Modern Cryptography Primer: Theoretical Foundations and Practical Applications

246 Pages·2013·6.79 MB·English

by  Czesław Kościelny

Czesław Kościelny · Mirosław Kurkowski
Marian Srebrny
Modern
Cryptography
Primer
Theoretical Foundations
and Practical Applications
Modern Cryptography Primer
Czesław Kos´cielny (cid:2) Mirosław Kurkowski (cid:2)
Marian Srebrny
Modern
Cryptography
Primer
Theoretical Foundations
and Practical Applications
CzesławKos´cielny MarianSrebrny
FacultyofInformationTechnology InstituteofComputerScience
WrocławSchoolofInformationTechnology PolishAcademyofSciences
Wrocław,Poland Warsaw,Poland
and
MirosławKurkowski
SectionofInformatics
Inst.ofComputerandInformationSciences
UniversityofCommerce
CzestochowaUniversityofTechnology
Kielce,Poland
Czestochowa,Poland
and
EuropeanUniversityofInformation
TechnologyandEconomics
Warsaw,Poland
ISBN978-3-642-41385-8 ISBN978-3-642-41386-5(eBook)
DOI10.1007/978-3-642-41386-5
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2013955235
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Preface
Forcenturies,theneedtoensureconfidentialityofsomegatheredortransmittedin-
formationgotalotofattentioninvariouspoliticalormilitarycontexts.Nowadays,
in the era of a general necessity for privacy, and the conscious awareness of one’s
rightstoit,cryptographyisfoundusefulin awiderangeof practicalapplications.
Forthemostpart,itisusedforsecuringconfidentialityininterpersonalcomputer-
izedcommunication.Theturnofthe21stcenturyissometimescalledtheInternet
age,computerera;communicationtakesplaceinstantlyandwithouthindrance.Ob-
viously,noonecanimaginethefunctioningofvarioustypesofcommunicationand
telecommunicationnetworkswithouttheappropriatesecuritymeasuresagainstun-
desirablelisteninginonourinformation.
Modern cryptography would not exist without solid mathematical foundations,
especiallyinnumbertheory.Therecentandmostadvancedsecurityalgorithmsare
builtonsucharithmeticconstructsasintegerarithmeticdivisibility,moduloopera-
tions,primenumbers,ortheEulerfunction.
Today’s societies depend to a large extent on computers which process huge
amounts of information, often transferred via telecommunication networks, and
stored in databases. This information often needs adequate security protection
against being read by unauthorized users of computer systems and networks, par-
ticularly illegal users. Cryptography provides economical means that enable this
protection.Theexpertsincryptographyworkonmoreandmoreefficientmethods
of ensuring the secrecy of information and electronic documents which require it.
Strikingadvancesintheproliferationofelectronicdatastorage,linkage,andtrans-
missionhavecreatedsignificantnewchallengesinmaintainingconfidentialityand
developingadequatemethodsofauthentication.Theambitionofcryptanalysisand
cryptanalystsistobreakthesecuritycodesandforgeencryptedmessagesinsucha
waythattheylookauthentic.
Untilquiterecently,cryptographywasappliedonlyintheareaofmilitaryforces
anddiplomacy.Thisisalsowhycryptographersusuallyworkedinagenciesdealing
withstatesecurity,andallresearchworkconcerningcryptography,aswellascrypt-
analysis, was classified. It was not until the late 1960s that a multinational group
ofscholars,whowerenotcontrolledbysecurityagencies,becameinterestedinthe
v
vi Preface
problemsofcryptologyandstartedtopublishtheirresearchpapersonthissubject,
thankstowhichcryptographicdataprotectionwasfoundusefulalsoinvariouscivil-
ianfields.Thenewparadigmrequiresthatthecryptographicalgorithmsbepublicly
known,whereasonlytheprivatekeysmustbesecret.Nowadays,thepublicaccess
tothealgorithmsistreatedasasafeguardoftheirsecurity,assurancethatthereare
noflawsdueeithertopoor,unprofessionalworkbytheirdesignersortodeliberate
insertionofso-calledhiddenbackdoors(e.g.,collectingcopiesofprivatekeys).
Cryptographicmethodsarethemostefficientwaysofsecureprotectionofmod-
ern telecommunication network users against computer break-ins, which have by
nowbecomeaplague.Thatiswhybusinesspromotestheuseofcryptographysince
a basic requirement for worldwide economic growth is the development of secure
worldwidecomputernetworksunderlyingtheinformationsocietyeconomicinfras-
tructure.Inthiscontext,possibleadministrativelimitationsontheuseofcryptogra-
phyareconsideredresponsibleforasubstantialdeclineinacountry’sattractiveness
intheeyesofforeigninvestors.Cryptographicsecuritymeansareinevitableinor-
dertoimprovetradingandlegalproceedingsintheelectroniceconomy,aswellas
toensureatleasttheminimumofcivilprivacyandfreedom.
The aim of this book is to introduce the currently most interesting and most
important issues of modern applied cryptography in the technological practice of
telecommunication networks, along with the necessary basic mathematics. Cryp-
tographyisanareaontheedgeofmathematicsandpracticalsoftwareengineering.
Likenoother,itcombinesimmense,challengingunsolvedmathematicalproblems
withtheissuesofauthenticuseinpracticalsecuritytoolsincurrentlydeployedvital
datacommunicationsystems.
Wepresentallthebestknownandmostoftenusedtechnologies,algorithmsand
protocols, and methods of their design and analysis. The algorithms are presented
in readable pseudocode; i.e., written in English with some mathematical or pro-
gramming symbols, or simple graphics and diagrams. We will not go into details
onfindingimplementationbugsormethodsofprogramengineeringdependingon
thefeaturesofaparticularprogrammingenvironment,specificationandimplemen-
tationinanyfavoriteprogramminglanguage.
We bring particular attention in this book to performance analysis of the pre-
sentedalgorithmsandprotocolsbecausesincethelate1980sefficiencyhasessen-
tially become the central concept to understanding modern cryptographic mecha-
nisms,theirusage,andmanyrelatedproblems,especiallytheproblemsofbreaking
thecodes.
There are many very good publications on the market devoted to cryptography
and/or its usage. However, only very few of them can serve as course textbooks.
Thematerialtheypresentseemstouseitherextensivelybroadortoonarrowfora
graduatecourse,oftentoomathematical,andthereforeverydifficultforthemajority
ofstudentreaderswithnodeepmathematicalbackground.
Thisbookiswrittenatthelevelofagraduatelecturecoursetextbookforstudents
ofanytechnicaluniversityintheEuropeanUnionorNorthAmerica.Asprerequi-
sitesitrequiresonlysomeverybasicelementarymathematicalexperienceinalge-
bra, number theory, probability, data structures, as well as the design and efficient
Preface vii
analysisofalgorithms.Thematerialpresentedinthebookcanconstituteaone-year
graduatecourse,aswellasprovidingmaterialforshortercoursesonselectedtopics
tobeusedwithouttheneedtosearchotherpartsofthebook.Eachchaptercontains
allthenecessarybackgroundinformationconcerningtheproblemsbeingdiscussed.
Selectedchapterscanconstituteareasonablebasisforfurtherstudiesofthesubject,
e.g.,intheformofseminarortermcreditpapers,etc.Thereferencesprovidedwill
definitelybeofhelpincompletingsuchtasks.Forthesamereason,thisbookcanbe
treatedasausefulsourceofinformationinthefieldofdataandnetworktransactions
securityforpractitionersandresearchersjustaftertheirstudies.
Today’s cryptography is a very broad and lively field. We are aware that many
areas need much broader treatment. For example, the elliptic curve algorithms,
quantumcryptography,secretsharing,andvariouscryptanalytictechniques.Cryp-
tographichashalgorithmsarelimitedinthisbooktosignalingthebasicapproaches
andchallenges,withnocoverageofthemostrecentveryinterestingadvances.These
areashavegotalotofattentioninthelastfewyears,withmanydifferentmethods
andtheirownchallenges.Thesetopicswillbecoveredinfulldetailinourfollow-up
textbooktoappearsoon.
Thisbookconsistsofninechaptersdiscussingtoday’sactualpracticeinapplied
cryptographyfromtheverybasicstostrongstate-of-the-artsecurityalgorithmsand
protocols.
Thefirstchapterintroducesthebasicconceptsofcryptography.Thegeneraldi-
agramofencryption/decryption,aswellasthenotionofacryptographicalgorithm
andthedefinitionofcryptographickeysarediscussed.Therulesforbuildingstrong
cryptographiccodesareintroduced.Thechapteralsopresentsthefundamentalno-
tionsoftheoreticalandpracticalcomputationalcomplexity,anddiscussesitsmean-
ing for determining the difficulty of breaking cryptosystems. Next, we introduce
codesknownfromhistorysuchasCaesar’sancientcode,andPlayfairandEnigma,
whichwereappliedduringtheWorldWars.
Modern cryptography would not exist without solid mathematical foundations,
thereforeinChap.2werecollectandpresentmathematicalconceptsandproperties
requiredforcontinuingthecourse.Elementsofthetheoryofalgebraicstructures,as
wellaselementsofnumbertheory,arepresented.Also,wepresentsimplearithmetic
algorithmsappliedincryptography.Thechapterendswithadiscussiononcurrently
appliedalgorithmsfortestingintegerprimality,andcomputationallyhardproblems
innumbertheory.
InChap.3themostimportantsymmetricciphersarepresented,amongthemthe
standardsofsymmetricencryptionappliedinwidespreadpracticetoday.TheDES
(Data Encryption Standard) algorithm, its modifications and modes of operation
are given and discussed in detail. A lot of attention is focused on the most recent
Americanstandardforsymmetriccipher,theAES(AdvancedEncryptionStandard)
algorithm.TheIDEAalgorithm,aswellasthealgorithmsoftheRCfamilyarepre-
sented. As an interesting detail illustrating the resistance of encryption algorithms
againstattemptstobreakthem,wepresenttheprocessoftheglobalcompetitionin
breakingRCalgorithms,andtheresults.
InChap.4thereaderwillfindexactdescriptionsofasymmetricalgorithms,be-
ginningwiththeDiffie-Hellmanscheme,throughtheElGamalalgorithm.Next,the
viii Preface
well known RSA algorithm, and various issues concerning unceasing attempts to
break it are discussed. An interesting detail is the discussion on the results of the
RSAfactorizationchallenge,illustratingthecryptographicpoweroftheRSAcode.
Chapter5presentsoneofthemostimportantmodernapplicationsofcryptogra-
phy,namelytheelectronicsignature.Thegeneralscheme,aswellasseveralofthe
currentlymostessentialandmostinterestingappliedalgorithmsforgenerationand
verificationofthevalidityofe-signaturearecovered.Wepresentvariousalgorithms
ofdigitalsignatureandhashfunctions.Wediscussthecurrentissuesconcerningthe
usageofthesefunctions,andtheirsecurity.
InChap.6thereaderwillfindtheexactdescriptionofthepopularcryptosystem
PGP (Pretty Good Privacy). The overall scheme of the system and the algorithms
usedinitaresurveyed.TheinstallationandtheusageofPGParedescribed,encryp-
tionandsigningdocuments(messages,e-mails,files)amongothers.Inthischapter,
the authors introduce other, non-commercial solutions enabling the application of
strongcryptographybyanycomputeruser.
Chapter 7 is devoted to the public key infrastructure as a solution enabling ap-
plicationoftheelectronicsignatureforbusinessandlegalproceedingsintheform
requiredbylegislationinmostcountries.Theroleoftheso-calledtrustedthirdparty
incontemporarysolutions,aswellastheissuesconcerningcertificationofcrypto-
graphickeys,arepresented.
Another important feature of cryptography in day-to-day reality is the crypto-
graphicprotocolsappliedofteninmassscaleinallkindsofcommunicationviacom-
puter networks, especially for entity authentication and preventing identity theft.
Thegoalstobeachievedbythecryptographicprotocols,aswellastheirexamples,
are presented. Issues and problems of their specification, design and application,
methods of complexity analysis as well as methods of verification of correctness,
andthesecurityofcryptographicprotocolsareintroducedandcoveredmorebroadly
thaninanyothertextbookavailablesofar.
InChap.9theremainingaspectsoftheapplicationofcryptographyindataand
transactionsecurityaretakenup.Theproblemsandsolutionsofpreservingthese-
crecy and privacy of electronic mail, as well as secure exchange of documents in
electronicformarediscussed.ThecommonlyappliedSSH(SecureSHell)andSSL
(SecureSocketLayer)protocolsarealsostudied.
Likeeverybook,oursissurelynotflawless.Incaseofanyerrors,mistakesorin-
accuraciesinthispublication,wewouldappreciateifthereadercouldkindlysubmit
[e-mail]ated.
In return, we promise an up-to-date list of corrections, a constantly revised corri-
gendum.
Our thanksfor helpand supportin various stages of the process of writingand
editing this book are due to many of our friends and collaborators, as well as our
students, audience and participants in lectures and seminars given by each of us.
Our special thanks must be given to Professor Leonard Bolc (1934–2013) of the
Institute of Computer Science of the Polish Academy of Sciences, without whose
kindandgentlebuttenaciouslyongoingsystematicencouragementthisbookwould
mostdefinitelyneverhavecomeintoexistence.Veryspecialacknowledgmentsgo
Preface ix
to Professor Andrzej Borzyszkowski for his fruitful cooperation on the early ver-
sions of the materials for the chapter on the security protocols, their specification
andverificationofcorrectness.SimilarlytoMaciejOrzechowski.Thethirdauthor
gratefullyacknowledgesmanyusefulconversationsanddiscussionswithProfessors
PawełMorawiecki,StanisławSpiez˙,andJerzyUrbanowicz(1951–2012).Thelatter
wasentirelyresponsiblefordraggingthethirdauthorinafriendlymannerintothe
worldofcryptologicresearchandpractice,andforeducatinghimonthefield’sspe-
cial beauty and problems, splendors and shadows. The first author acknowledges
support from Wrocław School of Information Technology. The second author ac-
knowledgessupportfromCzestochowaUniversityofTechnologyandtheEuropean
UniversityofInformationTechnologyandEconomics,Warsaw.Wewouldalsolike
to thank Kasia Grygiel, Gosia Berezowska, Ewelina Gajek and Janek Jay Halicki
for their help in the preparation of the English version of our book. Last but not
least,theauthorsthankthecopyeditorforhisexcellentcarefulwork,andSpringer’s
RonanNugentforsuccessfullyandnicelydrivingusthroughthewholeeditorialand
productionprocess.
Poland CzesławKos´cielny
August2013 MirosławKurkowski
MarianSrebrny
Contents
1 BasicConceptsandHistoricalOverview . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Encryption . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 AlgorithmsandKeys . . . . . . . . . . . . . . . . . . . 2
1.1.3 StrongCryptosystemsDesignPrinciples . . . . . . . . . 4
1.1.4 ComputationalComplexityofAlgorithms . . . . . . . . 5
1.2 SimpleStreamCiphers . . . . . . . . . . . . . . . . . . . . . . 10
1.2.1 CaesarCipher . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.2 XOREncryption(VernamCipher) . . . . . . . . . . . . 11
1.3 SimpleBlockCiphers . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.1 Permutations . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.2 Transpositions . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.3 ExampleofaSimpleTranspositionCipher . . . . . . . . 14
1.3.4 ExampleofaSubstitutionBlockCipher . . . . . . . . . 17
1.3.5 ExampleofaProductCipher . . . . . . . . . . . . . . . 17
1.3.6 GeneralizedSubstitutions—Bigrams . . . . . . . . . . . 18
1.3.7 PolyalphabeticSubstitutions. . . . . . . . . . . . . . . . 20
1.3.8 VigenèreCipher . . . . . . . . . . . . . . . . . . . . . . 20
1.4 WheelCipherandRotorMachines . . . . . . . . . . . . . . . . 21
1.4.1 WheelCipher . . . . . . . . . . . . . . . . . . . . . . . 21
1.4.2 RotorMachines . . . . . . . . . . . . . . . . . . . . . . 22
1.5 Enigma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.5.1 HistoryoftheEnigma . . . . . . . . . . . . . . . . . . . 24
1.5.2 ConstructionoftheEnigma . . . . . . . . . . . . . . . . 26
1.5.3 EnigmaOperation . . . . . . . . . . . . . . . . . . . . . 29
1.5.4 BreakingtheEnigmaCipher . . . . . . . . . . . . . . . 31
xi