942 JOURNAL OF SOFTWARE, VOL. 5, NO. 9, SEPTEMBER 2010

Transcription

1 94 JOUNL OF SOFWE VOL. 5 NO. 9 SEPEME 010 eceip-free oercion-resisn emoe Inerne Voing Proocol wihou Physicl ssumpions hrough Denible Encrypion nd rpdoor ommimen Scheme o Meng School of ompuer Souh-ener Universiy for Nionliies Wuhn hin Emil: mengscuec@gmil.com Zimo Li nd Jun Qin School of ompuer Souh-ener Universiy for Nionliies Wuhn hin Emil: {lizm@sdu.edu.cn wr_q@homil.com} bsrc he secure remoe Inerne voing proocol ply n imporn role in Inerne voing sysem. he direcion of developmen of remoe Inerne voing proocol is h implemenion of receip-freeness nd coercion-resisnce is from wih srong physicl ssumpions o wih wek physicl ssumpions. he finl purpose is h receipfreeness nd coercion-resisnce is implemened wihou physicl ssumpions. In his pper firsly receip-free coercion-resisn remoe Inerne voing proocol bsed on MW denible encrypion scheme nd commimen scheme is developed. o our bes knowledge he proposed remoe Inerne voing proocol which hs receip-freeness nd coercion-resisnce is he firs remoe Inerne voing proocol implemened wihou physicl ssumpions. Secondly we nlyze receip-freeness nd coercionresisnce of he proposed remoe Inerne voing proocol. Finlly we compre securiy properies of severl ypicl proocols wih our presen proocol. Index erms physicl ssumpions remoe Inerne voing denible encrypion rpdoor commimen scheme proocol securiy I. INODUION Wih he progress of sociey nd developmen of democrcy of nion people cn use he elecion o express heir opinions. Owning o he populriy of Inerne nd informion echnology mny rdiionl rnscions re processed hrough Inerne. People my wn o use he personl compuer heir home o voe in elecion which is clled remoe Inerne voing. hus he secure remoe Inerne voing sysem plys n imporn role in remoe Inerne voing. he secure Inerne voing proocol is he bse of he remoe Inerne voing sysem. he secure nd prcicl remoe Inerne voing orresponding uhor: o Meng School of ompuer Souh-ener Universiy for Nionliies Wuhn hin his work ws suppored by Nionl Nurl Science Foundion of hin nd Nurl Science Foundion of Hubei Province (00734) proocol should hve he following properies: sic properies: privcy compleeness soundness unreusbiliy firness eligibiliy nd invribleness. Expnded properies: universl verifibiliy receip-freeness[1] coercion-resisnce [3] eceip-freeness: he voer cn no produce receip o prove h he voes specil bllo. Is purpose is o proec gins voe buying. Noion of receip-freeness ws inroduced by enloh nd uinsr [1]. hey propose receip-free scheme wih srong physicl ssumpions: voing-booh. Hir nd Sko in [4] poin ou h heir scheme is no receip-free. oercion-resisnce: coercion-resisn voing proocol should offer no only receip-freeness bu lso i cn preven rndomizion ck forced-bsenion ck nd simulion ck. he direcion of developmen of remoe Inerne voing proocol is implemenion of receip-freeness nd coercion-resisnce wihou physicl ssumpions nd consrins. he finl purpose is h receip-freeness nd coercion-resisnce is implemened wihou physicl ssumpions. People hve developed lo of Inerne voing proocols wih receip-freeness nd coercionresisnce. u ccording o our nlysis we found h he wekes physicl ssumpion mong implemenions of receip-freeness nd coercion-resisnce is one wy nonymous chnnel. o our bes knowledge up o now he remoe Inerne voing proocol wih receip-freeness nd coercion-resisnce implemened wihou physicl ssumpions does no exis. Moived by his in his pper we pply denible encrypion nd rpdoor commimen scheme o implemen he receip-freeness nd coercion-resisnce in he remoe Inerne voing proocol wihou physicl ssumpions. he min conribuions of his pper re summrized s follows. receip-free coercion-resisn remoe Inerne voing proocol is inroduced. 010 DEMY LISHE doi: /sw

2 JOUNL OF SOFWE VOL. 5 NO. 9 SEPEME Implemened receip-freeness nd coercionresisnce wihou physicl ssumpions nd consrins sed on denible encrypion scheme nd rpdoor commimen scheme. Orgnizion of he pper: In secion II reled works is discussed. he reled crypogrphic primiives re inroduced in secion III. In secion IV he remoe Inerne voing proocol wih receip-freeness nd coercionresisnce implemened wihou physicl ssumpions nd consrins is proposed. hen we nlyze he proposed proocol in secion V. II.ELED WOKS he direcion of developmen of remoe Inerne voing proocol is h implemenion of receip-freeness nd coercion-resisnce is from wih srong physicl ssumpions o wih wek physicl ssumpions. he finl purpose is h receip-freeness nd coercionresisnce is implemened wihou physicl ssumpions [34]. In he ps lo of Inerne voing proocols hve used srong physicl ssumpions o ccomplish receipfreeness nd coercion-resisnce. For exmple voing booh[15678]; unppble prive chnnel[910]; secre communicion chnnel nd smrcrd[11]; visul crypogrphy[56]; mper resisn rndomizer[1]; secure chnnel[13];ec. Severl Inerne voing proocols hve been proposed wih wek physicl ssumpions in recen yers. o our bes knowledge he wekes physicl ssumpions mong implemenions of receip-freeness nd coercionresisnce is one wy nonymous chnnel. Juels nd Jkobsson [3] firsly ddress he problem of chieving receip-freeness nd coercion-resisnce wihou unprcicl ssumpions which does no require unppble chnnels bu insed ssumes voer ccess o n nonymous chnnel some poin during he voing process. Ler hey give new version [14].heir proocol is bsed on Plinex Equivlence es mix ne nd zero knowledge proof. ccording o our nlysis we find h i hs he following problems: (1) do no defense gins forced-bsenion nd simulion cks ;() cn no suppor wrie in bllo. sed on JJ ide [14] Smih [15] poins ou JJ scheme is no secure gins 1009 ck nd ime smping ck nd hen proposes n improved coercion-resisn scheme wih wek physicl ssumpions: nonymous chnnel. His scheme replces he inefficien comprison mechnism of JJ by new one h compues he voing resuls in liner ime. In ddiion i includes n ddiionl mix sep in he llying phse nd uses imesmps. He performs globl blind comprison of cipherexs insed of employing he cosly plinex equivlence es. u r uo nd ror [16] nd lrkson e l. [17] poin ou h he mehod is no secure: n dversry cn use he ml mllebiliy o deermine wheher coerced voer gve him vlid or fke credenil. Weber [18] nd Weber e l. [19] lso poin ou weknesses on Smih s proposl nd fixed he JJ scheme nd Smih scheme. heir proocol is wih unppble prive chnnel. heir mehod is bsed on he Shmir secre shring [0] nd Pedersen disribued key generion proocol [1]. pplying some of he JJ ides [3] cquisi [] proposes coercion-resisn receipfree voing proocol wih wek physicl ssumpions: n nonymous chnnel. Is ide is h elecion uhoriies provide shres of credenils o ech voer long wih designed verifier proofs of ech shre s vlidiy. Voer cn che he coercer by producing flse credenil. Owning o designe verifier proof he coercer cn no verify he proof. Meng poins ou h i is no receipfreeness nd coercion-resisnce in [3]. skov [4] uses denible encrypion o implemen he receip-freeness. ecuse his denible encrypion is only process one bi in ech run his mehod cn no suppor he oher voing bllo forms. Such s chose one from mny wrie in bllo. r uo nd ror [16] presen coercion-resisn voing scheme h employs some of he JJ ides nd h compues elecion resuls in liner ime bsed on LSW ssumpions [5]. heir proocol is wih wek physicl ssumpions: n nonymous chnnel. hen e l. [6] inroduce he noion of linkble ring signure for designed verifiers nd hen use i o propose new receip-free elecronic voing scheme. he voing scheme chieves receip-freeness by llowing he voers o voe muli-imes wih wek physicl ssumpions: n nonymous chnnel. pplying some of cquisi ides Meng [3] presens receip-free coercion-resisn Inerne voing proocol bsed on non-inercive denible uhenicion proocol nd n improved proof proocol h wo cipherexs re encrypion of he sme plinex. His proocol hs receipfreeness nd coercion-resisnce nd i wih wek physicl ssumpions: one wy nonymous chnnel beween voer nd uhoriy. Meng [7] lso proposes n Inerne voing proocol pplied designed verifier proof nd proof of knowledge of wo cipherexs of he sme plinex bsed he sme ide. he proocol lso supposes here is one wy nonymous chnnel beween voer nd uhoriy. o our bes knowledge up o now i does no exis h he remoe Inerne voing proocol wih receip-freeness nd coercion-resisnce implemened wihou physicl ssumpions. Denible encrypion cn be used gins reveling informion h he owner of he informion my decryp i in n lernive wy o differen plinex. Nmely if his user opens ll his inpus including he climed encryped messge o coercer he coercer fils o prove he vlidiy or invlidiy of he opened messge. Moived by his we pply denible encrypion scheme nd rpdoor commimen scheme o implemen he receip-freeness nd coercion-resisnce wihou physicl ssumpions. III.ELED YPOGPHI PIMIIVES In his secion we inroduce he reled crypogrphic primiives which re used o develop our proposed remoe Inerne voing proocol. hese crypogrphic 010 DEMY LISHE

3 944 JOUNL OF SOFWE VOL. 5 NO. 9 SEPEME 010 primiives include commimen scheme nd MW denible encrypion scheme.. ommimen Scheme rpdoor commimen scheme is funcion wih ssocied pir of mching public nd prive keys. he min propery we wn from such funcion is collision-resisnce: unless one knows he rpdoor i is infesible o find wo inpus h mp o he sme vlue. On he oher hnd knowledge of he rpdoor suffices o find collisions esily. commimen scheme [30] is bsed on cryposysem [30]. rpdoor commimen scheme consiss of key generion lgorihm commimen funcion nd collision-finding funcion. Key Generion he key generion lgorihm on inpu securiy prmeer l produces modulus N produc of wo sfe primes of size l / ogeher wih squre h of mximl order in G. he public key is given by N nd h. he fcorizion of he modulus is he prive key pq. ommiing Messge o commi o messge m he sender chooses rndom number r N nd N/ ses r m h r 1 mnmodn nd sen rm o he receiver. ollision-finding funcion Now given commimen r m G ogeher wih he corresponding rm knowing he fcorizion of he modulus one cn find collisions for ny messge ' r' r m m' d N mod N N /. m s follows hus he receiver cn ge r m r' m' G N.. MW Denible Encrypion Scheme Denible encrypion cn be used gins reveling informion h he owner of he informion my decryp i in n lernive wy o differen plinex. Nmely if his user opens ll his inpus including he climed encryped messge o coercer he coercer fils o prove he vlidiy or invlidiy of he opened messge. MW denible encrypion scheme [3] consiss of preliminries encrypion decrypion nd dishones opening phses. Preliminries he receiver chooses rndom elemen nd ses g mod N publishes publicly N N g. hen he sender ges N g nd chooses rndom number 1 ord G h g mod N nd compues publish publicly g.he public key of he receiver is given by he riple N g h while he corresponding secre key is prive key pq. he sme ime he sender cn generes his public key N g h nd prive key bsed on cryposysem. Finlly he crees his prive key nd public key y g mod p ccording o ml cryposysem [8 9]. ecuse everyone cn know he public key N g h of he sender he receiver cn ge he sender prive key owning o he knowledge of h g mod N nd N p q. Encrypion he sender choose rndom numbers r g fer h he sender genere he messge m N which will be sen o he receiver in denible encrypion scheme. he sender compues r m r m h r 1 mn modn bsed on commimen scheme. Genering he fke ' messge m he cn find r1 r mm' d Nmod NN/ which mke ' r m r m.hen he compues 1 hsh( r ) hsh( r ) g r1 y r1 r using ml cryposysem. is he cipherex of r. Finlly he sends nd r m o he receiver. Decrypion he receiver uses he prive key pq o recover 1mod / mod m D N N N bsed on cryposysem. Dishones Opening he receiver uses he prive key o recover he plinex k x k r wih 1 1 hen he cn compue hshr r y r r g r nd ges r g hsh r. r1 he receiver compues 1 g mod N nd r g mod N bsed on cryposysem hen he recovers m1 N N 1 1mod 1 nd m 1mod N N wih he decrypion lgorihm. If m m1 hen r r1 ; If m m hen r r. ccording o he encrypion lgorihm le r r he sme ime he receiver knows m so he cn ge r m m 1 mod r N N h which r m r m'. hus if he receiver mkes DEMY LISHE

4 JOUNL OF SOFWE VOL. 5 NO. 9 SEPEME coerced he cn provide he fke messge m ' o he coercer. he coercer cn no verify he fke messge. IV.HE POPOSED EMOE INENE VOING POOOL. ssumpions nd Model In proposed remoe Inerne voing proocol when coerced by he coercer he voer wns o lie bou he decryped messge o coercer nd hence escpe coercion. On one hnd he voer is ble o decryp he correc messge from he regisrion uhoriy on he oher hnd ll he informion held by he voer when opened o coercer do no llow his coercer o verify he encryped messge or he coercer cn no find he messge is fke messge. onsequenly bribing or coercing he voer becomes useless from he very beginning. he pricipns in our proocol consis of he voer regisrion uhoriy llying uhoriy coercer nd briber. s usul he regisrion uhoriy nd llying uhoriy cn be beyond he rech of ny coercer by inroducing hreshold encrypion while he voer is possibly coerced or bribed. he briber cn bribe he voer nd voer wn o provide he evidence o prove h he voe specil bllo ccording o requiremen of he briber. he briber hs he biliy o monior he communicion chnnels. he briber is pssive cker. he coercer hs he power o pproch he voer coercing him o revel he decryped messge he decrypion key nd ll he prmeers he used during decrypion. In our proposed proocol we ssume h he coercer hs he biliy o evesdrop ll he communicion chnnels. In our proposed proocol we lso ssume h he chnnel beween he voer nd regisrion uhoriy nd he voer nd bullein bord re ppble chnnel. h is men everyone including briber nd coercer cn ge he conen on he chnnel.. he Ide of he Proposed emoe Inerne Voing Proocol he ide of he proposed Inerne voing proocol wih receip-freeness nd coercion-resisnce is h: if everyone knows h he voer hs he biliy h generes he fke credenil nd he bllo when he voer provides he evidence o he voe-buyer or briber or coercer hey hs no he biliy o verify he evidence so he voe-buyer does no give he money o he voer. he sme ime he voer cn escpe he coercion.so he proposed Inerne voing proocol hs receip-freeness nd coercion-resisnce. How o mke he voer o hve biliy h generes he fke credenil nd he bllo wih he condiion he briber nd coercer cn evesdrop he communicion chnnel? Owning o he propery of MW denible encrypion nd commimen scheme we cn use i o implemen he biliy. he proposed Inerne voing proocol pplies he encrypion echnologies which include ml cryposysem hreshold ml cryposysem mix ne denible encrypion nd commimen scheme.. he Proposed Proocol In order o express he ide clerly we suppose h here is only one regisrion uhoriy nd one llying uhoriy. he proposed remoe Inerne voing proocol includes four phses: preprion phse regisrion phse voing phse nd llying phse. Noion definiion: : he regisrion uhoriy; : he llying uhoriy; V ( 1 l) : he h legl voer; : llo voed ; 1 l : crees he rndom number forv. I is he credenil ofv ; P : he public key nd prive key of bsed on cryposysem which is used when voer regiser; P :he public key nd prive key of bsed on ml cryposysem which is used when voer regiser; P :he public key nd prive key of bsed on commimen scheme which is used when voer voe; P :he public key nd prive key ofv bsed on cryposysem; P :he public key nd prive key ofv bsed on ml cryposysem; P( m ): Sign m wih prive key P ; ( m ): Encryp m wih prive key ; : Self blinding operion; Idenif : Idenificion ofv ; Preprion phse he regisrion uhoriy elemen nd ses g N chooses rndom mod N publishes publicly N g. hen he voer V ges N g nd chooses rndom number 1 ord G h g mod N nd publish publicly compues g.he public key of he regisrion uhoriy is given by he N g h while he corresponding secre riple key is prive key P voer p q. he sme ime he V cn generes his public key N g h nd prive key P bsed on cryposysem. Finlly he lso crees his prive key P nd public key y g mod p ccording o ml cryposysem. ecuse everyone N g h of cn know he public key 010 DEMY LISHE

5 946 JOUNL OF SOFWE VOL. 5 NO. 9 SEPEME 010 regisrion uhoriy regisrion uhoriy he voer V cn ge he prive key P hrough he knowledge of h g mod N nd N p q. Finlly he regisrion uhoriy key nd prive key cryposysem egisrion uhoriy bllo nd send bord denoed by. llying uhoriy generes his public P bsed on ml generes he nd is digil signure o bullein generes his public key P p q N h nd prive key ccording o commimen scheme. egisrion phse (1) Firsly voer V generes he Idenif secondly produces messge P Idenif Idenif nd send i o regisrion uhoriy. egisrion uhoriy receives he messge nd uses is prive key o verify he digil signure. egisrion uhoriy checks Idenif h wheher he hs regisered or no. If he hs regisered regisrion uhoriy sends he error messge ov. he proocol ends. If he hs no regisered regisrion uhoriy execues <> sep. Figure 1 describes he regisrion phse. () ccording o requiremens of MW denible encrypion scheme regisrion uhoriy P r produces hen send r i o he voer by ppble chnnel. (3). egisrion uhoriy sends P o in ble III. Voer V egisrion uhoriy 1 P Idenif Idenif P r r 3 P. Figure 1. egisrion phse Voing phse Voer V chooses his fvor bllo. Using llying uhoriy public key N h generes r r 1 1 voer V wih commimen scheme nd sends i o ble I rndomly in by ppble chnnel. llying phse (1) ccording o he rules he llying uhoriy r r. elimines he duplice 1 1 he resuls re sored in ble II. () Mixing uhoriy mixes r r in ble II. he 1 1 corresponding resuls re r1 r1 nd sored in ble IV nd ble V. (3) llying uhoriy decryps 1 1 r r in ble IV nd ble V nd ges nd. he sme ime he verifies decryp P nd le regisrion uhoriy nd ges in ble III. (4) llying uhoriy llies he bllo nd publishes he resuls. LE I. LE II. LLOS EFOE LLYING r r LLO ELIMINED HE DUPLIE 010 DEMY LISHE

6 JOUNL OF SOFWE VOL. 5 NO. 9 SEPEME r r LE III. HE P P Proof LE IV. E r1 r Proof LE V. HE r V. POPEIES NLYSIS Owning o he spce limiion we only nlysis receip-freeness nd coercion-resisnce. eceip-freeness he proposed Inerne voing proocol ccomplishes receip-freeness by MW denible encrypion scheme nd commimen scheme. ccording o he proposed proocol in regisrion phse he voer ge he rel credenil which cn be verified by he voer himself hrough hones opening in MW denible encrypion scheme from he regisrion uhoriy. pplying he dishones opening in MW denible encrypion scheme he voer cn genere fke credenil fke o sisfy P r r fker fke which is used o che briber. lhough he briber hs he biliy o monior he communicion chnnel beween voer nd regisrion uhoriy becuse he voer cn provide he r he briber cn verify i rnscrips of fke fke r1 Proof nd cn no find fke is fke credenil. he sme ime in voing phse he voer send he bllo nd credenil o by commimen scheme. Own o he propery of commimen scheme he voer lso r r cn find collisions: 1 fke 1 fke r1 fker1 fke nd provide he rnscrip of fker1 fke fker1 fke which cn be verified by he briber lhough he briber hs he biliy o evesdrop he communicion chnnel beween voer nd. In word he voer hs he biliy o produce he fke credenil nd bllo which cn be verified by briber or voer buyer. So he voe buyer or briber does no give he money o he voer. Hence he proocol is receip-freeness.. oercion-resisnce We hve lredy nlyzed h i is receip-freeness in previous secion. In he following we nlyze h i cn preven rndomizion ck forced-bsenion ck nd simulion ck. (1) ndomizion ck he ide of ndomizion ck is for n cker o coerce voer by requiring h she submi rndomly composed blloing meril. he effec of he ck is o nullify he choice of he voer. We suppose h voer wns o preven rndomizion ck. u fer voing by coercer he voe cn voe his fvorie bllo becuse he voe cn voe severl imes ccording o he proposed proocol. So he proocol cn preven rndomizion ck. () forced-bsenion ck his is n ck reled o he previous one bsed on rndomizion. In his cse he cker coerces voer by demnding h she refrin from voing. ecuse he coercer hs he biliy o evesdrop he communicion chnnel beween he voer nd regisrion uhoriy he cn ge P r r nd P Idenif Idenif hence he curren version of he proposed proocol is no gins his ck. u we cn use offline wy in regisrion phse hus ccording o proocol coercer cn no know if voer hs regisered bsed on. In voing phse he r r by coercer cn ge 1 1 monior he communicions beween he voer nd. Owning o propery of commimen scheme he coercer cn no idenify he credenil of he voer nd find who voe he bllo. So he proocol cn preven forced-bsenion ck. (3) Simulion ck Simulion ck is h n cker coerces voers ino divulging prive keys or buying prive keys from voers nd hen simuling hese voers will i.e. voing on heir behlf. oercer cn voe on voer behlf fer geing prive key of voer in our proposed proocol. u fer voing by coercer he voe cn voe his fvorie bllo becuse he voe cn voe severl imes ccording o he proposed proocol. Hence he proocol cn preven simulion ck. VI. ONLUSION Inerne voing proocol is bse of Inerne voing sysem. In his pper firsly receip-free coercionresisn remoe Inerne voing proocol bsed on MW denible encrypion scheme nd commimen scheme is developed. he proposed proocol is he firs remoe Inerne voing proocol which hs receipfreeness nd coercion-resisnce nd is implemened wihou physicl ssumpions. Secondly we nlyze receip-freeness nd coercion-resisnce of he proposed remoe Inerne voing proocol. hirdly we compre securiy properies of severl ypicl proocols wih our 010 DEMY LISHE

7 948 JOUNL OF SOFWE VOL. 5 NO. 9 SEPEME 010 presen proocol. Owning o he spce limiion we only give he resul described in ble VI ble VII nd ble VIII. In he fuure we will use he proocol nlyzer ProVerif [33] bsed on he pplied pi clculus o nlyze receipfreeness nd coercion-resisnce properies of he proposed Inerne voing proocol. he sme ime we will develop n Inerne voing sysem bsed on our proposed proocol. LE VI. HE ESUL OF NLYZING EEIP-FEENESS ND WH PHYSIL SSUMPIONS E USED HE MK EPESENS HE POOOL IS WIH PHYSIL SSUMPIONS; HE MK EPESENS HE POOOL HS HE POPEY; HE MK F EPESENS HE POOOL HS NO HE POPEY Physicl ssumpions [1] [4] [9] [11] [56] [6] [1] [] Voing booh Unppble one-wy chnnels Unppble prive chnnel Secre communicion chnnel Smr crd Visul crypogrphy nonymous chnnel mper resisn rndomizer ndomizer ppble chnnel Securiy eceip-freeness F LE VII. HE ESUL OF NLYZING EEIP-FEENESS ND WH PHYSIL SSUMPIONS E USED HE MK EPESENS HE POOOL IS WIH PHYSIL SSUMPIONS; HE MK EPESENS HE POOOL HS HE POPEY Physicl ssumpions [10] [7] [3] [] [314] [8] our Voing booh Unppble prive chnnel Privcy commission members nonymous chnnel Securiy eceip-freeness LE VIII. HE ESUL OF NLYZING OEION-ESISNE ND WH PHYSIL SSUMPIONS E USED;HE MK EPESENS HE POOOL IS WIH PHYSIL SSUMPIONS; HE MK EPESENS HE POOOL HS HE POPEY; HE MK F EPESENS HE POOOL HS NO HE POPEY Physicl ssumpions [3] [15] [1819] [16] [17] [] [3] [7] our Unppble prive chnnel nonymous chnnel ppble chnnel Securiy oercion-resisnce F F F F EFEENES [1] J.enlohD.uinsr eceip-free secre-bllo elecions In he proceeding of SO 94 pp []. Okmoo eceip-free elecronic voing schemes for lrge scle elecions In he proceeding of Securiy Proocols Workshop Springer-Verlg LNS 1361 pp [3].Juels M. Jkobsson oercion-resisn elecronic elecions hp:// [4] M.HirK.Sko Efficien receip-free voing bsed on homomorphic encrypion In he proceeding of EUOYP 00 Springer-Verlg LNS 1807 pp [5] D.hum Secre-bllo receips nd rnspren inegriy Drf hp://voingindusry.com/ech_orner/hum_ricle.pdf 00. [6] D.hum Secre-llo eceips: rue Voer-Verifible Elecions IEEE Securiy nd Privcy vol. no. 1 pp Jn [7].I. Fn W.Z. Sun n efficien muli-receip mechnism for uncoercible nonymous elecronic voing Mhemicl nd ompuer Modeling Volume 48 Issues 9-10 pp November 008. [8]. Neff Deecing mlicious poll sie voing cliens hp:// [9] K. Sko J. Kilin eceip-free Mix-ype Voing Scheme prcicl soluion o he implemenion of voing booh dvnces in rypology EUOYP 95 pp [10]. Morn M. Nor eceip-free Universlly-Verifible Voing wih Everlsing Privcy dvnces in rypology - YPO 006 Volume 4117/006.pp [11] O. udron P.Fouque D. Poinchevl J. Sern nd G. Pouprd Prcicl muli-cndide elecion sysem In Proceedings of he wenieh nnul M Symposium on Principles of Disribued ompuing (Newpor hode Islnd Unied Ses). POD '01. M New York NY pp [1]. Lee. oyd E. Dwson K. Kim J. Yng nd S. Yoo Providing eceip-freeness in Mixne-bsed Voing Proocols 010 DEMY LISHE

8 JOUNL OF SOFWE VOL. 5 NO. 9 SEPEME hp://cislb.icu.c.kr/pper/pper_files/003/iis03/mnvo ing-finl-icisc003.pdf003. [13] H.Zhong L.S.Hung nd Y.L.Luo Muli-ndide Elecronic Voing Scheme sed on Secure Sum Proocol Journl of ompuer eserch nd Developmen 43(8).pp [14].Juels D. lno nd M. Jkobsson oercionresisn elecronic elecions In Proceedings of he 005 M Workshop on Privcy in he Elecronic Sociey (lexndri V US November ). WPES '05. M New York NY pp [15] W.D. Smih New crypogrphic voing scheme wih bes-known heoreicl properies In Workshop on Froniers in Elecronic Elecions (FEE 005) Miln Ily hp:// Sepember 005. [16] S.F.r uo J..ror prcicl nd secure coercionresisn scheme for remoe elecions Froniers of Elecronic Voing hp://drops.dgsuhl.de/opus/vollexe/008/195/ 008 [17] M. lrkson S. hong nd..myers ivis: Secure emoe Voing Sysem echnicl repor ornell Universiy ompuing nd Informion Science echnology epor hp://drops.dgsuhl.de/opus/vollexe/008/196/ My 007. [18] S. Weber oercion-esisn rypogrphic Voing Proocol- Evluion nd Prooype Implemenion Drmsd Universiy of echnology hp:// [19] S.G.Weber.ruo nd J. uchmnn On oercion- esisn Elecronic Elecions wih Liner Work In Proceedings of he Second inernionl onference on vilbiliy elibiliy nd Securiy (pril ). ES. IEEE ompuer Sociey Wshingon D pp [0]. Shmir How o shre secre ommon. M 11 pp Nov [1]. P. Pedersen hreshold cryposysem wihou rused pry (exended bsrc) In dvnces in rypology - EUOYP 91 volume 547 of LNS pp pril [].cquisi eceip-free Homomorphic Elecions nd Wrie-in Voer Verified llos echnicl epor 004/105 Inernionl ssociion for rypologic eserch My 004 nd rnegie Mellon Insiue for Sofwre eserch Inernionl MU-ISI hp:// [3]. Meng Secure Inerne Voing Proocol sed on Non-inercive Denible uhenicion Proocol nd Proof Proocol h wo ipherexs re Encrypion of he Sme Plinex. Journl of Neworks 4(5) pp [4] Z. skov Elecronic Voing Schemes Mser hesies. Deprmen of ompuer Science Fculy of Mhemics Physics nd Informics omenius Universiy rislv pril 00. [5] J. menisch. Lysynsky Signure schemes nd nonymous credenils from biliner mps dvnces in rypology YPO 004pp [6] G. hen. Wu W. Hn X. hen H. Lee nd K. Kim New eceip-free Voing Scheme sed on Linkble ing Signure for Designed Verifiers In Proceedings of he 008 inernionl onference on Embedded Sofwre nd Sysems Symposi - Volume 00 (July ). IESSSYMPOSI. IEEE ompuer Sociey Wshingon D pp [7]. Meng n Inerne Voing Proocol wih eceip-free nd oercion-esisn In Proceedings of he 7h IEEE inernionl onference on ompuer nd informion echnology (Ocober ). I. IEEE ompuer Sociey Wshingon D pp [8]. ml public key cryposysem nd signure scheme bsed on discree logrihms In: lkely G.. hum D. (eds.) YPO LNS vol. 196 pp Springer Heidelberg [9]. ml public key cryposysem nd signure scheme bsed on discree logrihms IEEE rns. Inf. heory 31(4) pp [30] E.resson D. lnond D. Poinchevl simple public key cryposysem wih double rpdoor decrypion mechnism nd is pplicions. In: Lih S ed. cicryp 003. LNS 894 erlin: Springer-Verlg pp [31] M. Klonowski P. Kubik nd M. Kuyowsk Prcicl Denible Encrypion SOFSEM 008: heory nd Prcice of ompuer Science34h onference on urren rends in heory nd Prcice of ompuer Science Nový Smokovec Slovki Jnury pp [3].Meng J.Q.Wng n Efficien eceiver Denible Encrypion Scheme nd Is pplicions (cceped). [33]. lnche n Efficien rypogrphic Proocol Verifier sed on Prolog ules In Proceedings of he 14h IEEE WSF nd pp.8-96 June [34].Meng riicl eview of eceip-freeness nd oercion-esisnce Informion echnology Journl 8(7) pp o Meng ws born in 1974 in P..hin. He received his M.S. degree in compuer science nd echnology Ph.D. degree in rffic informion engineering nd conrol from Wuhn Universiy of echnology Wuhn P..hin in respecively. From 004 o 006 he works in Wuhn Universiy P..hin s Posdocorl resercher in informion securiy. urrenly he is n ssocie Professor in school of compuer Souh-ener Universiy for Nionliies P..hin. He hs uhored/couhored over 40 ppers in Inernionl/Nionl ournls nd conferences. His curren reserch ineress include elecronic commerce Inerne voing nd proocol securiy. Zimo Li ws born in He received his.s. degree in Mhemics in 1996 M.Eng degree in ompuer Science in 1999 boh from Shndong Universiy P..hin nd Ph.D degree in ompuer Science from iy Universiy of Hong Kong Hong Kong in 00. He is currenly n ssocie Professor in he School of ompuer Science Souh-ener Universiy for Nionliies P.. hin. His reserch ineress re design nd nlysis of lgorihms complexiy heory nd compuionl biology. Jun Qin ws born in 1968 in P..hin. She received her M.S. degree in compuer science in 1995 from Huzhong Universiy of Science nd echnology nd Ph.D. degree in compuer sofwre heory in 005 from Wuhn Universiy respecively Wuhn P..hin in 006; she worked in Wisconsin Universiy U.S.. s n inernionl visiing scholr in informion securiy. urrenly she is Professor of school of compuer Souh- ener Universiy for Nionliies P..hin. She hs uhored/couhored over 50 ppers in Inernionl/Nionl ournls nd conferences. Her curren reserch ineress include elecronic commerce securiy inelligen lgorihm. 010 DEMY LISHE