A Cryptographic Key Assignment Scheme with Adaptable Timetoken Constraint in a Hierarchy

Transcription

1 Inenaona Jouna of Mueda Ubquous Engneeng Vo 3 No 4 Ocobe 2008 A ypogaphc Key Assgnen Schee wh Adapabe Teoen onsan n a Heachy Hsng-hung hen Depaen of opue Scence and Engneeng Asa Unvesy Tachung ouny Tawan 4345 E-Ma: shn8409@s6hnene Shuh-Jeng Wang Depaen of Infoaon Manageen ena Poce Unvesy Taoyuan ouny Tawan 333 E-Ma: sjwang@acpueduw Jyh-Hong Wen Depaen of Eecca Engneeng Thongha Unvesy Tachung ouny Tawan E-Ma: jhwen@hueduw Absac A schee whch uses fexbe cypogaphc ey anageen upon adapabe e-oen consan fo a use heachy access cono (UHA) schee s poposed n hs pape Fo adapng he changeaby n a UHA syse we popose a echnque of assgnng ndependen e-oen whch s dsbued by a used agency seve o epy an auhozed use fo once secue access eques The ey feaue of he echnque s o adap soe secue paaees n dsbued e-oen fo espondng o each ega access eques Fuhe a cass eys w be updaed poacvey by he concep of poacve ey anageen whch aes he advanage ha s poven and fee fo he scenao of he cousve aac exape whch poposed by Y e a n [8] Ths cypogaphc ey assgnen schee based on he dffcuy n sovng a dscee ogah wh adapabe e-oen consan can acheve bee secuy and oe effcen anageen han he convenona UHA schee Besdes ou schee povdes a fexbe anne and dynac ey anageen o ncease he avaaby of use access n UHA sucue Keywods: ey assgnen poacve ey anageen access cono adapabe e-oen Inoducon Due o he connung gowh of copue newos and u-use copue echnooges he shang of newo esouces s becong nceasngy wdespead The adnsaon of hese esouces n a u-use copue envonen has aso gown oe copex; access cono hough he pope auhozaon pocedues s heefoe becong oe and oe poan n he ea wod The pobe of access cono ases n oganzaons havng a heachca sucue; such oganzaons can ange fo ay o govenena depaens o pvae copoaons Many appcaons exs soe secue access pobes n busness o ohe aeas of he pvae secos; eg soe poeced daabases conanng sensve nfoaon o ndusa seces Snce A & Tayo n 983 [] fs poposed a cypogaphc ey assgnen fo access cono n a paa-ode heachy (caed ey assgnen heeafe) based on he degee of dffcuy of sovng he dscee ogah pobe any ehods of heachca access cono [4 9 0] have been poposed A heachca sucue (aso caed use heachca access cono schee UHA) s consuced by dvdng uses no a nube of dsjoned secuy casses 2 whch ae paay odeed wh a bnay eaonshp π In a heachy he saeen jπ eans ha he secuy eve of cass j s owe han ha of cass and π addonay denoes he possby ha he secuy eve of j oespondence

2 Inenaona Jouna of Mueda Ubquous Engneeng Vo 3 No 4 Ocobe 2008 cass j can equa cass whee j s a successo of cass and s a pedecesso of cass j The eanng of jπ s ha uses n cass can access any nfoaon hed by uses n cass j whe he oppose s no aowed To go hough heachca access cono cean ey assgnen ehods have coon pocedues as saed beow The ena Auhoy (caed A heeafe) agency cacuaes he cypogaphc ey fo each cass of each sau n advance whee each cass s accodng o hs ebeshp ha coes fo vaous assgnens The A hen dsbues he cypogaphc ey o uses who ae ebes n hs cass Thus he ey assgnen assgns a cypogaphc ey o a uses n cass so ha hey can use o deve j f and ony f he cass jπ In ohe wods he convenona UHA s he eanngs of hose uses ae aowed o deve cass ey dependng on he ndvdua access gh whou any neacon wh he A Hence he use n cass can use o decyp he daa whch ae encyped wh and he use n he cass uses o deve he cass ey j whch s hen used o decyp he encyped daa n cass j The advanage of A and Tayo s schee s ha he ey geneaon and ey devaon agohs ae spe Howeve A and Tayo s schee s no pacca fo peenng dynac access cono because he whoe syse us be e-esabshed once a cass nseon o deeon occus To aow a dynac change of casses os eseaches of hs opc have poposed schees [4 9 0] ha pefo bee n aowng nseon and deeon of casses whn he heachy n a UHA schee Fuheoe hese ey assgnen schees [ 4 9 0] have no been concened wh a pacca suaon: Uses gh be assgned o a cass fo ony a peod If he use has esgned fo he/hs cass bu he peedaedy eavesdops on daa ansssons hen he can aso decyp he daa n cass j f and ony f he cass jπ Thus a essages ae ey o be eveaed dung he syse s peod of change Tzeng [6] fs poposed a e-bound cypogaphc ey assgnen schee a UHA schee wh e consan fo access cono n a paa-ode heachy n whch he cypogaphc eys of a cass wee dffeen fo each peod A speca feaue of Tzeng s schee es n he fac ha each cass had soe e-dependen eys each of whch coud ony be used dung a cean peod Accodng o Tzeng s schee once he ey nfoaon exped s owne coud no access any subsequen cass eys Hs ehod s oe fexbe fo soe appcaons such as boadcasng dga daa o auhozed uses wh ueve-secuy o consucng a fexbe cypogaphc ey bacup syse Ahough boadcasng daa can save a o of bandwdh ove pon-o-pon anssson he pobe s s ha anyone on he boadcas channe can eavesdop To peven eavesdoppng Tzeng s schee encyped he daa befoe boadcasng so ha ony auhozed uses wh pope eys coud decyp he daa and oban eanngfu essages Howeve Y e a [8] showed ha he poposa gven n Tzeng s schee [6] was no secue agans cousve aacs wheeby hee non-auhozed uses ay conspe o access soe cass eys o whch hey had no access Y e a [8] bough ou he fac ha Tzeng had no poposed a way o ovecoe hs ype of couson Foowng he Tzeng s schee [6] Huang e a [8] poposed a new cypogaphc ey assgnen wh e-consan schee fo a paa-ode use s cass heachy apped o a UHA schee Neveheess Tang e a [3] showed ha Huang e a s schee had poena secuy vuneabes whch enabe acous pacpans and aaces o voae he syse The ohe eseaches of hs opc ae shown beow hen [5] poposed a souon based on he assupons of ow-cos and ape-essan equpen o he sudes of e-bound heachca ey assgnens Unfounaey De Sans e a [2] showed ha hen s schee [5] s ees he couson aacs Wang e a [7] poposed a echnque caed 2

3 Inenaona Jouna of Mueda Ubquous Engneeng Vo 3 No 4 Ocobe 2008 egng and have used o consuc an effcen e bound heachca ey assgnen schee whee he councaon oad of ansng upe eys s one snge aggegae ey The schee has a good soage and copuaona pefoance These schees [ ] a o povde effcen access cono ehods wh egad o use s casses whch ae oganzed heachcay and he peod In hs way hey offe a wohy secuy eve n UHA schee wh he e consan especvey Whaeve soe suaons have been happened when a use eaves a cass he eys of ha cass and a he descenden casses us be enewed and whee he pveges of uses change fequeny o whee hee ae any casses change fequeny he councaon oad fo ey edsbuons s vey age [7] Howeve hee s a cassca dea caed poacve secuy ha ay pove he cass ey anageen wos fo ganng oe fexby and secuy In ode o ee he desed deands fo ganng oe fexbe cass ey anageen and enfocng he fuhe secuy n appcaons we heefoe poposed ye anohe oe fexbe ey assgnen n he UHA schee The sophscaed souons poposed n ou schee ae based he deas of poacve secuy and op-down ey assgnen n [ ] Poacve secuy fs suggesed by Osovsy and Yung [4] n 99 efes o secuy and avaaby n he pesence of hs obe advesay aac whch ay coup a pacpans houghou he fee of he syse n a non-onoonc fashon; hs advesay aac s ed howeve o he nube of pacpans can coup dung any dsnc peod Fane e a [6] poposed a poacve echans o povde an nceased eve of secuy and avaaby o an RSA pubc-ey syse va dsbuon of a pvae ey and acve councaon beween shaehodes They ephaszed ha poacve secuy concens ae va n deang wh he nceasng nube of heas o councaon newo doans and fo secung ong-ved cypogaphc eys ha canno be easy epaced eg basc cypogaphc nfasucue funcons The poposed schee was engaged n a poacve anenance of ey shang poecng he agans an advesay aepng o uncove he sece o dsup he opeaon In addon o poecon poacve anenance echnques povde fexbe and dynac ey anageen Owng o s spe agoh and fewe paaee equeens he RSA pubc-ey syse [0] eans he os popua cyposyse wh wodwde sandads; hus we adoped hs syse n ou poposed schee n whch he cypogaphc ey of cass a a peod s The peod does no necessay have o be a ea e howeve ay be one wee one onh o haf a yea; copeey depends on he anageen of poacve echans n he syse We acuay dvded he oa e T no Z peods nang wh and endng wh z e T = { 2 z } Suppose ha a use u n cass has goen he nfoaon I ( T u ) wh he auhozed peod se T u T T u conssng of he peods whch ae fo he/hs begnnng peod s o he/hs endng peod e eg T u = { s s + + e } Theefoe she/he can use he nfoaon I ( T u ) ogehe wh a e-oen τ u o copue he cass ey j of cass j a he peod f and ony f he condons jπ and T u ae sasfed whee he e-oen τ u s ssued fo a ena Auhencaon and Auhoy (AA fo sho) seve whch acs fo a used agency n ou syse Once he auhozed e duaon Tu eapses he nfoaon owne canno access any subsequen cass eys Theefoe ou ey devaon s consaned no ony by he cass eaonshp bu aso by he e-oen coespondng o use s auhozed peod se especvey In hs poposed ehod he e-oens ae consuced usng he dsnc pes dsbued fo he AA seve when he uses acvae he equess fo accessng he syse Ths eans ha a he use u who s ony assgned a he auhozed e peod se Tu canno decy use he/hs pe-assgned ey nfoaon he ey o deve he 3

4 Inenaona Jouna of Mueda Ubquous Engneeng Vo 3 No 4 Ocobe 2008 sece ey whee T u and u coud no oban he auhozed e-oen τ u fo AA n whch he e peod does no beong o he e duaon e T u Moeove hs feaue dffes fo Tzeng s schee [6] Huang e a s schee [8] and he ohe above-enoned schees [ ] In he schees he ey echanss ae no offeed o efesh a of cass eys and poec fuue essages Moeove on when any casses nseon o deeon fequeny occus can be seen ha os of he pevousy poposed schees have o be epeaedy ecopued and epubsh he eaed nfoaon such as he uses nfoaon and coesponded pubc/pvae paaees By ou poposed ehod hese ass ae ngenous ecopued by AA; on he conay he auhozed uses can avod beng e-updaed he use nfoaon fequeny Fuheoe ou poposed ehod has he foowng popees: () Bee secuy and ease anageen as povdes a UHA echans wh eoen consan fo cypogaphc ey assgnen n a heachy; aso offes geae secuy agans aacs of couson () Dynac and fexbe access cono can be easy peened because he syse s na eys o nfoaon es do no eque changng once casses nseon o deeon have occued () Agohs fo ey geneaon and ey devaon usng dsnc e-oens ae que spe (v) If he access e s ou of he auhozed peod se eg T u ncudng he peods befoe s and he eanng ( z e ) peods he cass ey wh e-oen consan owne canno decyp he poeced daa o nfoaon Fo he above popees can be seen ha he ey anageen poposed n hs pape s oe fexbe and oe pacca snce a peson ay be epoyed fo ony soe auhozed peod se Fo exape we ay consde a secue appcaon of a ey assgnen by ega auhoes such as an auhozed use n cass who wans o ead he e-dependen essages encyped wh paaees coespondng o a peod n cass j If he ey assgnen schee s updaed by egua peodca peod coespondng o he e-oen τ u he appopae ey s j fo desed peod The use u can decyp he e-dependen essages f and ony f jπ and he/hs access peod s vad In he sae anne an auhozed pacpan can boadcas daa so ha ony auhozed uses wh appopae eys n he vad e duaon can decyp he essages and oban eanngfu nfoaon Boadcasng essages can save a gea dea of bandwdh ove pon-o-pon anssson [6] Hence ou schee s suabe fo soe appcaons n oday s copue newo envonen eg eeconc pape subscpon and dga TV boadcasng [6 ] n whch a use ay be assgned o a cean cass fo ony a peod Moeove he heachca access cono echanss [ ] do no ean copee access ecods as hs woud undene secuy The eande of hs pape s oganzed as foows: ou ey assgnen schee fo dynac and fexbe access cono n a heachy s poposed n Secon 2 The dscussons ae gven n Secon 3 A bef concuson s offeed n Secon 4 2 Ou Schee n Key Assgnens A new fexbe cypogaphc ey assgnen schee s poposed n hs secon n whch he cass eys ae peodcay updaed by changng he peods fo noa sevce e and he cass eys coud be efeshed n ea e whe dynac change of casses o uses happenng Ths povdes a poacve pocy o avod he suaon ha he sece cass ey o 4

5 Inenaona Jouna of Mueda Ubquous Engneeng Vo 3 No 4 Ocobe 2008 be boen (caced) w be conoed ahe han espondng afe he fac A speca feaue of ou schee s ha each cass has soe evsed e-dependen eys (caed cass eys fo spy) none of whch can be used excep dung cean peods Once he cass ey and use nfoaon expes s owne canno access any subsequen cass eys Ou schee s aso based on an RSA assupon [0] usng an dea of poacve echans [ ] n whch he cass eys ae peodcay updaed by changng he peods Assue ha a paa-ode heachy has a nube of dsjon casses 2 odeed by he bnay eaon π and ha he syse e dung whch he desed heachy s vad s dvded no peods nubeed peod peod 2 peod z n whch he peods ae aso denoed as peod peod 2 peod z Each of peods s assgned a consan nube such as = = 2 2 z = z Ou schee can be suazed as foows: 2 Penay Poposon Gven an oupu of y y ( α) x ( odn) s copuaonay nfeasbe o fnd α based on he assupon of RSA whee x s a posve nege esced n RSA assupon and n s he poduc of wo age sece pes 22 Ina copuaon Sep : The AA chooses wo age pes p and q whee p = 2p + and q = 2p 2 + p and p 2 ae wo age pes and n = p q Then he AA chooses a sece ey d c and fnds he pubc ey e c whee he sece ey sasfes ec dc ( odφ( n) ) Sep 2: The AA andoy chooses dsnc pes e e2 e fo casses a a peod whee each e s o be as sa as possbe so ha = e < φ( n) and each e s ased o be a pe eaed o φ ( n) Then he AA copues he unquey coespondng nubes of d d2 d such ha e d ( odφ( n) ) fo = 2 whee φ () s he we-nown Eue s oen funcon and eeps a d s secesep 3: The AA andoy chooses dsnc pe nubes a a a a 2 z and eeps he sece whee each pe s a pe eaed o n Each of he pes a s w be hen used o geneae he dsnc cass eys fo a vad peod whee T ( ) Sep 4: The AA copues he na eys a d d d d ev a v ( n) 2 π π/ od fo and T whee he na eys ae epoyed fo cass ng fo o z Sep 5: The AA andoy chooses eavey pe nubes se Γ = { a u au a } whee 2 u each a Γ fo a { 2} sasfyng gcd ( a n) = u u and gcd( a u a ) = Then hey w be assgned o dsnc uses u u2 u Theeupon he AA copues he nvese nube fo each a u Γ denoed as ( a ) whee { 2 } u such ha sasfyng a ( ) u a ( od n) The AA eeps each pa of nubes u a and ( a ) fo a u u { 2} sece Sep 6: Fo each peod he AA andoy chooses one of he dsnc pes g g g g whee any g 2 z e fo any and and eeps he sece; Tha s fo each peod ene casses shoud be andoy assgned he dsnc pes g g g g and each of he shoud be as sa as possbe so ha 2 z 3 g << p 3 g << p2 sasfyng gcd ( φ ( n) g ) = fo a T The dsnc pes ae hen used o geneae dsnc e-oens Fnay he dsnc e-oens ae used o copue he coespondng cass eys fo each cass a he peod 5

6 Inenaona Jouna of Mueda Ubquous Engneeng Vo 3 No 4 Ocobe Key assgnen In hs ey assgnen phase he AA copues he cass ey fo cass na eys whee 0 and a he peod as foows whee he AA seve eeps he pe nube g { g g g g z } 2 24 Infoaon assgnen sece fo he The AA hen chooses a pe nube a u whch has been andoy chosen fo he pe se { a u au au au } fo he use u 2 who s assgned a e-bound T u = { s s + e e } n he cass ; he use s e nevas ae fo s o e sasfyng he condon of T u Tha s o say he use u s assgned o cass and she/he s aowed o oban he/hs cass eys wh he ony e duaon T u sasfyng Tu T Foowng hs he AA geneaes he nfoaon I ( T u ) whch s used o denfy he use u as foows I( Tu ) = ( u s e) (2) d whee u ( a ) π ( n) u od and he sybo denoes a concaenaon opeao o he fxed opeands of u s and e Fnay he AA hen sends he use s nfoaon I ( T u ) bac o he use u 25 Key devaon 25 Auhencaon phase Assue a use u assocaed wh wans o deve he cass ey a a peod whee T u The use u fs chooses a ando pe nube x and a age pe n whee z << n < n and gcd( n φ ( n) ) = fo a new eques e-oen phase Subsequeny she/he copues he nvese of he nube x y ( x) ( od n) sasfyng ec x y ( od n) and sends he eques nfoaon ( u y n ) ( n) od o he AA seve n ode o oban he e-oen bac Fo deang wh he eques he AA d e c seve w copue fsy ( ) ) c u y n ( u y n) ( od n) and auhencae hs eques va checng whehe he use nfoaon s ega o no e by ev checng whehe he equaon ( u ) v ( od n) s equa o a π u o no and vadang whehe hese condons z T u and n >> g ae sasfyng o no If he use s eques passes he use auhencaon and e-bound vadaon hen he AA seve w ae an access ecod o eaed og and connue he nex phases as he foowng subsecons 252 Te-oen geneaon phase If he eques of he use u passes he use auhencaon and access-ng vadaon hen he AA seve w copue he e-oen fo accessng he cass jπ a he peod as foows: d g g g ( d d 2 d ) ev ( ) ( a ) π ( a ) v )( od n) () π/ ( ) ( ) u ( u su ) τ = (3) d g whee u ( a ) a n u od and s ( ) u y g od n Subsequeny he e-oen w send bac o he use fo he cass accessng jπ a he peod 6

7 Inenaona Jouna of Mueda Ubquous Engneeng Vo 3 No 4 Ocobe Key devaon phase The use u can deve he cass eys fo cass and a of he paay odeed casses j a he vad peod f he eaon jπ eans n he heachy schee Key devaon pocesses ae shown n dea n he foowng wo cases In ase we show ha he use u can deve he cass ey fo cass a he peod ; In ase 2 we show ha he use u can aso deve he cass ey fo a of he paay odeed casses j f and ony f jπ n he heachy schee a he peod ase Fo he gven nfoaon I( Tu ) = ( u s e) a ando pe nube x and he pubc paaees assocaed wh auhencaon pocedue a he peod whch sasfes T u he use u assocaed wh hen obans he e-oen τ u ( ) = u s u bac fo he AA seve and can deve he cass ey Thus she/he can oban xˆ su x g ( od n) and deve he cass ey by xˆ ( u ) ( od n) u (4) The foowng Theoe ensues he coecness of he cass ey devaon of ase Theoe If I( Tu ) = ( u s e) and he e-oen u = ( u su ) τ ae he ey nfoaon poduced by he poposed schee n (2) and (3) hen he use u who s n he cass can deve he by (4) whee s he cass ey assocaed wh a he peod The poof of Theoe s showed n he appendx ase 2 When he use u succeeds n passng he use auhencaon and e-bound vadaon he use w eceve he e-oen τ u ( ) = u s u fo he AA seve Usng he gven nfoaon I( u Tu ) = ( u s e) and he pubc paaees use u who beongs o cass can deve he ey j whee he ey s a evsed e-dependen ey of cass j a a peod f he cass eaon jπ s eans n hs heachy schee and he peod sasfes he condon copued as: T u π od n π/ j j u u Agan he foowng Theoe 2 ensues he coecness of he cass ey devaon of ase 2 Theoe 2 If I( Tu ) = ( u s e) and he e-oen u = ( u su ) τ ae he ey nfoaon poduced by he poposed schee n (2) and (3) hen he use u who s n he cass can oban he j by (5) whee j s he cass ey assocaed wh j sasfyng jπ a he peod sasfyng T u The poof of Theoe 2 s aso showed n he appendx xˆ e ( ) ) ( ) (5) 254 Pefoance of cass ey devaon In genea he copuaon e on a oduus n fo a odua exponenaon opeaon s abou O ( n) es whee n denoes he b engh of n eg s engh s usuay aen fo 52 bs o 024 bs [5] In hs subsecon we sepaae wo cases o anayze he cass ey devaon phase n Subsecon 253 Fo ase gven he pubc paaees nfoaon I( Tu ) = ( u s e) whee d u ( a ) ( n) u π od and he e-oen τ ( ) u = u s u o deve he use u who xˆ s he ebeshp of cass us copue ( ) ( n) u u od whee 7

8 Inenaona Jouna of Mueda Ubquous Engneeng Vo 3 No 4 Ocobe 2008 ( ) ( ) g du su x g ( od n) u u ( a ) a n u π od and s ( ) u y g od n xˆ Ony wo odua upcaons and one odua exponena opeaon ae equed a he use s copuaon effos I s heefoe copuaon savng n hs pesenaon See he copuaon equeens n he pa of AA seve Thee ae ξ + odua exponenaon opeaons one nvese copuaon and one odua upcaons fo devng g d ( a ) a ) u u π ( n) od and one odua upcaons fo devng s u equed whee ξ denoes a nube of casses n whch each cass sasfes π Fo ase 2 gven he pubc paaees nfoaon I( Tu ) = ( u s e) and he eoen τ u ( ) = u s u he use u who s he ebeshp of cass wans o deve j xˆ e She/he us copue π π/ j j ( ) ) ( n) u u od whee xˆ su x g ( odn) g d ( a ) a ) u ( n) u π od and s ( ) u y g od n onsde he copuaons n AA seve The copung coss of ξ + odua exponenaon opeaons one nvese g d copuaon and one odua upcaons fo devng ( a ) a ) π u ( n) u od ae equed whee ξ s a nube of casses sasfyng π ; Besdes AA needs o spend one exa odua upcaons fo devng s u On he ohe hand n he way of use s effos wo odua upcaons and η + odua exponena opeaon ae ony equed whee η s a nube of casses sasfyng π and π/ j I can be seen ha he copung effos ae ahe effcen n ou souon 26 Dynac change of casses dung a vad peod 26 Addng a cass Suppose ha a new cass + s added o he exsng syse whn a vad peod In esponse o hs change even he AA seve w andoy chooses a sa nege e + whch s eaed o φ ( n) and deves d + such ha e+ d+ ( odφ( n) ) Fuhe he AA seve w ean he cass ey copued by () fo he cass f he cass eaon sasfes π/ + afe he new cass + s added and updae he cass ey fo he cass f he cass eaon sasfyng + copued as π by upyng a new sece powe paaee d + and ao an adapabe e-oen fo any upcong use s access eques Tha s he adapabe e-oen w seve o he use who eans n he casses sasfyng π + fo he peod Afe hs change f a use u whee she/he s eans n he cass sasfyng π + and he/hs use nfoaon I ( u T u ) doesn need o be upgaded acvaes a new access eques n he peod he AA seve w geneae and send bac he adapabe e-oen τ u ( ) = u s u (7) whee d ( ) ( ) ) ( ) ( ) ( ) + g d g d ( a ) a π + π u a a od n and s y g d y d g od n u u u + + Evey eaned use n he syse w s eep he/hs own use nfoaon whch had assgned afe he cass + s added Accodng o Theoe and Theoe 2 he use u can deve he eys and j by usng he/hs use nfoaon and he adapabe eoen copued by (7) f he cass eaon π + s sasfed and he peod sasfes he condon T u d n + d g ( a ) π + ( od ) (6) 8

9 Inenaona Jouna of Mueda Ubquous Engneeng Vo 3 No 4 Ocobe Deeng a cass Suppose ha a cass s deeed fo he exsng syse a he peod The AA seve w ean he cass ey copued by () fo he ogna cass f he cass eaon sasfed π/ befoe he cass s deeed and updae he cass ey by (8) fo he ogna cass f he cass eaon sasfyng π befoe he cass s deeed copued as d d g g a a π od n π va upyng he powe nube e whch s he nvese nube of he paaee d and ao an adapabe e-oen fo any upcong use s access eques The AA seve ony updaes he e-oens coespondng o he new eaed upcong use s access eques whch seve o he nfuenced casses; he na cass eys and a of he exsng use e g d g d π ( a ) a ) π u ( a ) a ) ( odn) u u nfoaon do no need o econsuc anyoe Soon afe ha he AA seve ejecs a access equess fo he cass by geneang he new e-oen n whch he sece paaee d w be dscaded Tha s he AA w geneae he new e-oen τ u ( ) = u s u whee and su y e g ( odn) fo a uses who beong o he es casses fo sasfyng π and 263 Use change Suppose ha a use u ef unexpecedy fo he/hs esponsby n he syse a he peod whn he/hs pe-assgned auhozed peod se Ahough he use u acvaes an access eques n he e beongng o hose peods n pe-assgned auhozed peod se he AA seve w ejec o dsbue any e-oen f he use u has ef 27 Acvae a poacve phase fo a nex new peod ( ) ( ) ( ) (8) In hs phase he AA w updae a cass eys fo acvang a new poacve phase fo a peodca peod + The AA copues he new cass ey by efeshng boh he + pe nubes: g { g g g g z } nsead of g and a nsead of a + fo he cass fo he coespondng na ey whee 0 and + + > as foows d g g + + g+ ( d d2 d) ev ( ) ( a ) ( a ) ( odn) (9) π vπ/ whee he pe nube g s ep sece by he AA seve + We assue ha a use u d who beongs o he cass sasfyng jπ a he peod + acvaes a secue access eques and f he eques passes he use auhencaon and accessng vadaon hen he AA seve w copue he new e-oen fo fuhe accessng d g he cass jπ as foows τ u = ( ) d + ud s + ud whee + ( a ) a ) + u u ( odn) d π + d + and su y g ( od n) d+ Subsequeny he adapabe e-oen w send bac o he + use u d Then he use u d can deve (9) accodng o Theoe and deve j by usng + Theoe 2 e 9

10 Inenaona Jouna of Mueda Ubquous Engneeng Vo 3 No 4 Ocobe Dscussons In hs secon we dscuss he pacs of appyng poacve echans o convenona UHA schee and ae soe pefoance copasons beween he efeences [8 6] and ou schee The deas ae showed as foows 3 Povson of poacve cypogaphc ey assgnen schee The cypogaphc ey assgnen n ou poposed schee s condonay consaned upon he concep of peod so ha he cass ey s coespondng o a dsnc e-oen whch s secey and fequeny updaed by he AA In ohe wods he cypogaphc ey assgnen of evsed e-dependen feaue schee povdes he poacve anageen echans of he ey assgnen Tha s o say he poacve cass eys ae peodcay updaed hough he change of assocaed e-oens In hs way he aep of beang he cass ey can be effceny deeed The AA acvey changes a of he cass eys by povdng peodcay efeshng e oens fo each peod ha have e-dependen popees n whch hee ae coespondng and dsnc paaees u and s u o send o uses who have nvoed access equess fo he cass eys Assue ha a ega use u n cass s assgned he nfoaon I ( T u ) whch has he na deny u wh an auhozed e fo s o e Afe auhencaon he use can oban he e-oen τ u copsed of he paaees u (wh he sece poduc of ( a ) a n u od ) and s u Then he use u can boh deve he cass ey by (4) and he cass ey j by (5) f and ony f jπ and T u Thus we can pove ha a of he poacve cass eys can be changed by peodcay updang he e-oens dung a peod dsbued by he AA In hs way ou schee can acuay povde a poacve echans fo a cypogaphc ey assgnen schee n a heachy 32 Ou schee ade a gea pac on UHA As convenona UHA s unabe o effceny efec he use s exped epoyen e o povde efeshen of sece cass eys he pac of a poacve echans n a convenona UHA schee s dscussed beow () Peodcay efeshng cass eys by changng he e-oens n a UHA schee eans ha uses have nohng o do wh cass eys n he access cono echans of he heachy () hangng he e-oens n a UHA schee aows oe fexby Te-oens wh aocaed ghs and obgaons can be conoed by he AA Ou schee need no change any na paaees o pubshed nfoaon when casses ae ehe nceased o deceased () The pac of ou schee on he secuy of convenona UHA echanss n a heachy s as foows: a Uses canno ouch he pes of he e-dependen sece paaees such as a u and a whch effecvey pevens he eveang of sece cass ey b Uses access behavos can be ep by he AA seve n ou schee hough eques ecods If any dsubance o eaage occus he ecods w asss n pnponng he esponsby 33 opasons Nex we consde he copasons of copuaon e fo he cass ey devaon phase fo a vew of use-end aong ou schee and he wo schees [8] and [6] especvey 0

11 Inenaona Jouna of Mueda Ubquous Engneeng Vo 3 No 4 Ocobe 2008 Fo convenence a copasons we assue ha he copasons ae bounded o he peod fo devng a cass ey by a vad use Theefoe he devaon of a cass ey j n copuaons s suazed n Tabe Tabe opasons of a cass ey Schees j devaon opason Ies Nube of odua exponenaon copuaons Nube of odua upcaon copuaons Nube of Lucas opeaons copuaons Nube of opeaons f ( ) funcon copuaons Nube of hashng Tzeng s schee [6] Huang e a s schee [8] Ou schee +η z + η η + e s e s z copuaons Noe: we assue ha a e bound whch s fo he sa e s o he end e e s epesened as ( s e ) and he peod sasfes he condon T u In Tseng s schee [6] accodng o he nfoaon I( ) ( x y) s e = and he pubc paaees g g2 f f2 e e2 e n n2 he use us ae he copuaons of e s g g 2 π π/ j e ( x) α ( od n) and V e s f ( y) ( od n2) f β Upon he obsevaon he 2 copuaons of α and β e s + η odua exponenaons opeaons and e s Lucas opeaons ae equed especvey whee η s he nube of casses sasfyng π and π/ j Theefoe he copung cos of j = H( α β) needs e s + η odua exponenaons e s Lucas opeaons and a hash opeaon of H ( ) funcon especvey On he ohe hand n Huang e a s schee [8] he nfoaon I ( z) f ( ) d j a j π = z ( od n) f s spe funcon andoy povded by AA eg he z In and soe pubc paaees whee ( ) z ( f ( ) = n ode o deve he cass ey ( I( z) ) ) j ( n) π π/ e = f j od z e ( copuaon of f ( ) ) I z ( n) π π/ j = od s equed whee jπ and N

12 Inenaona Jouna of Mueda Ubquous Engneeng Vo 3 No 4 Ocobe 2008 hs expesson obvousy hee ae z + η odua exponenaon opeaons and z opeaons of funcon f ( ) equed whee η s a nube of casses sasfyng π and π/ j Fnay exane ou schee In ou schee when gvng he pubc paaees nfoaon of I( Tu ) = ( u s e) and he e-oen of τ ( ) u = u s u he copung cos fo a use n devng he ey of u π odn π/ j j u u g du whee cu c u ( a ) a ) ( n) u π od and s ( ) u y g od n wo odua upcaons and η + odua exponena opeaon ae equed whee η s a nube of casses ha sasfy π and π/ 4 oncusons j In hs pape we have poposed an adapabe souon fo cypogaphc ey assgnen schee wh adapabe e-oen consan whch s oe secue and effecve han a UHA schee A new echnque s poposed n he pape ha s used o adap he changeaby n dynac scenaos of he UHA schee eg he scenaos of he dynac change exapes of cass dung a vad peod shown n Subsecon 26 and Subsecon 262 he scenaos of he use change shown n he Subsecon 263 A cass eys w be updaed poacvey by he concep of poacve ey anageen whch we show n Subsecon 27; n hs way can ae he advanage ha s poven and fee fo he scenao of he cousve aac exape whch poposed by Y e a n [8] Tha s o say ou schee can acheve oe secue and oe effcen dynac anageen fo UHA schee Refeences ) ( s x odn ( ) e ) ( ) [] S G A and P D Tayo ypogaphc Souon o a Pobe of Access ono n a Heachy AM Tansacons on opue Syses vo no3 pp [2] achn K Kusawe A Lysyansaya and R Sob ypogaphy: Asynchonous Vefabe Sece Shang and Poacve yposyses Poceedngs of he 9h AM onfeence on opue and ouncaons Secuy Nov 2002 [3] R ane A Gennao Hezbeg and D Nao Poacve Secuy: Long-Te Poecon agans Beans ypobyes vo 3 no pp [4] hang R J Hwang and T Wu ypogaphc Key Assgnen Schee fo Access ono n a Heachy Infoaon Syses vo 7 no3 pp [5] H Y hen Effcen Te-Bound Heachca Key Assgnen Schee IEEE Tansacons On Knowedge And Daa Engneeng vo 6 no 0 pp Oc 2004 [6] Y Fane P Gee P D MacKenze and M Yung Poacve RSA Advances n ypoogy ypo`97 Poceedngs on Lecue Noes n opue Scence Spnge Veag pp [7] A Hezbeg M Jaobsson S Jaec H Kawczy and M Yung Poacve Pubc Key and Sgnaue Syses Poceedngs of he 4 h AM onfeence on opues and ouncaon Secuy pp 00 0 Ap 997 [8] H F Huang and hang A New ypogaphc Key Assgnen Schee wh Te-consan Access ono n a Heachy opue Sandads & Inefaces vo 26 ssue 3 pp May

13 Inenaona Jouna of Mueda Ubquous Engneeng Vo 3 No 4 Ocobe 2008 [9] F H Kuo V R L Shen T S hen and F La ypogaphc Key Assgnen Schee fo Dynac Access ono n a Use Heachy IEE Poceedngs on opues and Dga Technques vo 46 no 5 pp Sep 999 [0] S J Macnnon P D Tayo H Heje and S G A An Opa Agoh fo Assgnng ypogaphc Keys o ono Access n a Heachy IEEE Tansacons on opues vo 34 no 9 pp [] BM Macq and J-J Qusquae ypoogy fo Dga TV Boadcasng Poc IEEE vo 83 no 6 pp [2] A D Sans A L Feaa and B Masucc Enfocng he secuy of a e-bound heachca ey assgnen schee Infoaon Scences n Pess oeced Poof Avaabe Onne 9 Augus 2005 [3] Q Tang and J Mche oens on a ypogaphc Key Assgnen Schee opue Sandads & Inefaces vo 27 pp [4] R Osovsy and M Yung How o Whsand Mobe Vus Aacs AM Syposu on Pncpes of Dsbued opung (POD) pp [5] G J Sons onepoay ypoogy: The Scence of Infoaon Inegy IEEE Pess N Y 992 [6] W G Tzeng A Te-bound ypogaphc Key Assgnen Schee fo Access ono n a Heachy IEEE Tansacons on Knowedge and Daa Engneeng vo 4 no pp Feb 2002 [7] S Y Wang S Lah A Te-bound ypogaphc Key Assgnen Schee fo Access ono n a Heachy IEEE Tansacons on Dependabe and Secue opung vo 3 no pp 9 00 Jan-Ma 2006 [8] X Y and Y Ye Secuy of Tzeng s Te-bound Key Assgnen Schee fo Access ono n a Heachy IEEE Tansacons on Knowedge and Daa Engneeng vo 5 no 4 pp Augus

14 Inenaona Jouna of Mueda Ubquous Engneeng Vo 3 No 4 Ocobe 2008 Appendxes The poof of Theoe : u u d π Snce ( a ) ( od n) ( a ) ) g a d ( od n) n >> g Then we have xˆ ( ) ( ) ( s ) u x od n u ( od n) u u u ( ) ) (( ) od ) d g y x n a u π ( a ) u g d π a u ( a u ) a od Thus he heoe u π s y g ( ) and u u odn g d π ( a ) ( od n) ( ) ( n) ( od n) The poof of Theoe 2: Snce d g d ( a ) π ( od n) ( a ) a ) π ( odn) s y g ( ) u u u soe pubc paaees Then we have xˆ e ( ) ) ( ) ( s od ) u x n u π π/ j u u Thus he heoe u u odn n >>g and e ( ) π j π/ u j ( odn) ( ) (( ) od ) e g y x n g d d j j π au ( a ) a ) ( odn) u π π/ π e g d j j π ( au ( a ) a ) ( odn) u π π/ g d e ( a ) ) j π π π/ j ( odn) g d e ( a ) ) j j π π π/ ( odn) g du ( a ) u π j ( odn) j ( odn) 4

15 Inenaona Jouna of Mueda Ubquous Engneeng Vo 3 No 4 Ocobe 2008 Auhos Hsng-hung hen was bon n Tawan 966 He eceved he BS degee n Eeconc Engneeng fo Naona Tawan Unvesy of Scence and Technoogy Tape Tawan n 994 and he MS degee n Indusa Educaon fo Naona Noa Unvesy Tape Tawan n 996 especvey He eceved he PhD degee n Eeconc Engneeng fo Naona hung heng Unvesy ha-y Tawan n 2007 Dung he yeas he had seved as a Syse Engnee a he Depaen of Mobe Busness Goup hunghwa Teeco o Ld Fo Febuay 2008 pesen he has been he Asssan Pofesso of he Depaen of opue Scence and Infoaon Engneeng a Asa Unvesy n Tachung ouny of Tawan ueny he s neesed n eseachng Musesson ypogaphy Roe-based Access ono Fuzzy ono Gey Theoec and Weess ouncaons He s a ebe of he hnese ypoogy and Infoaon Secuy Assocaon (ISA) He s aso a ebe of he Inenaona Fuzzy Syse Assocaon (IFSA) he ebe of he hnese Gey Syses Assocaon He jons he nenaona coee on Inenaona onfeence on onvegence and Hybd Infoaon Technoogy (IIT) sees Now he s aso he evewe of he IET ouncaons (foey IEE Poceedngs ouncaons) Shuh-Jeng Wang was bon n Tawan 967 He eceved he MS degee n Apped Maheacs fo Naona hung-hsng Unvesy Tachung Tawan n 99 He eceved hs PhD degee n Eecca Engneeng a Naona Tawan Unvesy Tape Tawan n 996 He s cueny wh Dep of Infoaon Manageen a ena Poce Unvesy Taoyuan Tawan whee he decs he Infoaon ypoogy and onsucon Laboaoy (IL hp://heacpueduw) He was a ecpen of he 5h Ace Long-Tung Mase Thess Awad and he 0h Ace Long-Tung PhD Dsseaon Awad n 99 and 996 especvey D Wang was a vsng schoa of opue Scence Dep a Foda Sae Unvesy (FSU) USA n 2002 and 2004 He aso was a vsng schoa of Dep of opue and Infoaon Scence and Engneeng a Unvesy of Foda (UF) fo Aug 2004 o Feb 2005 He seved he edo-n-chef of he ouncaons of he ISA n Tawan fo He has been eeced as he Pane Deco of hnese ypoogy and Infoaon Secuy Assocaon (ISA) snce Sep 2006 D Wang acadecay oued he ylab wh Schoo of opue Scence n anege Meon Unvesy USA n Jan 2007 fo nenaona pojec coaboaon nspecon He s aso he auho/co-auho of sx boos (n hnese vesons): Infoaon Secuy ypogaphy and Newo Secuy Sae of he A on Inene Secuy and Dga Foenscs Eyes of Pvacy Infoaon Secuy and opue Foenscs Infoaon Mueda Secuy and opue Foenscs and Dga Evdence pubshed n and 2007 especvey He s a fu pofesso and a ebe of he IEEE AM Hs cuen neess ncude nfoaon secuy dga nvesgaon and copue foenscs seganogaphy cypogaphy daa consucon and engneeng 5

16 Inenaona Jouna of Mueda Ubquous Engneeng Vo 3 No 4 Ocobe 2008 Jyh-Hong Wen eceved he BS degee n eeconc engneeng fo he Naona hao Tung Unvesy Hsng-hu Tawan n 979 and he PhD degee n eecca engneeng fo Naona Tawan Unvesy Tape n 990 Fo 98 o 983 he was a Reseach Asssan wh he Teecouncaon Laboaoy Mnsy of Tanspoaon and ouncaons hung-l Tawan Fo 983 o 99 he was a Reseach Asssan wh he Insue of Nucea Enegy Reseach Taoyun Tawan Fo Febuay 99 o Juy 2007 he was wh he Insue of Eecca Engneeng Naona hung heng Unvesy ha-y Tawan fs as an Assocae Pofesso and snce 2000 as a Pofesso He was aso he Managng Deco of he ene fo Teecouncaon Reseach Naona hung heng Unvesy fo Aug 200 o Juy 2004 and he Dean of Genea Affas Naona h Nan Unvesy fo Aug 2004 o Juy 2006 Snce Aug 2007 he has been he Depaen Head of Eecca Engneeng Tungha Unvesy Tachung Tawan He s an Assocae Edo of he Jouna of he hnese Gey Syse Assocaon Hs cuen eseach neess ncude copue councaon newos ceua obe councaons pesona councaons spead-specu echnques weess boadband syses and gay heoy Pof Wen s a ebe of he IEEE ouncaon Socey he IEEE Vehcua Technoogy Socey he IEEE Infoaon Socey he IEEE cus and Syses Socey he Insue of Eeconcs Infoaon and ouncaon Engnees he Inenaona Assocaon of Scence and Technoogy fo Deveopen he hnese Gey Syse Assocaon and he hnese Insue of Eecca Engneeng 6