПТОАНАЛИЗ ГЕНЕРАТОРА А5/1

Решалась методом сведения к логическому уравнению. Далее решалась задача выполнимости (SAT).

Распределенная среда:1.MVS-100k (МСЦ РАН) 2.СКИФ-МГУ (МГУ им. Ломоносова)3.Blue-Gene (МГУ им. Ломоносова)4.Кластер РНЦ (РНЦ «Курчатовский Институт»)

Проводились длительные расчеты (неделя и более) на 1000-6000 вычислительных ядер одновременно. В результате были взломаны три тестовые задачи криптоанализа для генератора A5/1. На решение одной задачи было затрачивалось 2-4 суток расчетов.

Решение задач оптимизации в распределённой вычислительной среде А. П. Афанасьев ИСА РАН, МФТИSlide 2Slide 3Slide 4Задача оптимального управления: Требуемые ресурсыSlide 6Slide 7Slide 8Slide 9Программная инфраструктураMathCloud,BNB,jLiteSlide 12Slide 13Slide 14DesktopGridSlide 16Slide 17Slide 18MathCloud. Общее описание.MathCloud. КонтейнерMathCloud. СУСRESTopt-ideaRESTopt-genPurpCOIN OSxOur approachОпт. модельAMLAML-listОбщая схемаAtomic-RESToptWUIComposite-RESToptampl-opt-ser-WFampl-opt-srv-WUIСтрАн ПостановкаСтрАн Постановка 2Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Постановка задачи оптимального управления со смешанными ограничениямиBNB-SolverBNB-GridАРХИТЕКТУРАBNB-GRID: ПОИСК КОНФИГУРАЦИИ АТОМОВ С МИНИМАЛЬНОЙ ЭНЕРГИЕЙ ВЗАИМОДЕЙСТВИЯSlide 53Криптоанализ генераторовBNB-GRID: КРИПТОАНАЛИЗ ГЕНЕРАТОРА А5/1Slide 56Slide 57Slide 58