TELKOMNIKATelecommunication,Computing,ElectronicsandControl
Vol.21,No.4,August2023,pp.762∼770
ISSN:1693-6930,DOI:10.12928/TELKOMNIKA.v21i4.24789 ❒ 762
Onetomany(newschemeforsymmetriccryptography)
AlzDannyWowor1,BambangSusanto2
1DepartmentofInformaticsEngineering,FacultyofInformationTechnology,SatyaWacanaChristianUniversity,Salatiga,Indonesia
2DepartmentofMathematics,FacultyofScienceandMathematics,SatyaWacanaChristianUniversity,Salatiga,Indonesia
ArticleInfo
Articlehistory:
ReceivedJun19,2020
RevisedOct07,2020
AcceptedFeb08,2021
Keywords:
Cryptanalyst
One-to-manyscheme
Symmetriccryptography
ABSTRACT
Symmetriccryptographywillalwaysproducethesameciphertextiftheplaintextandthe givenkeyarethesamerepeatedly.Thisconditionwillmakeiteasierforcryptanalysts toperformcryptanalysis.Thisresearchintroducesaone-to-manycryptographyscheme, whichcanproducedifferentciphertextseveniftheinputgivenisthesamerepeatedly. Theone-to-manyencryptionschemecanproduceseveralciphertextswithdifferencesof upto50%.Theavalancheeffecttestobtainedanaverageof52.20%,betterthanmoderncryptographyBlowfishby25.46%and6%betterthanadvancedencryptionstandard (AES).One-to-manycanproducedifferent n-ciphertexts,whichwillcertainlymakeit moredifficultforcryptanalyststoperformcryptanalysisandrequire n-timeslongerto breakthanothersymmetriccryptography.
Thisisanopenaccessarticleunderthe CCBY-SA license.
CorrespondingAuthor:
AlzDannyWowor
DepartmentofInformaticsEngineering,FacultyofInformationTechnology,SatyaWacanaChristianUniversity Jl.Notohamidjojo1-10,Blotongan,Salatiga,Indonesia
Email:alzdanny.wowor@uksw.edu
1. INTRODUCTION
Theneedforinformationsecuritybecomesanextraordinarytransformationinthefieldofcryptography. Cryptographerscreatealgorithmstosecureinformationbyemphasizingthestrengthofmathematicsintaking advantageofthecomplexityofalgorithmsandkeysecrecy.Themorecomplexthealgorithmdesign,thebetterthe informationsecurity.Ontheotherhand,thespeedoftheprocessinalgorithmisalsotakenintoaccount.Thisis thefocusamongcryptographers,namelyhowtocreateapowerfulalgorithmagainsttheattackofcryptanalystsyet hasafastprocessingtime.
Symmetriccryptographyisstillaninterestingstudyandisstillveryfeasibletostudy[1].Oneofthemis theadvancedencryptionstandard(AES)hasbecomeapopularcriterionandiswidelyusedcommercially.There areseveralstudies[2]-[14]thatusealgorithmsrecommendedbytheNationalInstituteofStandardsandTechnology (NIST)astheinformationsecurity,althoughseveralstudieshavebeenclaimedtobreakthealgorithm[15]-[20].
Today’sadvancementofcomputertechnologyalsohascreatedachallengeforthedevelopmentofcryptography.Theideaofquantumcomputationcanenhancevariouscryptanalysistechniquesbecausequantummechanicalsystemcalculationwillproduceamuchlesstimecomplexitythanthatofclassicalcalculationmodel[21], [22].Computationaladvancementcertainlyencouragescryptographerstoreviewthecryptographicschemesthat willbeused.
Therealotofmethodsthatcanbedonetomakeanalgorithmtobemoreresistanttoattacks.Henriques andVernekar[23]combinedsymmetricandasymmetricalgorithmstosecurecommunicationbetweendevicesin anIoTsystem.In[24]proposedtheuseofacousticechocancellation(AEC)andellipticcurvecryptography (ECC)encryptiontechniqueswithacombinationofsymmetricandasymmetricalgorithms.In[25]modifiedshift rowandmixcolumninAES,sothattheprocessingtimecanbefaster.In[26]developedacryptographictechnique
basedonquantumkeydistribution(QKD).In[27]designedandimplementedareal-timecryptographicalgorithm tosecuremedicaldevicesthatprovideahighlevelofsecurityforremotehealthmonitoringsystems.
Theexistingsymmetricalcryptographyisthetypeofone-to-oneencryptionscheme,whichmeansthat everyinputplaintextandkeyalwaysproducesthesameciphertexteverytimeaprocessiscarriedout.Insolving ofcryptography,acriptanalystwillcertainlytrytolookforpatternsfrompercipextandmakesananalysisofkeys andplaintexts.Theexistingcryptographyalgorithmssometimesatcertainpartsareveryvulnerabletoextreme testingandasaresultthepatternsinciphertextwillbeeasiertobefound.
Thisresearchdesignsanewschemethatcananswerthatproblem,whichistheone-to-manyscheme. Thisschemewillcreatedifferentciphertexteventhoughtheinputplaintextandkeysarealwaysthesame.Any changesthatoccurinciphertextwilltakelongertimeandcertainlywillalsomakeitdifficultforcryptanalyststo seetherelationshipbetweenplaintextandciphertext.Thus,thisschemecertainlyismoresecurethanone-to-one encryptionscheme.Theinitialdesignofthisschemeismoreonhowtogetseveralbalancedciphertextthanonthe complexityofalgorithmintheencryption-decryptionprocess.
2. PROPOSEDRESEARCH
2.1. Onetomanyscheme
One-to-manyisanencryptionschemethatcancreatedifferentchipertexts,althoughusingthesameplaintextandkey,anddecryptionprocessthatcanretrievetheplaintext.Etymologically,one-to-manyconsistsoftwo words,“one”isaplaintext,and“many”isaprocessgeneratingadifferentciphertextforeachtimeitisencrypted.
EK (pa)= cai (1)
Theone-to-manyschemeencryptionisdescribedin(1).Theencryption (Ek) usesplaintext (pa) andkey asinputs,whichcancreateciphertext cai ,i ∈ Z+.Allencryptionprocessescancreatedifferent cai althoughwith thesameinput.
DK (cai )= pa (2)
Incontrast,theprocessof DK decryptionfunctionin(2)usesakeyandciphertextasinputs.Aone-tomanyschemeshouldbeabletoreturneachdifferentciphertext (cai ) resultingfromtheencryptionprocesstobe aplaintext.Thisstudyusesarandomnumbergeneratortoshowthattheone-to-manyschemecanbeappliedin cryptographicprocessesasshowninFigure1.
2.2. Implementationofone-to-manyscheme
Thedesignofone-to-manyalgorithmschemeisshowninFigure1.Theplaintextinput (P ) andkey (K) areintheformoftext. K isprocessedintoseed (x0) incryptographicallysecurepseudorandomnumber generator(CSPRNG)chaoswhichwillproduce n-numberofrandomnumberssequence {A1,A2, ,An}. The chosekeyprocessschemewillmanageandselectthecompatiblekeyfortheencryption-decryptionprocesssothat itproducestheappropriateplaintext.
Figure1.Generalschemeofonetomanyencryption
K = {k1,k2, ,kn} isthesymbolofthekeyand P = {p1,p2, ,pn} isthesymbolofplaintext. Each ki ∈ K playsroleasinputtotheexaminationscheme[28],andproduces x0 astheseedfortheCSPRNG chaosfunction (F )
F (x0)= {
2, ··· An} (3)
Each Ai,i =1, 2, ,n isthedatasetofCSPRNGchaosrandomnumbers,where A1 = {a11,a12, ,a1k},
From(3),usingthechosenkey A∗ n fromthekey selectionscheme,theencryptionprocessisobtainedas:
Onetomany(newschemeforsymmetriccryptography)(AlzDannyWowor)
Inthegeneral,thefollowingequationisobtion:
Thedecryptionprocesscanalsobedonebygeneratingeachrandomnumberusingkeyinputaswell.
Let K = {k1,k2, ··· ,kn} asthekey,andciphertext C = {c1,c2, ··· ,cn}.Eachrandomnumberfrom CSPRNGchaosisobtainedfrom F (K)= {A1,A
chosenkeyforthedecryptionprocess.
2.3. Keygeneration
Thekeygenerationstartsfromtheexaminationprocess[28],eachkeyinput (ki) andtheindexconstant (bi),where ki,bi ∈ Z256 for i =1, 2, , 8 whichisusedtofindtheratio x0 = pa/qa,where pa and qa are obtainedfrom(8)and(9).
Thevalueof x0 isusedastheseedin(10)thatgeneratesaCSPRNGchaos-basednumberserial.This processisinaccordancewiththesearchfunction F (x0) asshowninFigure1.Therandomnumberwillbeused asakeyintheencryptionordecryptionprocess.
Eachchaoticnumberisindecimalformandcannotbeusedasakey,soitisconvertedtoanintegerusing thetruncationfunctionin(11).
The“chosekeyscheme”isthemostimportantprocess,becauseherealgorithmwillchoosethekeyavailabilityandsetwhichkeywillbeselectedasthechosenkey A∗ n tobeusedintheencryptionprocessin(4)or decryptionin(6).Thedesignedalgorithmcanproduceseveraldifferentandbalancedkeysets {A1,A2, ,An} asshownearlierin(3).Afterselectingasetwhichwillbeusedasthekey,algorithmwillprovideamarkerthatis includedintheciphertext,sothatintheprocessofdecryption,algorithmcanrecognizethemarkerandwillrefer tothesetofkeysused.
3. RESULTANDANALYSIS
3.1. Testofthekeychanges
Testofkeychangesinone-to-manyschemeiscarriedouttoseehowwellanalgorithmproducesciphertext ifthereisasmallchange(1-bitchange)inthekey.Theplaintext“satyawacana”andtwokeys“ftiuksw”and“ftj uksw”areselected,wherethechangefromtheletter i to j isa1-bitdifference.Thistestalsousesthecorrelation statisticaltestandthemeandifference,toseethedifferencebetweeneachciphertextproduced.
TELKOMNIKATelecommunComputElControl,Vol.21,No.4,August2023:762–770
Testofkeychangesinone-to-manyschemeiscarriedouttoseehowwellanalgorithmproducesciphertext ifthereisasmallchange(1-bitchange)inthekey.Theplaintext“satyawacana
ftiuksw”and“ftj uksw”areselected,wherethechangefromtheletter i to j isa1-bitdifference.Thistestalsousesthecorrelation statisticaltestandthemeandifference,toseethedifferencebetweeneachciphertextproduced.
Testofkeychangesinone-to-manyschemeiscarriedouttoseehowwellanalgorithmproducesciphertext ifthereisasmallchange(1-bitchange)inthekey.Theplaintext“satyawacana”andtwokeys“ftiuksw”and“ftj uksw”areselected,wherethechangefromtheletter i to j isa1-bitdifference.Thistestalsousesthecorrelation statisticaltestandthemeandifference,toseethedifferencebetweeneachciphertextproduced.
ixi bil-1bil-2bil-3bil-4bil-5
10.099998932494109099998932494109
20.359996583976590359996583976590
30.921596174007104921596174007104
40.289026664250287289026664250287
50.821961006410555821961006410555
60.585364441404410585364441404410
70.970851648574852970851648574852
Figure3.Logisticfunctioniterationwith“ftiuksw”key.(a)Dataofthefirst7iteration,(b)Thefirst200Iteration
Figure2.Logisticfunctioniterationwith“ftiuksw”key.(a)Dataofthefirst7iteration,(b)Thefirst200Iteration
Thefirsttestusesthekey“ftiuksw”,andtheindexvalue B =1, 2, , 8 isselected.BasedonEquation 8andEquation9, x0 =0 0256580696623239 isobtained.TogeneratearandomvalueofCSPRNGchaos,value t =4 isusedinEquation10.Theresultsofthefirst7iterationvaluesareshowninFigure3(a)andtheresultsof thefirst200iterationsareshowninnFigure3(b).Incryptography,keysmustbeinintegernumber.Therefore,the resultofiterationisdividedtobefiveintegers,i.e.set-i, {1, 2, 3, 4, 5} respectively.Eachset-i is Ai inEquation3, whichisusedasthekeyforencryption-decryptionprocessesinEquation5andEquation7.
Figure2.Logisticfunctioniterationwith“ftiuksw”key:(a)dataofthefirst7iterationand(b)thefirst200 iteration
Thefirsttestusesthekey“ftiuksw”,andtheindexvalue B =1, 2, ··· , 8 isselected.Basedon(8)and (9), x0 =0 0256580696623239 isobtained.TogeneratearandomvalueofCSPRNGchaos,value t =4 isused in(10).Theresultsofthefirst7iterationvaluesareshowninFigure2(a)andtheresultsofthefirst200iterations areshowninnFigure2(b).Incryptography,keysmustbeinintegernumber.Therefore,theresultofiterationis dividedtobefiveintegers,i.e.,set-i, {1, 2, 3, 4, 5} respectively.Eachset-i is Ai in(3),whichisusedasthekeyfor encryption-decryptionprocessesin(5)and(7).
ThescatterplotinFigure3(b)isavisualizationofthefirst200iterations,whichprovesthatthelogistic functionwiththekeyinput“ftiuksw”cangeneraterandomnumbers.BasedonthetableinFigure3(a),thereare fivedatasetsthatcanbeusedaskeys.UsingEquation3,weobtain A1
ThescatterplotinFigure2(b)isavisualizationofthefirst200iterations,whichprovesthatthelogistic functionwiththekeyinput“ftiuksw”cangeneraterandomnumbers.BasedonthetableinFigure2(a),thereare fivedatasetsthatcanbeusedaskeys.Using(3),weobtain A1 =set-1, A2 =set-2, , A5 =set-5.
, A5
BasedonEquation4,thekeyselectionprocesscanbecarriedout.Theselectionschemewillchoose thekeythatwillbeusedintheencryptionprocess.Table1showstheresultoffiveencryptionsusingthekey “ftiuksw”.Theseresultsindicatethatone-to-manyschemecanproducedifferentciphertextforeachencryption process.Thedifferencebetweeneachciphertextandplaintextcanbeseenusingthecorrelationvalue,which respectivelytherearetwociphertextsthathaverelationshipwithplaintextsinmoderateandlowcategories,and oneciphertextthathasarelationshipwiththeverylowcategory.
Basedon(4),thekeyselectionprocesscanbecarriedout.Theselectionschemewillchoosethekeythat willbeusedintheencryptionprocess.Table1showstheresultoffiveencryptionsusingthekey“ftiuksw”.These resultsindicatethatone-to-manyschemecanproducedifferentciphertextforeachencryptionprocess.Thedifferencebetweeneachciphertextandplaintextcanbeseenusingthecorrelationvalue,whichrespectivelythereare twociphertextsthathaverelationshipwithplaintextsinmoderateandlowcategories,andoneciphertextthathasa relationshipwiththeverylowcategory.
MeanDifferenceistheaverageabsolutedifferencebetweenplaintextandciphertext.Thegreaterthe distancebetweenplaintextandciphertext,thebetteritwillbe.TheresultsobtainedinTable1showthemean differencevalueofdifferentciphertexts.Theseresultsprovideinformationthatone-to-manyschemecancreate differentciphertextforeachencryption.Thus,cryptanalystswillneedmoreworktobeabletosolvethisalgorithm.
Meandifferenceistheaverageabsolutedifferencebetweenplaintextandciphertext.Thegreaterthe distancebetweenplaintextandciphertext,thebetteritwillbe.TheresultsobtainedinTable1showthemean differencevalueofdifferentciphertexts.Theseresultsprovideinformationthatone-to-manyschemecancreate differentciphertextforeachencryption.Thus,cryptanalystswillneedmoreworktobeabletosolvethisalgorithm.
plaintext
ciphertext1
ciphertext2
ciphertext3
ciphertext4
ciphertext5
Visualizationofeachciphertextofthekey“ftiuksw”inCartesiancoordinatesinFigure5showsasequence ofdifferentnumbersanddonotformapatternthatfacilitatesdirectguessing.Itappearsthateachciphertextobtainedisdifferentalthoughwiththesameinput.Thisresultindicatesthatone-to-manyschemecanmakeplaintext andciphertextthatdonothaveastrongrelationshipstatistically.
Visualizationofeachciphertextofthekey“ftiuksw”inCartesiancoordinatesinFigure3showsasequenceofdifferentnumbersanddonotformapatternthatfacilitatesdirectguessing.Itappearsthateachciphertext
Onetomany(newschemeforsymmetriccryptography)(AlzDannyWowor)
TELKOMNIKATelecommunComputElControl,Vol.x,No.x,February202x:xx–xx
”andtwokeys“
Indexofcharacter
ISSN:1693-6930
obtainedisdifferentalthoughwiththesameinput.Thisresultindicatesthatone-to-manyschemecanmakeplaintextandciphertextthatdonothaveastrongrelationshipstatistically.
Visualizationofeachciphertextofthekey“ftiuksw”inCartesiancoordinatesinFigure5showsasequence ofdifferentnumbersanddonotformapatternthatfacilitatesdirectguessing.Itappearsthateachciphertextobtainedisdifferentalthoughwiththesameinput.Thisresultindicatesthatone-to-manyschemecanmakeplaintext andciphertextthatdonothaveastrongrelationshipstatistically.
Visualizationofeachciphertextofthekey“ftiuksw”inCartesiancoordinatesinFigure4showsasequence ofdifferentnumbersanddonotformapatternthatfacilitatesdirectguessing.Itappearsthateachciphertextobtainedisdifferentalthoughwiththesameinput.Thisresultindicatesthatone-to-manyschemecanmakeplaintext andciphertextthatdonothaveastrongrelationshipstatistically.
ixi set-1set-2set-3set-4set-5
TELKOMNIKATelecommunComputElControl,Vol.x,No.x,February202x:xx–xx
10.100089355076193100089355076193
20.360285904306499360285904306499
30.921919885858189921919885858189
40.287934439669651287934439669651
50.820112792487100820112792487100
60.590111200344443590111200344443
70.967519886289935967519886289935
Figure4.Logisticfunctioniterationwith“ftjuksw”key:(a)dataofthefirst7iterationand(b)thefirst200 iteration
Figure4.Logisticfunctioniterationwith“ftjuksw”key.(a)Dataofthefirst7iteration,(b)Thefirst200Iteration
TELKOMNIKATelecommunComputElControl,Vol.x,No.x,February202x:xx–xx
Figure5.Logisticfunctioniterationwith“ftjuksw”key.(a)Dataofthefirst7iteration,(b)Thefirst200Iteration Thesecondtestusingthekey“
Thesecondtestusingthekey“ftjuksw”,andusingthesameindexvalue B =1, 2, , 8, x0 = 0 0256818986893376 isobtained.Theresultsofthefirst7iterationvaluesareshowninFigure4(a)andthe resultsofthefirst200iterationsareshowninnFigure4(b).Takingthevalueof t =4,theiterationresultsare obtainedasshowninFigure4(a).Fivedatasets A1 =set-1, A2 =set-2, ··· , A5 =set-5areusedaskeysinthe encryption-decryptionprocesses.
0.0256818986893376 isobtained.Theresultsofthefirst7iterationvaluesareshowninFigure5(a)andthe resultsofthefirst200iterationsareshowninnFigure5(b).Takingthevalueof t =4,theiterationresultsare obtainedasshowninFigure5(a).Fivedatasets A1 =set-1, A2 =set-2, , A5 =set-5areusedaskeysinthe encryption-decryptionprocesses.
Theiterationresultofthelogisticfunctionwiththe“ftjuksw”keyisverydifferentfromthe“ftiuksw”as showninFigure2(b)andFigure4(b).Theseresultsindicatethattheexaminationalgorithmisdesignedtobeable toproduceauniqueinitializationvalueof x0,soitisverysensitivetowardssmall(1-bit)changesintheinput.The natureofthebutterflyeffect,whichhasalargeeffectonoutputeventhoughitisasmallchangeininput,alsohasa significanteffectontheencryptionresults.ThiscanbeseeninthedifferencesofeachciphertextasshowninTable 1andTable2.
Theiterationresultofthelogisticfunctionwiththe“ftjuksw”keyisverydifferentfromthe“ftiuksw”as showninFigure3(b)andFigure5(b).Theseresultsindicatethattheexaminationalgorithmisdesignedtobeable toproduceauniqueinitializationvalueof x0 ,soitisverysensitivetowardssmall(1-bit)changesintheinput.The natureofthebutterflyeffect,whichhasalargeeffectonoutputeventhoughitisasmallchangeininput,alsohasa significanteffectontheencryptionresults.ThiscanbeseeninthedifferencesofeachciphertextasshowninTable 1andTable2.
ftjuksw”
Table2showsthetestresultsusingthekey“ftjuksw”,whichitindicatesthataone-to-manyschemecan producefivedifferentciphertextsateachencryptionprocess.Statistically,theresultingcorrelationvalueisclose to 0 withsufficientandverylowcategories.Itindicatesthatthealgorithminmakingofplaintextandciphertext hasnostatisticalrelationship.ThevisualizationinFigure5alsoshowsthateachciphertextproducedisdifferent althoughwiththesameinput.Testof1-bitkeydifferenceshowsthatone-to-manyschemecanproducedifferent ciphertext,eventhoughgivenkeyinputswithasmalldifferent.Thevisualizationofthegraphicshowsadifferent ciphertextwhichitproducesadifferentsequenceofnumbersanddoesnotformapatternthatfacilitatesdirect guessing,andasaresult,cryptanalystswillneedmoreworktosolvethisalgorithm.
Table2showsthetestresultsusingthekey“ftjuksw”,whichitindicatesthataone-to-manyschemecan producefivedifferentciphertextsateachencryptionprocess.Statistically,theresultingcorrelationvalueisclose to 0 withsufficientandverylowcategories.Itindicatesthatthealgorithminmakingofplaintextandciphertext hasnostatisticalrelationship.ThevisualizationinFigure6alsoshowsthateachciphertextproducedisdifferent althoughwiththesameinput.
plaintext
ciphertext1
ciphertext2
ciphertext3
ciphertext4
ciphertext5
Testof1-bitkeydifferenceshowsthatone-to-manyschemecanproducedifferentciphertext,eventhough givenkeyinputswithasmalldifferent.Thevisualizationofthegraphicshowsadifferentciphertextwhichit producesadifferentsequenceofnumbersanddoesnotformapatternthatfacilitatesdirectguessing,andasa result,cryptanalystswillneedmoreworktosolvethisalgorithm.
TELKOMNIKATelecommunComputElControl,Vol.21,No.4,August2023:762–770
3.2. Bitdifferencesoneachciphertext
Thenexttestistoseethebitdifferenceoneachciphertext.Thebiggerthebitdifferenceforeachciphertext,thebetteritis.Theone-to-manyschemeproducesfiveciphertexts,sothatthenumberofcomparisons foreachciphertextis C5 2 =10.Table3showsthecomparisonofciphertextsforeachkey.With m,n tobethe selectedciphertext, m = n ∈{1, 2, 3, 4, 5}.Thesymbol“><”denotesthecomparisonofeachciphertext.
Table3.Bitdifferencesoneachciphertext
Theaveragechangeofbitciphertextforthekey“ftiuksw”is 66 4 bitsor 51 87%.Meanwhile,forthekey “ftjuksw”anaverageof 64 6 bits (50 47%) isobtained.Theminimumscorefortheoveralldatais 54(42 1875%), andthemaximumscoreis 73(57 03%),andoverall,themeanciphertextdifferenceis 50%.Theseresultsindicate thatone-to-manyschemecanproducedifferentciphertextandbalancedciphertext.
3.3. Differencestestplaintext-ciphertext
Thistestisdonetoseewhetherthechangein1bitcanmakeadifferenceintheoverallciphertextproduced.Thegreaterthedistancebetweenplaintextandciphertextindicatesthealgorithmthatisdesignedisalso gettingbetter.Conversely,thesmallerthedifferencebetweentheplaintextandtheciphertextproducedtheless wellthealgorithmdesigned.TheabsolutedifferencebetweenplaintextandciphertextisshowninTable4using key“ftiuksw”and“ftjuksw”.
Table4.Differencesciphertext-plaintextbykey
Itcanbeseenfrombothtablesthattheplaintext-ciphertextdistanceproducedbythealgorithmdesignis quitegood.Thedifferenceof1bitinthekey,doesnotmakethedifferenceinthedistanceineachciphertextfrom thetwotablesalsodifferby1bit.Theresultsshownarequitevariedandspreadwell.However,furthertesting needstobedonetoensurethatthespreadofdistancethatoccursisalreadygood.Thisbecomesanoteinthenext studytobeabletotesttheplaintext-ciphertextdifferencewithmorekeyvariations.
3.4. Avalancheeffecttest
Comparisonofone-to-manyschemewithseveralothercryptographsisdonebyobservingtheavalanche effectvalueincarryingouttheencryptionprocess.In[29]hastestedseveralclassicalandmoderncryptographic
algorithmswhilethisresearchcontinuesitsstudywithtestingonAESandalsooneone-to-manyscheme.Table5 showstheresultoftheavalancheeffecttestforfiveencryptionprocessesusingthesamekeyandplaintext.Oneto-manyschemecanproducedifferentavalancheeffectvalueforeachencryption,differentfromotheralgorithms thatalwaysproducethesamevalue.
Table5.Resultavalancheeffecttest
Thedataencryptionstandard(DES)algorithmhasthehighestavalancheeffectvalueandthelowest Caesarciphervalue.TheseresultsarereasonablebecausebothDESandAESuseallblockcipherprinciples incompilingtheiralgorithms,whileCaesarcipheronlyusestranspositionforeachtextinput.Theone-to-many schemealsodoesnotuseblockcipherprinciplebecausetherandomnessofthegeneratedkeysusethelogistical functionisadeterminingfactorintheencryption-decryptionprocesses.Onaverage,one-to-manyschemecan produceanavalancheeffectvalueof 52.20%.Although,itisstilllowerthanDES,butitisstillbetterthanmodern Blowfishcryptographyby 25 46% and 6% morethanAES,bothofwhicharestillwidelyusedasinformation securityalgorithms.
3.5. Timerequirementofcryptanalysis
Supposeanalgorithmusesakeyblocklengthof128bits,thetimeneededtoperformcryptanalysisis 2128 units.Ifacomputercancrack 106 keysinonesecond,thetimeneededtocrackthekeyis 5 4 × 1024 years. Asthefirststep,theone-to-manyschemealsouses128bitswhichitsalgorithmcanproduceseveralciphertexts. Ingeneral,supposethatone-to-manyschemecanproducedifferent n-ciphertexts,theciphertextsearchprocess requires n × 5 4 × 1024 years.Thisresultwillcertainlycomplicatethecryptanalysis.Althoughthepossibility ofperformingthecryptanalysisstillremainsbutitwilltaken-timesprocesslongertimethancrackingordinary cryptography.
4. CONCLUSION
Theone-to-manyencryptionschemeproducesfiveciphertextsthathavedifferentandbalancedvisualization.Theplaintext-ciphertextcorrelationtestisalsoclosetozero.Thisconditionillustratesthatthealgorithmcan makeplaintextthatisnotstatisticallyrelatedtociphertext.Aplaintextinputwillproduceseveralciphertexts,and eachofthemhasavarietyofmorethan 50%.Anaverageof 52 20% isobtainedfromtheavalancheeffecttest, whichisbetterthanmodernBlowfishcryptographyby 25 46% andAESby 6%,bothofwhicharestillwidelyused asinformationsecurityalgorithms.Thisconditionwillbepreferablebecauseitmakesdifficultforcryptanalyststo findtherelationshipbetweenplaintextandciphertextdirectlybyaprocessoftrialanderror.Manydifferentforms ofciphertextproducedbyone-to-manyschemewillmakeitverydifficultforperformingacryptanalysis.Although thecryptanalysisprocesscanstillbedonebutitwillrequirealongerprocessandtimecomparedtoalgorithmsthat aresolvedordinarily.Iftherearenciphertexts,itwilltaken-timesfortimeandprocesstofindtheplaintext.
ACKNOWLEDGEMENT
TheauthorsaregratefultoSatyaWacanaChristianUniversityResearchandCommunityServiceCenter (BP3M)fortheresearchfundingsupportthroughtheInternalFundamentalResearchschemeinthe 2017/2018 fiscalyear.
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Onetomany(newschemeforsymmetriccryptography)(AlzDannyWowor)
BIOGRAPHIESOFAUTHORS
AlzDannyWowor iscurrentlyalecturerattheFacultyofInformationTechnology, SatyaWacanaChristianUniversityinSalatiga,Indonesia.Hereceivedbachelorandmasterdegreein mathematicsandinformaticsfromSatyaWacanaChristianUniversity,in2005and2011respectively. HisresearchesareinfieldsofPrimitiveCryptography,SymmetricCryptography:BlockCipherand Pseudorandom.Hecanbecontactedatemail:alzdanny.wowor@uksw.edu.
BambangSusanto HeiscurrentlyalecturerattheDepartmentofMathematics,Faculty ofscienceandmathematics,SatyaWacanaChristianUniversityinSalatiga,Indonesia.Hisobtained BachelorDegreeinMathematicsfromDiponegoroUniversity(Indonesia)in1988.Hisreceived masteranddoctordegreeinmathematicsfromBandungInstituteofTechnology,in1992and2005 respectively.HisresearchesareinfieldsofDataMining,BigDataAnalysis,BusinessIntelligence, RiskAnalysis,PrimitiveCryptography,SymmetricCryptography.Hecanbecontactedatemail: bambang.susanto@uksw.edu.