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INSIGHTRIVIERACADEMICJOURNAL,VOLUME6,NUMBER2,FALL2010COPYRIGHT2010BYDOUGLASSELENTPUBLISHEDBYRIVIERCOLLEGE,WITHPERMISSION1ISSN15599388ONLINEVERSION,ISSN15599396CDROMVERSIONABSTRACTADVANCEDENCRYPTIONSTANDARDAESISTHECURRENTSTANDARDFORSECRETKEYENCRYPTIONAESWASCREATEDBYTWOBELGIANCRYPTOGRAPHERS,VINCENTRIJMENANDJOANDAEMEN,REPLACINGTHEOLDDATAENCRYPTIONSTANDARDDESTHEFEDERALINFORMATIONPROCESSINGSTANDARD197USEDASTANDARDIZEDVERSIONOFTHEALGORITHMCALLEDRIJNDAELFORTHEADVANCEDENCRYPTIONSTANDARDTHEALGORITHMUSESACOMBINATIONOFEXCLUSIVEOROPERATIONSXOR,OCTETSUBSTITUTIONWITHANSBOX,ROWANDCOLUMNROTATIONS,ANDAMIXCOLUMNITWASSUCCESSFULBECAUSEITWASEASYTOIMPLEMENTANDCOULDRUNINAREASONABLEAMOUNTOFTIMEONAREGULARCOMPUTER1INTRODUCTIONONJANUARY2,1997THENATIONALINSTITUTEOFSTANDARDSANDTECHNOLOGYNISTHELDACONTESTFORANEWENCRYPTIONSTANDARDTHEPREVIOUSSTANDARD,DES,WASNOLONGERADEQUATEFORSECURITYITHADBEENTHESTANDARDSINCENOVEMBER23,1976COMPUTINGPOWERHADINCREASEDALOTSINCETHENANDTHEALGORITHMWASNOLONGERCONSIDEREDSAFEIN1998DESWASCRACKEDINLESSTHANTHREEDAYSBYASPECIALLYMADECOMPUTERCALLEDTHEDESCRACKERTHEDESCRACKERWASCREATEDBYTHEELECTRONICFRONTIERFOUNDATIONFORLESSTHAN250,000ANDWONTHERSADESCHALLENGEII21CURRENTALTERNATIVESTOANEWENCRYPTIONSTANDARDWERETRIPLEDES3DESANDINTERNATIONALDATAENCRYPTIONALGORITHMIDEATHEPROBLEMWASIDEAAND3DESWERETOOSLOWANDIDEAWASNOTFREETOIMPLEMENTDUETOPATENTSNISTWANTEDAFREEANDEASYTOIMPLEMENTALGORITHMTHATWOULDPROVIDEGOODSECURITYADDITIONALLYTHEYWANTEDTHEALGORITHMTOBEEFFICIENTANDFLEXIBLE2AFTERHOLDINGTHECONTESTFORTHREEYEARS,NISTCHOSEANALGORITHMCREATEDBYTWOBELGIANCOMPUTERSCIENTISTS,VINCENTRIJMENANDJOANDAEMENTHEYNAMEDTHEIRALGORITHMRIJNDAELAFTERTHEMSELVES2SUPPOSEDLYRIJNDAELCANONLYBEPRONOUNCEDCORRECTLYBYPEOPLEWHOCANSPEAKDUTCHANDTHECLOSESTENGLISHAPPROXIMATIONIS“RHINEDAHL”3ONNOVEMBER26,2001THEFEDERALINFORMATIONPROCESSINGSTANDARDSPUBLICATION197ANNOUNCEDASTANDARDIZEDFORMOFTHERIJNDAELALGORITHMASTHENEWSTANDARDFORENCRYPTIONTHISSTANDARDWASCALLEDADVANCEDENCRYPTIONSTANDARDANDISCURRENTLYSTILLTHESTANDARDFORENCRYPTION42RIJNDAELBLOCKANDKEYBEFOREAPPLYINGTHEALGORITHMTOTHEDATA,THEBLOCKANDKEYSIZESMUSTBEDETERMINEDAESALLOWSFORBLOCKSIZESOF128,168,192,224,AND256BITSAESALLOWSKEYSIZESOF128,192,AND256BITS2THESTANDARDENCRYPTIONUSESAES128WHEREBOTHTHEBLOCKANDKEYSIZEARE128BITSTHEBLOCKSIZEISCOMMONLYDENOTEDASNBANDTHEKEYSIZEISCOMMONLYDENOTEDASNKNBREFERSTOTHENUMBEROFCOLUMNSINTHEBLOCKWHEREEACHROWINTHECOLUMNCONSISTSOFFOURCELLSOF8BYTESEACHFORAES1285THEFOLLOWINGEXAMPLEWILLSHOWHOWDATAISBROKENUPINTOBLOCKSUSINGAES128MEANSTHATEACHBLOCKWILLCONSISTOF128BITSNBCANBECALCULATEDBYDIVIDING128BY32THE32COMESFROMTHEADVANCEDENCRYPTIONSTANDARDDOUGLASSELENTSTUDENT,MSPROGRAMINCOMPUTERSCIENCE,RIVIERCOLLEGEDOUGLASSELENT2NUMBEROFBYTESINEACHCOLUMNINTHISCASE,NBIS4THEORIGINALPLAINTEXTISSTOREDINBYTESINABLOCKFOREXAMPLE,THETEXT“THISISATEST”WILLBESTOREDINABLOCKASSHOWNBELOWINFIGURE1FIGURE1AES128BLOCKEXAMPLEEACHCHARACTERISSTOREDINACELLOFTHEBLOCKTHEBLANKCELLSSHOWNINTHEDIAGRAMARENOTREALLYBLANKASTHEYREPRESENTTHESPACESINTHETEXTDEPENDINGONHOWTHEALGORITHMISIMPLEMENTEDTHECHARACTERSMAYBESTOREDASINTEGERVALUES,HEXADECIMALVALUES,OREVENBINARYSTRINGSALLTHREEWAYSREPRESENTTHESAMEDATAMOSTDIAGRAMSSHOWTHEHEXADECIMALVALUES,HOWEVERINTEGERANDSTRINGMANIPULATIONISMUCHEASIERTODOWHENACTUALLYPROGRAMMINGAESFIGURE1SHOWSTHEVALUESASCHARACTERSFORDEMONSTRATIONPURPOSESTOSHOWHOWTHETEXTISSTOREDINTOTHEBLOCKTHEPLAINTEXTISSTOREDINTOBLOCKSCOLUMNBYCOLUMNANDBLOCKBYBLOCKUNTILALLTHEDATAISSTORED5INTHEEXAMPLEUSEDABOVETHEREWEREEXACTLY16CHARACTERSUSEDFORSIMPLICITYINORDERTOUSETHERIJNDAELALGORITHMTHEDATAMUSTBEAMULTIPLEOFTHEBLOCKSIZE,SINCEALLBLOCKSNEEDTOBECOMPLETEWHENTHEDATAISNOTAMULTIPLEOFTHEBLOCKSIZESOMEFORMOFPADDINGMUSTBEUSEDPADDINGISWHENEXTRABITSAREADDEDTOTHEORIGINALDATAONEFORMSOFPADDINGINCLUDESADDINGTHESAMEBYTESUNTILTHEDESIREDSIZEISREACHEDANOTHEROPTIONISPADDINGWITHALLZEROSANDHAVINGTHELASTBYTEREPRESENTTHENUMBEROFZEROSPADDINGWITHNULLCHARACTERSORRANDOMCHARACTERSAREALSOFORMSOFPADDINGTHATCANBEUSED6ONCEAFORMOFPADDINGISCHOSENTHEDATAISREPRESENTEDASSOMENUMBEROFCOMPLETEBLOCKSTHELASTTHINGNEEDEDBEFOREUSINGTHEALGORITHMISTHEKEYTHEKEYALSOKNOWNASTHECIPHERKEYISALSOTHESAMESIZEASTHEBLOCKINTHISEXAMPLEUNLIKEMOSTDATAANDTRANSFORMATIONSTHECIPHERKEYCANHAVEANYVALUESCHOSENBYTHEDESIGNERWITHNORESTRICTIONSASLONGASTHEKEYISTHECORRECTLENGTHTHEKEYISALSOSTOREDASABLOCKSIMILARTOTHEPLAINTEXT5WHENTHEPLAINTEXTDATAISSTOREDINTOBLOCKSANDTHEKEYISCHOSENTHERIJNDAELENCRYPTIONALGORITHMCANBEAPPLIEDSOMEOFTHEFOLLOWINGSTEPSCOULDBEDONEBEFORETHEENCRYPTIONPROCESSSTARTS,BUTFORSIMPLICITYTHEYWILLBEDISCUSSEDWHENTHEYARENEEDED3ADVANCEDENCRYPTIONSTANDARD3RIJNDAELROUNDSATABASICLEVELTHERIJNDAELALGORITHMUSESANUMBEROFROUNDSTOTRANSFORMTHEDATAFOREACHBLOCKTHENUMBEROFROUNDSUSEDIS6THEMAXIMUMOFNBANDNKFOLLOWINGFROMTHEPREVIOUSEXAMPLEOFAES128,THENUMBEROFROUNDSIS10THISISCALCULATEDFROM6PLUSTHEMAXIMUMOF4,4SINCENBANDNKAREBOTH4,THENUMBEROFROUNDSIS64102THEINITIALBLOCKALSOKNOWNASASTATEISADDEDTOANEXPANDEDKEYDERIVEDFROMTHEINITIALCIPHERKEYTHENTHEROUNDPROCESSINGOCCURSCONSISTINGOFOPERATIONSOFTHESBOX,SHIFTS,ANDAMIXCOLUMNTHERESULTSTATEISTHENADDEDTOTHENEXTEXPANDEDKEYTHISISDONEFORALLTENROUNDS,WITHTHEEXCEPTIONOFTHEMIXCOLUMNOPERATIONOFTHEFINALROUNDTHEFINALRESULTISTHEENCRYPTEDCIPHERBLOCK54RIJNDAELKEYEXPANSIONTHEORIGINALCIPHERKEYNEEDSTOBEEXPANDEDFROM16BYTESTO16R1BYTESINTHEEXAMPLE,THEREARETENROUNDSSOR10AROUNDKEYISNEEDEDAFTEREACHROUNDANDBEFORETHEFIRSTROUNDEACHROUNDKEYNEEDSTOBE16BYTESBECAUSETHEBLOCKSIZEIS16BYTESTHEREFORE,THECIPHERKEYNEEDSTOBEEXPANDEDFROM16BYTESTO16R1BYTESOR176BYTESTHEEXPANDEDKEYISTHENBROKENUPINTOROUNDKEYSROUNDKEYSAREADDEDTOTHECURRENTSTATEAFTEREACHROUNDANDBEFORETHEFIRSTROUNDTHEDETAILSONTHEKEYEXPANSIONALGORITHMARECOMPLEXANDWILLBESKIPPED45RIJNDAELSBOXTHEFIRSTSTEPTOAROUNDISTODOABYTEBYBYTESUBSTITUTIONWITHALOOKUPTABLECALLEDANSBOXANSBOXISAONETOONEMAPPINGFORALLBYTEVALUESFROM0TO255THESBOXISUSEDTOCHANGETHEORIGINALPLAINTEXTINBYTESTOCIPHERTEXTTHESBOXISSHOWNBELOWINFIGURE2ALLVALUESAREREPRESENTEDINHEXADECIMALNOTATIONTHISISHOWTHESBOXISCOMMONLYVIEWED5FIGURE2SBOXFROMHTTP/WWWSAMIAMORG/SBOXHTMLDOUGLASSELENT4FOREXAMPLEIFWEHADTHEPLAINTEXTOFONECHARACTER“D”ITWOULDTRANSLATETOTHEHEXADECIMALVALUEOF44BYUSINGANASCIILOOKUPTABLEWHENUSINGTHESBOXTHEFIRSTDIGITINHEXADECIMALREPRESENTSTHEROWSOFTHETABLEORTHEVALUESONTHELEFTSIDEGOINGDOWNTHESECONDDIGITREPRESENTSTHECOLUMNOFTHESBOX,WHICH,INTHISEXAMPLE,ISALSO4USINGTHESBOXWEFINDROWNUMBER4ANDCOLUMNNUMBER4ANDFINDTHATTHEHEXADECIMALVALUEINTHATCELLIS“1B”THISISHOWTHESBOXWORKSUSINGTHISMETHODWITHALLTHEPLAINTEXTWILLGENERATETHENEWHEXADECIMALVALUESTHATAREUSEDLATERINTHEALGORITHMTHEOBVIOUSQUESTIONISWHEREDIDTHESBOXCOMEFROMTHISGOESINTOMODULARARITHMETICANDAGALOISFIELDAGALOISFIELDISAFIELDWITHAFINITENUMBEROFELEMENTSTHEGALOISFIELDISALWAYSAFIELDTHATISAPOWEROFAPRIMEFOREACHPRIMENUMBERTHEREEXISTSEXACTLYONEGALOISFIELDTHENOTATIONTOREPRESENTAGALOISFIELDISGFP,WHEREPISTHEPRIMENUMBER8FORTHESBOX,THEFIELDGF28WASCHOSENTHEREARESEVERALREASONSTOWHYTHISFIELDWASCHOSENONEOBVIOUSREASONISTHATTHEPOWEROF8WASCHOSENBECAUSETHEREARE8BITSINABYTETHEPRIME2WASCHOSENBECAUSEBINARYISREPRESENTEDASTWOPOSSIBLEDIGITSA1ORA0INADDITIONARITHMETICISSIMPLETODOINTHISFIELDBECAUSEADDITIONANDSUBTRACTIONAREREDEFINEDASTHEEXCLUSIONORXOROPERATIONINVERTABILITYANDRESISTANCETOALGEBRAICATTACKSWEREALSOCONSIDEREDWHENFORMINGTHESBOX5TOACTUALLYGENERATETHESBOXFROMTHECHOSENFIELDREQUIRESMUCHMOREWORKCAREFULTHOUGHTWASPUTINTOTHETRANSFORMATIONFORSECURITYPURPOSESUSINGPLAINTEXTFORTHENEXTSTEPSOFTHEALGORITHMWOULDMAKEITMOREVULNERABLESOABYTESUBSTITUTIONINTHEFORMOFTHESBOXWASUSEDTHEORIGINALBYTESARETRANSFORMEDBYUSINGTHEMULTIPLICATIVEINVERSEANDANAFFINITYMATRIXSHOWNINFIGURE3TOMAKETHECIPHERTEXTRESISTANTTOALGEBRAICATTACKS7FIGURE3AFFINITYMATRIXFROMHTTP/WWWSAMIAMORG/SBOXHTMLFIGURE4MULTIPLICATIVEINVERSETABLEGF28FROMHTTP/WWWSAMIAMORG/GALOISHTMLINVERSE5ADVANCEDENCRYPTIONSTANDARDTOCALCULATETHEMULTIPLICATIVEINVERSEISCOMPLICATEDANDTOOMUCHOFADIGRESSIONTHEREFORE,AGIVENTABLEWILLBEUSEDINSTEADTHEFIELDOFALLTHEMULTIPLICATIVEINVERSESISSHOWNINFIGURE47USINGANEXAMPLEOFTHEHEXADECIMALVALUE“31”FROMTHEMULTIPLICATIVEINVERSETABLEWEGETTHEVALUE“45”FROMTHETABLETHISISTHEVALUEWEWILLUSEOURAFFINITYMATRIXISINBINARYTHEREFORETHENUMBERMUSTBEINBINARYASWELL45HIS01000101INBINARYANEASIERWAYTOVIEWTHEMATRIXMULTIPLICATIONISASPOLYNOMIALMULTIPLICATIONTHEVALUE01000101CANBEREPRESENTEDASTHEPOLYNOMIAL0X71X60X50X40X31X20X11THISCANBEREWRITTENANDSIMPLIFIEDASX6X21TAKINGTHEFIRSTROWOFTHEAFFINITYMATRIXWECANASSIGNEACHBITAVARIABLETHEREFORE,10001111CANBEREPRESENTEDASN0N1N2N3N4N5N6N7THISISGENERALIZEDTOALLTHEROWS,SOALLROWSCANBEREPRESENTEDWITHTHESAMEVARIABLESINTHESAMEORDERTODOTHEMULTIPLICATIONSTARTWITHTHEFIRSTROWANDSEEWHICHVARIABLESAREA1INTHEAFFINITYMATRIXSINCETHEFIRSTROWIS10001111,WEONLYHAVETOWORRYABOUTTHEVALUESN0N4N5N6N7NEXT,WELOOKATTHEPOLYNOMIALX6X21THEPOWERSOFTHISPOLYNOMIALAREWHATCORRESPONDTOTHESUBSCRIPTSOFNWHEREVERTHEPOWERINTHEPOLYNOMIALISALSOINTHESUBSCRIPTOFNWECANASSIGNAVALUEOF1OTHERWISEWEASSIGNTHEVALUEOF0THISMAKESN0N4N5N6N7CHANGETO10010AFURTHERSHORTCUTCANBETAKENTOIGNOREALL0SCOMPLETELYTHISCANBEDONEBECAUSEADDITIONINTHEFIELDGF28ISJUSTTHEXOROPERATIONTHEREFORE,ADDINGANEVENNUMBEROF1SWILLRESULTINAVALUEOF0ANDADDINGANODDNUMBEROF1SWILLRESULTINAVALUEOF1SHOWNBELOWINFIGURE5ISTHESIMPLIFIEDMATHEMATICSFORTHEENTIREAFFINETRANSFORMATION7ROW110001111N0N4N5N6N7100100ROW211000111N0N1N5N6N7100100ROW311100011N0N1N2N6N7101101ROW411110001N0N1N2N3N7101000ROW511111000N0N1N2N3N4101000ROW601111100N1N2N3N4N5010001ROW700111110N2N3N4N5N6100010ROW800011111N3N4N5N6N7000101FIGURE5SIMPLIFIEDMULTIPLICATIONEXAMPLEROWSAREMULTIPLIEDBYTHEPOLYNOMIALX6X21THERESULTOFTHEMULTIPLICATIONISTHEVECTOR00100101THEFINALSTEPTOTHETRANSFORMATIONISTOADDTHEVECTOR11000110TOOURVECTORTHISGIVESUSTHEFINALBINARYSTRINGOF11100011SINCEWEWANTTHELASTROWREPRESENTEDASTHEFIRSTBITWENEEDTOREVERSETHISSTRINGGIVINGUSTHENEWBINARYSTRINGOF11000111INHEXADECIMALTHISVALUEISC77WEARENOWFINISHEDTOKNOWTHATWEDIDEVERYTHINGRIGHTWELOOKBACKTOWHEREWESTARTEDWESTARTEDWITHTHEHEXADECIMALVALUEOF31FROMTHEORIGINALTABLEANDAFTERALLTHEWORKOBTAINEDTHEVALUEC7THEREFORE,IFWELOOKATTHESBOXVALUEFOR31,WESHOULDSEEC7ALLTHEVALUESINTHESBOXARECALCULATEDTHESAMEWAYWEDIDFOROUREXAMPLEUSINGTHEPREVIOUSEXAMPLE“THISISATEST”,THEFOLLOWINGBLOCKISARESULTOFTHESBOXSUBSTITUTIONANASCIILOOKUPTABLEWASALSOUSEDTOCONVERTTHECHARACTERVALUESINTOHEXADECIMALVALUESTHERESULTINGBLOCK/STATEHASALLVALUESSHOWNINHEXADECIMALNOTATIONNOTETHATKEYADDITIONWASNOTAPPLIEDIFTHISWEREAREALIMPLEMENTATIONTHEKEYADDITIONWOULDBEAPPLIEDTOTHESTATEBEFOREDOUGLASSELENT6THEFIRSTROUNDTHEREFORE,THESBOXSUBSTITUTIONWOULDBEDONEWITHTHESTATEAFTERTHEKEYADDITIONTHEBLOCKISSHOWNINFIGURE6FIGURE6BLOCK/STATEAFTERSBOXSUBSTITUTION6RIJNDAELSHIFTSTHENEXTSTEPINTHEROUNDISTOSHIFTTHEROWSOFTHESTATETHEROWSARESHIFTEDXNUMBEROFBYTESTOTHELEFTWHEREXISTHEROWNUMBERTHISMEANSROW0WILLNOTBESHIFTED,ROW1WILLBESHIFTED1BYTETOTHELEFT,ROW2WILLBESHIFTED2BYTESTOTHELEFT,ANDROW3WILLBESHIFTED3BYTESTOTHELEFTTHERESULTINGSTATEISSHOWNINFIGURE7BYAPPLYINGTHESHIFTSTOTHEPREVIOUSSTATENOTETHATTHESHIFTSDONOTAFFECTTHEBYTESUBSTITUTIONSOTHESHIFTINGANDSBOXOPERATIONSCOULDBEDONEINADIFFERENTORDER9FIGURE7BLOCK/STATEAFTERSHIFTING7ADVANCEDENCRYPTIONSTANDARD7RIJNDAELMIXCOLUMNAFTERAPPLYINGTHESBOXANDSHIFTSTOTHESTATETHEOPERATIONOFAMIXCOLUMNISUSEDTHEMIXCOLUMNLOOKUPTABLETAKESABYTEANDTRANSFORMSITINTOFOURBYTESTHEMIXCOLUMNTABLEISGENERATEDBYTHEFOLLOWINGALGORITHMEACHELEMENTINTHETABLECONSISTSOFFOURBYTESUSUALLYREPRESENTEDASHEXADECIMALVALUESTHESECONDANDTHIRDBYTESAREALWAYSSAMEASTHEINPUTBYTESOFORTHEVALUEOF54WOULDRESULTINASECONDANDTHIRDVALUEOF54ASWELLTHEFIRSTBYTEISTHEINPUTBYTEMULTIPLIEDBY2IFTHERESULTISGREATERTHAN0XFF,THERESULTISXOREDWITHTHEVALUE0X1BANDMOD100THEREFOREOURTHEBYTE0X54IS54XOR1BMOD100A8THELASTBYTEISTHEINPUTBYTEADDEDTOTHEFIRSTBYTE9SO,THELASTBYTEISA8XOR54FCTHISISASIMPLEWAYTOGENERATETHEMIXCOLUMNTABLESHOWNINFIGURE8FIGURE8MIXCOLUMNTABLEIMAGEFROMNETWORKSECURITYPRIVATECOMMUNICATIONINAPUBLICWORLD,PAGE86DOUGLASSELENT8WHATISREALLYHAPPENINGISAMATRIXMULTIPLICATIONOFTHEINPUTWITHTHEMATRIXINFIGURE9FOROURPURPOSESTHESHORTCUTISMOREPRACTICALATGENERATINGTHETABLEITALSOAVOIDSTHEMULTIPLICATIONOPERATIONWHICHISSOMEWHATCOMPLICATEDINTHEFIELDGF282311123111233112FIGURE9MATRIXFORGENERATINGTHEMIXCOLUMNTABLEFROMHTTP/WWWSAMIAMORG/MIXCOLUMNHTMLTHENEXTQUESTIONISHOWTOUSETHEMIXCOLUMNTABLEFOROUREXAMPLEWENEEDTOSPLITUPOUTSTATEINTOCOLUMNSEACHCOLUMNWILLHAVEITSOWNMIXCOLUMNOPERATIONAPPLIEDTOITUSINGTHELOOKUPTABLEFORALLTHEVALUESINTHEFIRSTCOLUMNOFOURSTATEWEGETTHEFOLLOWING0X20402020600XF9E9F9F9100X923F9292AD0X3162313153FIGURE10FIRSTCOLUMNTRANSFORMEDWITHTHEMIXCOLUMNTABLE9ADVANCEDENCRYPTIONSTANDARDTHEMIXCOLUMNSTEPISBESTSHOWNASADIAGRAMTHEDIAGRAMISSHOWNINFIGURE1140B3F3E9209C553FF92053B56292F96069319210B331AD9C53FIGURE11MIXCOLUMNOPERATIONTHERESULTOFUSINGTHEMIXCOLUMNOPERATIONONTHEFIRSTCOLUMNISTHEBYTES0X49,0X34,0XA7,AND0XBDTHEBLUEVALUESINTHEDIAGRAMINDICATETHATRESULTISUSEDINTHEFINALADDITIONSIMILARLYTHEOTHERCOLUMNSINTHESTATEGOTHROUGHTHESAMEPROCESSTHERESULTISASTATEWITHTHENEWVALUESAFTERTHEMIXCOLUMNPROCESS8RIJNDAELDECRYPTIONDECRYPTIONISSIMPLEAFTERUNDERSTANDINGTHEENCRYPTIONPROCESSITISBASICALLYJUSTTHEINVERSETHEALGORITHMWASDESIGNEDFORALLTHESTEPSTOBEINVERTIBLESODECRYPTIONISBASICALLYLIKEDOINGEVERYTHINGBACKWARDSTHEREFORE,FORDECRYPTIONSTARTSATTHELASTROUNDANDTHELASTROUNDKEYWHENPROCESSINGEACHROUNDDOTHEPROCESSBACKWARDSSO,THEROUNDKEYISADDEDFIRSTTOTHELASTROUNDADDITIONISITSOWNINVERSE,WHICHISNICETHENTHEMIXCOLUMNSTEPISAPPLIEDTHEMIXCOLUMNSTEPISAPPLIEDTOALLROUNDSEXCEPTTHELASTONEALSOTHEINVERSEMIXCOLUMNTABLEISUSED5THISTABLEISGENERATEDWITHANOTHERMATRIXSIMILARTOTHEWAYTHEMIXCOLUMNTABLEWASGENERATEDTHEDIFFERENCEISTHATTHEREARENOSHORTCUTSTOGENERATETHETABLETHEREFORE,THEMATRIXMULTIPLICATIONNEEDSTOBEPERFORMEDINTHEFIELDGF28THEMATRIXISSHOWNINFIGURE12ANDTHEINVERSETABLEISSHOWNINFIGURE13101411139914111313914111113914FIGURE12MATRIXFORGENERATINGTHEINVERSEMIXCOLUMNTABLETHISISTHEINTEGERREPRESENTATIONOFTHEHEXADECIMALDATAINTHETABLEFROMHTTP/CSRCNISTGOV/PUBLICATIONS/FIPS/FIPS197/FIPS197PDF,FIGURE510DOUGLASSELENT10FIGURE13INVERSEMIXCOLUMNTABLEFROMNETWORKSECURITYPRIVATECOMMUNICATIONINAPUBLICWORLD,P88ALLTHESHIFTSAREDONEBACKWARDSASWELLSO,INSTEADOFSHIFTINGLEFT,WESHIFTRIGHTLASTLY,THESBOXISAPPLIEDUSINGTHEINVERSESBOXTABLETHEINVERSESBOXTABLECANEASILYBEGENERATEDBYTAKINGTHESBOXVALUEATSOMEROWANDCOLUMNINDEXANDASSIGNINGTHEROWANDCOLUMNTOTHEINVERSESBOXVALUEATTHEINVERSESBOXINDEXDEFINEDBYTHESBOXVALUEFOREXAMPLE,THESBOXHASAVALUEOF0X00ATINDEX5,2THISTRANSLATESTOTHEINVERSESBOXHAVINGTHEVALUE0X52ATINDEX0,0THEINVERSESBOXTABLEISSHOWNINFIGURE142AFTERALLTHEROUNDSHAVEBEENCOMPLETEDINOPPOSITEORDERTHEFINALSTATEWILLCONTAINTHEORIGINALPLAINTEXT11ADVANCEDENCRYPTIONSTANDARDFIGURE14INVERSESBOXFROMHTTP/WWWSAMIAMORG/SBOXHTML9CONCLUSIONTHERIJNDAELALGORITHMWASCHOSENASTHENEWADVANCEDENCRYPTIONSTANDARDAESFORSEVERALREASONSTHEPURPOSEWASTOCREATEANALGORITHMTHATWASRESISTANTAGAINSTKNOWNATTACKS,SIMPLE,ANDQUICKTOCODECHOOSINGTOUSEFIELDGF28WASAVERYGOODDECISIONTHEINVERSEOFTHEADDITIONOPERATIONWASITSELF,MAKINGMUCHOFTHEALGORITHMEASYTODOINFACT,EVERYOPERATIONISINVERTIBLEBYDESIGNINADDITION,THEBLOCKSIZEANDKEYSIZECANVARYMAKINGTHEALGORITHMVERSATILEAESWASORIGINALLYDESIGNEDFORNONCLASSIFIEDUSGOVERNMENTINFORMATION,BUT,DUETOITSSUCCESS,AES256ISUSABLEFORTOPSECRETGOVERNMENTINFORMATION11ASOFJULY2009,NOPRACTICALATTACKSHAVEBEENSUCCESSFULONAES1210CODESAMPLESTHECODESAMPLESBELOWHAVEBEENDEVELOPEDBYTHEAUTHORTHEFOLLOWINGJAVACODEMODULECREATESTHEINVERSESBOXFROMTHEORIGINALSBOXBOTH“BOXES”STORETHEVALUESOFINTEGERSPUBLICVOIDCREATEINVERSESBOXFORINTI0I128MIXCOLUMNIJ0MIXCOLUMNIJ027256MIXCOLUMNIJ1I16JMIXCOLUMNIJ2I16JMIXCOLUMNIJ3MIXCOLUMNIJ0MIXCOLUMNIJ113ADVANCEDENCRYPTIONSTANDARDTHISMODULEPERFORMSTHESBOXSUBSTITUTIONWITHABYTEREPRESENTEDASANINTEGERPUBLICINTSBOXSUBSTITUTIONINTPLAINTEXTINTTABLESPOTIGETIVALUEPLAINTEXTINTTABLESPOTJPLAINTEXT16RETURNSBOXTABLESPOTITABLESPOTJTHISPROGRAMCREATESTHEBLOCKSOUTOFTHEPLAINTEXTREPRESENTEDASACHARACTERARRAYPUBLICINTCREATESTATESCHARTEXTARRAY,INTNUMSTATESINTSTATESNEWINTNUMSTATES44INTZ0/STATE,ROW,COLUMNFORINTI0INUMSTATESIFORINTJ0J4JFORINTK0K4KSTATESIKJINTTEXTARRAYZZRETURNSTATESTHISMODULEPERFORMSARIJNDAELROUND,BUTITISNOTCOMPLETELYFINISHEDYETPUBLICINTROUNDINTSNUM,INTROUNDNUM,INTSTATES,/EXPANDEDKEY/FORINTI0I4IFORINTJ0J4JSTATESSNUMIJSBOXSUBSTITUTIONSTATESSNUMIJFORINTI1I4IFORINTJ0JIJDOUGLASSELENT14INTTEMPSTATESSNUMI0STATESSNUMI0STATESSNUMI1STATESSNUMI1STATESSNUM
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