Semi-quantum private comparison protocol under an. almost-dishonest third party

Transcription

1 Sem-quntum prvte comprson protocol under n lmost-dshonest thrd prty Wen-Hn Chou Tzonelh Hwng nd Jun Gu Deprtment of Computer Scence nd nformton Engneerng Ntonl Cheng Kung Unversty No. Unversty Rd. Tnn Cty 700 Twn R.O.C @gml.com hwngtl@sml.cse.ncku.edu.tw sgujun@gml.com Responsle for correspondence: Tzonelh Hwng Dstngushed Professor Deprtment of Computer Scence nd nformton Engneerng Ntonl Cheng Kung Unversty No. Unversty Rd. Tnn Cty 700 Twn R.O.C. Eml: hwngtl@sml.cse.ncku.edu.tw TEL: ext. 654

2 Astrct Ths study presents the frst sem-quntum prvte comprson SQPC protocol under n lmost-dshonest thrd prty. The proposed protocol llows two clsscl prtcpnts to compre ther secret nformton wthout compromsng t s prvcy. The securty nlyses ndcte tht the protocol s free from severl well-known ttcks. Keywords: Sem-quntum prvte comprson; lmost-dshonest thrd-prty; outsder ttck; nsder ttck. ntroducton Snce the frst quntum key dstruton QKD protocol presented y ennett nd rssrd [] mny quntum cryptogrphc protocols such s teleportton [-7] quntum secret shrng QSS [8-6] quntum secure drect communcton QSDC [7-] nd so on hve een proposed to solve vrous securty prolems. Recently quntum prvte comprson QPC hs ecome nother populr topc for reserch. The gol of QPC protocol s to prvtely compre two prtcpnts undsclosed nformton for equlty. n prevous QPC protocols the prtcpnts need to e equpped wth dvnced quntum devces such s quntum memory quntum genertor or quntum untry opertons for comprson. However ths pper proposes the frst sem-quntum prvte comprson SQPC protocol for the prtcpnts who do not hve ny quntum cplty to compre ther secrets under n lmost-dshonest thrd-prty [ 3]. An lmost-dshonest TP my try to perform vrous possle ttcks for dsclosng the secret nformton of the prtcpnts ut he/she cnnot collude wth the prtcpnts.

3 n prevous oyer et l. [4 5] proposed two novel sem-quntum key dstruton SQKD protocols usng sngle photons. Accordng to ther defnton the term sem-quntum mples tht the sender Alce s powerful quntum communcnt wheres the recever o hs only clsscl cpltes. More precsely the sender Alce hs the lty to perform the followng opertons: prepre ny quntum stte such s sngle photons or ell sttes perform ny quntum mesurement such s ell mesurement or mult-qut jont mesurement nd 3 store quts n quntum memory. Conversely the clsscl o s restrcted to perform the followng opertons over the quntum chnnel: prepre new quts n the clsscl ss { 0 }.e. Z ss mesure quts n the clsscl ss 3 reorder the quts v dfferent dely lnes nd 4 send or reflect the quts wthout dsturnce. As the clsscl ss only consders the quts 0 nd the other quntum superpostons of sngle photons re not ssumed for the clsscl o. The clsscl o s opertons descred ove re equvlent to the trdtonl{0}computton. n ths pper we propose n SQPC protocol where the clsscl prtcpnts re lmted to perform the opertons nd 4. Tht s the prtcpnts do not hve ny quntum cpltes wheres the TP s the only one who hs the quntum cplty. A sem-quntum prvte comprson protocol cn reduce not only the computtonl urden of the communcnts ut lso the cost of the quntum hrdwre devces n prctcl mplementtons. Furthermore the proposed protocols re free from vrous well-known ttcks wth the ssumpton of only n lmost dshonest thrd prty. The rest of ths pper s orgnzed s follows: Secton proposes the sem-quntum prvte comprson SQPC protocol. Secton 3 presents securty 3

4 nlyse of the proposed SQPC protocol. Secton 4 summrzes our results. Proposed SQPC protocol Ths secton proposes new sem-quntum prvte comprson protocol under n lmost-dshonest thrd prty. Alce nd o re two prtcpnts who wnt to compre the equlty of ther secret nformton n the SQPC protocol. TP s ssumed to e n lmost-dshonest thrd prty who my try to derve nformton durng executng of the protocol. TP my modfy the procedure of the protocol to derve nformton ut he cnnot pulsh fke comprson result or collorte wth ny clent. The quntum chnnels re ssumed to e del.e. non-lossy nd noseless nd the pulc chnnels etween TP nd Alce TP nd o nd Alce nd o re lso ssumed to e uthentcted. sed on the three-prty scenro descred ove the process of the proposed protocol wll e descred n steps s follows.. Descrpton of the proposed SQPC protocol efore presentng the steps of the proposed protocol we refly descre some rules for mlcous ehvor detecton some symols nd entnglement swppng used n our protocol. n prtculr for ech receved qut the prtcpnt hs to set the vlues of nd for tht qut respectvely. =0/ denotes tht the prtcpnt selects the qut for mlcous ehvor detecton : =0 ndctes tht the qut s used to detect ttcks from ny mlcous users wheres = s used to detect ttcks from TP. ndctes the type of opertons performed on tht qut y the clent. =0 represents tht the prtcpnt performs the Z-ss mesurement nd = represents drect reflecton of the t to TP y the clent. The entnglement swppng llows one to mesure on ny two ndependent entngled photons the rest photons wll e entngled regrdless of the dstnce 4

5 etween them. For exmple ssume tht there re two ndependent EPR prs nmely the pr - nd the pr 3-4. Then f we perform ell mesurement on the qut nd the qut 3 then the qut nd the qut 4 whch re orgnlly ndependent wll e entngled mmedtely. f the mesurement result of the qut nd the qut 3 s then the stte of the qut nd the qut 4 must e s well. We my encode the ell mesurement result n the clsscl ts s follows: nd. The entnglement swppng follows the mth formul M ellqq M ellq3q 4 = M ellqq 3 M ellqq4 [6 7] where s the exclusve-or operton. n our scheme TP wll set vlue of M ccordng to ths mth formul. M=0 represents the mesurement results nd the mth formul mtch wheres M= represents the mesurement results nd the mth formul do not mtch. sed on the coordnton of the vlues of nd M the proposed SQPC llows two mutully untrusted prtcpnts to compre the equlty of ther secrets under the lmost dshonest TP. The detl of the protocol s descred n steps s follows: Step. TP rndomly genertes two sequences of ell sttes S { S S S... S } S { S S S... S } 3 A A A A3 A n n wth the length of n where S A { } S { } for = n. The ntl stte of ech pr n S A S s denoted s S A S S A nd S { }. Then TP dvdes these two sequences S A nd S nto four ordered sequences A { } A { } { } nd { } for = n whch denote ll the frst nd the second prtcles of ell sttes n S A nd S respectvely. 5

6 Step. After the Step s preprton TP retns the sequences A nd nd sends prtcle n the sequences A to Alce nd prtcle n to o respectvely. Step3. When Alce o receves qut n A she he hs to set the vlues of nd for tht qut. f =0 Alce o wll send nd ck to TP wheres when = Alce o wll only send ck to TP nd keep n her hs hnd. TP wll perform three dfferent opertons ccordng to nd s shown n Tle. n our scheme f prtcpnt wnts to check Eve s ttck he/she wll set =0. f prtcpnt wnts to check the honesty of TP then he/she sets =. TP cn only e checked when oth prtcpnts wnt to do so.e. = should e set y oth clents for tht qut. f only one prtcpnt wnts to check TP then he/she wll e gnored. The protocol cn e descred n the followng three cses. Step4. Cse. f Alce o sets 0 nd =0 then she he frst sends the vlue of nd the mesured qut to TP. ecuse Alce o mght chnge the stte of the photon whch comes from TP we use to denote the photon whch Alce o sends ck to TP. After TP receves =0 nd he pulcly nnounces n cknowledgment. When Alce o receves the cknowledgment Alce o sends =0 nd the mesurement result MR MR to TP. When TP receves the 6

7 mesurement result MR MR nd =0 TP performs Z-ss mesurement on nd otns the mesurement result MR MR. Then TP compres the mesurement result MR MR wth the mesurement result MR MR to check the exstence of n evesdropper. f the mesurement results re not equl then TP wll termnte the protocol nd strt from the egnnng. f the mesurement results re equl then TP wll follow the Step to send out the next quts to the clents. Cse. f Alce o sets =0 nd = then Alce o frst sends the orgnl qut nd =0 to TP. After TP receves the qut nd =0 he pulcly nnounces n cknowledgment. After Alce o receves the cknowledgment she he sends = to TP. TP then performs ell mesurement on the qut nd compres the ell mesurement result wth the ntl stte of A S S to see whether they re equl or not. f the mesurement results re not equl then TP wll termnte the protocol nd strt from the egnnng. f the mesurement results re equl then TP wll follow the Step to send out the next quts to the clents. Cse3. f Alce nd o oth set = then they send the quts nd = to TP. When TP receves oth = from Alce nd o TP performs two ell mesurements on the quts nd whch re denoted s M ell nd M ell respectvely. Then TP sets vlue for the vrle M ccordng to the mth formul mentoned erler.e. S A S = M ell M ell. M= f SA S s not equl to M ell M ell wheres M=0 f 7

8 S A S s equl to M ell M ell. Then the protocol contnues to the next step. Tle. Alce o TP =0 =0 =0 =0 Z-ss mesurement =0 =0 =0 = Z-ss mesurement ell mesurement =0 =0 = =0 Z-ss mesurement gnore o =0 =0 = = Z-ss mesurement gnore o =0 = =0 =0 ell mesurement Z-ss mesurement =0 = =0 = ell mesurement ell mesurement =0 = = =0 ell mesurement gnore o =0 = = = ell mesurement gnore o = =0 =0 =0 gnore Alce Z-ss mesurement 8

9 = =0 =0 = gnore Alce ell mesurement = =0 = =0 ell mesurement ell mesurement = =0 = = ell mesurement ell mesurement = = =0 =0 gnore Alce Z-ss mesurement = = =0 = gnore Alce ell mesurement = = = =0 ell mesurement ell mesurement = = = = ell mesurement ell mesurement Step5. f M = 0 TP hs to send M nd the ell mesurement result on the quts.e or to Alce nd o. After Alce nd o receve these M nd the ell mesurement result they wll perform pulc dscusson sed on the vlues of. f Alce nd o oth set = 0 n Step3 then they hve to send the Z-ss mesurement result on tht qut.e. MR nd MR to ech other v n uthentcted chnnel. Then Alce nd o 9

10 oth compre MR nd MR sed on M ell. Tht s: f M ell then MR nd MR must e ether 0 0 or. f M ell then MR nd MR must e ether 0 or 0. f the mesurement results do not mtch then t mples TP does not honestly follow the procedure of the protocol. Hence Alce nd o wll termnte the protocol nd strt from the egnnng. f the mesurement results mtch the protocol wll go ck to the Step for the next qut. For the other cses.e. Alce nd o oth set = or one sets = nd the other sets = 0 then t mples ether TP honestly follow the procedure of the protocol or the clents do not hve enough nformton to check the honesty of TP. Hence the protocol wll go ck to the Step for the next qut. On the other hnd f M = then TP hs to send M to Alce nd o. Herefter Alce nd o wll perform pulc dscusson sed on the vlue of. f Alce nd o oth set = n Step3 then t mples TP does not honestly follow the procedure of the protocol. Hence they wll termnte the protocol nd strt from the egnnng. For the other cses.e. one clent sets = nd the other clent sets = 0 then t mples tht the clents do not hve enough nformton to check the honesty of TP. The protocol wll go ck to the Step for the next qut. Only when Alce nd o oth set =0 the protocol wll contnue to the next step. Step6. Up to ths step we know tht oth Alce nd o hve set = nd = 0 nd hve receved M= from TP. n ths step Alce nd o wll use ther mesurement results to compre ther secret messges. Let M nd A M e the th t of secret messges of Alce nd o respectvely. Alce nd o ndvdully 0

11 compute nd R MR M nd then send R MR M A A R A nd R to TP. Upon recevng R nd A R TP trnsforms the ell mesurement result nto clsscl t strng C T 0 0 nd clcultes the comprson results R R R C. f there s t n R then TP termntes A T the protocol nd pulshes ndctng tht Alce s nd o s nformton s dfferent. Otherwse TP repets the protocol from Step to Step 6 untl ll the secret messges re compred. f there re ll zeros n R then TP nnounces tht the two prtcpnts nformton re dentcl. 3 Securty nlyses To nlyze the securty of the proposed protocol ths secton s dvded nto two prts to focus on two dfferent ttcks the outsder ttck nd the nsder ttck. The proposed protocol contns three nsders.e. n lmost-dshonest thrd prty TP nd two prtcpnts: Alce nd o. Whle Secton 3. nvestgtes the outsde evesdropper s ttck Secton 3. nlyzes the posslty for n nsder.e. TP or prtcpnt to otn the other prtcpnt s secret nformton. 3. Outsder ttck A mlcous outsder Eve my try to perform some well-known ttcks such s the ntercept-nd resend ttck [8] y nterceptng the qut sequences A nd trnsmtted from TP to Alce nd o respectvely n Step nd then mesurng the quts n the sequences. However snce Eve does not know the vlue of =0/ f Eve mesures on the trnsmtted sequences she wll e detected wth prolty of 7 n n Step4 where n denotes the numer of quts n the sequences. f n s lrge 8

12 enough the prolty wll e close to one. Ths s ecuse: Alce o hs prolty to set =0 nd to get the dfferent result from prolty to set S A S. Hence Eve hs = nd TP hs 7 8 prolty prolty to pss the detecton for ech qut. Hence wth n quts Eve wll e detected wth prolty of 7 8 n n Step4. For exmple: ssume the ntl stte S A S Eve ntercepts nd mesures wth Z ss to get 0 nd sends 0 to Alce o. Alce o sets =0 nd = nd sends the qut to TP. After TP receves from Alce o Alce o sends to TP. ecuse =0 nd = TP performs ell mesurement on. TP hs prolty of to get the mesurement result. f TP gets the dfferent result from S A S he/she knows tht there s n evesdropper. n some cses Eve mght ntercept the qut sequences A nd trnsmtted from TP to Alce nd o respectvely n Step nd send the fke quts to Alce nd o. After Alce nd o receve the fke quts nd set the vlues of nd they send the fke quts to TP. Then Eve ntercepts the fke quts nd resends the prevous qut sequences A nd to TP. However snce Eve does not know the vlue of =0/ f Eve sends the fke quts to Alce nd o she wll e detected wth prolty of 7 n n Step4 where n denotes the numer of quts n the 8 sequences. Snce Alce o hs prolty to set =0 nd prolty to set =0 nd TP hs prolty to get the dfferent result from M z M z

13 nd the mesurement result whch Alce o sends Eve hs 7 8 prolty to pss the detecton for ech qut. Hence wth n quts Eve wll e detected wth prolty of 7 8 n n Step4. For exmple: ssume tht the ntl stte S A S. Eve ntercepts nd sends fke qut 0 to Alce o. f Alce o sets =0 nd =0 then Alce o performs Z-ss mesurement on Eve s qut nd sends to TP. Eve ntercepts nd resends to TP. After TP receves from Eve Alce o sends nd the mesurement result of Eve s qut to TP. ecuse =0 nd =0 TP performs Z-ss mesurement on. Then TP hs prolty of to get the mesurement result. f M M s dfferent from the mesurement z z result whch Alce o sends then TP wll detect the exstence of n evesdropper. Consequently the outsde ttcker cnnot get ny useful nformton from the prtcpnts wthout eng detected. 3. nsder ttck n ths su-secton two cses of nsder ttcks re consdered. The frst cse dscusses the posslty for prtcpnt to otn the other prtcpnt s secret nformton. The second cse dscusses the posslty for TP to retreve the two prtcpnts secret nformton. Cse Prtcpnt ttck Suppose Alce s mlcous prtcpnt who tres to revel the other prtcpnt s o secret nformton. f Alce tres to ntercept the trnsmtted photons from TP to o she wll e cught s n outsde ttcker s descred n 3

14 Sect. 3.. ecuse when o sets =0 Alce cnnot nvolve n the dscusson of TP nd o. So f Alce wnts to revel o s nformton M she wll e detected y TP lke n Eve nd the detecton rte s the sme s descred n Sect. 3.. Smlrly f o tres to perform n ttck on the protocol he wll e detected too. Cse TP ttck ecuse TP s n lmost-dshonest thrd prty he mght not fthfully execute the procedure of the protocol nd try to revel prtcpnt s nformton. When =0 we detect ether Eve s ttck or prtcpnt s ttck wth TP s help. On the contrry we detect TP s ttck when Alce nd o oth set =. f TP wnts to revel prtcpnt s secret nformton he/she cn generte fke ntl sttes lke Z-ss sngle photons nsted of ell stte. When Alce nd o mesure the qut wth Z-ss nd pulsh R A nd R TP cn drectly lern Alce s nd o s secret nformton. However n our proposed protocol Alce nd o hve to dscuss the entnglement of M ell nd M ell n Step5. f TP genertes Z-ss sngle photons he does not know the entnglement of M ell nd M ell. Hence he does not know how to set the vlue of M. TP wll e detected n Step5 when prtcpnts oth set = nd = nd the detecton rte s out - 5 n. f n s 6 lrge enough the prolty wll e close to one. Ths s ecuse: Alce nd o oth hve prolty to set = nd prolty to set =. Hence TP hs prolty of 5 6 e detected wth prolty of to pss the detecton for ech qut. Hence wth n quts Eve wll 5 n n Step5. 6 TP could generte two ell sttes nd performs ell mesurement on 4

15 nsted on. Then TP compres the ell mesurement result wth S. f the two results re dfferent then t mples o sets = nd =0 TP wll perform Z-ss mesurement on to revel Alce s secret nformton nd set M=. f the two results re the sme TP wll set M=0. n ths ttck however f TP sets M=0 then TP does not know the ell mesurement result of. TP wll e detected n Step5 when prtcpnts oth set = nd =0 nd the detecton rte s out n. f n s lrge enough the prolty wll e close to one. Ths s ecuse: Alce nd o oth hve TP hs prolty to set 5 = nd prolty to send wrong ell mesurement result of o. Hence TP hs prolty of 3 3 wth n quts Eve wll e detected wth prolty of prolty to set =0 nd to Alce nd to pss the detecton for ech qut. Hence 3 n n Step5. 3 n our protocol only TP hs the nformton out the ntl stte. Therefore he cn revel the comprson result of oth prtcpnts ut TP cnnot know the prtcpnts secret nformton. 4 Conclusons Ths pper presents the frst sem-quntum prvte comprson SQPC protocol under n lmost-dshonest thrd-prty. A sem-quntum prvte comprson protocol cn reduce not only the computtonl urden of the communcnts ut lso the cost of the quntum hrdwre devces n prctcl mplementtons. The securty nlyss shows tht the proposed protocols re free from the outsder ttck nd the nsder ttck. t should lso e noted tht lke the other sem-quntum schemes the proposed protocol lso suffers from the Trojn-horse ttcks [9-3]. To prevent ths

16 knd of ttcks the photon numer spltter devce nd wvelength flter devce could e dopted [3 33]. Throughout ths pper we hve ssumed n lmost dshonest TP. n the future t could e very chllengng to further reduce the trustworthy news of the TP to n ndvdully dshonest s defned n [34] where TP cnnot even pulsh fke comprson result. Acknowledgment We would lke to thnk the Mnstry of Scence nd Technology of Repulc of Chn for fnncl support of ths reserch under Contrct No. MOST 04--E References [] H. ennett Ch nd G. rssrd "Quntum cryptogrphy: pulc key dstruton nd con tossng nt" n Conf. on Computers Systems nd Sgnl Processng nglore nd Dec pp [] C. H. ennett G. rssrd C. Crépeu R. Jozs A. Peres nd W. K. Wootters "Teleportng n unknown quntum stte v dul clsscl nd Ensten-Podolsky-Rosen chnnels" Physcl revew letters vol. 70 p [3] A. Furusw J. L. Sørensen S. L. runsten C. A. Fuchs H. J. Kmle nd E. S. Polzk "Uncondtonl quntum teleportton" Scence vol. 8 pp [4] Z.-J. Zhng nd Z.-X. Mn "Mny-gent controlled teleportton of mult-qut quntum nformton" Physcs Letters A vol. 34 pp [5] Z. Wen L. Y-Mn L. Jun nd Z. Zhn-Jun "Teleportton of rtrry unknown two-tom stte wth cluster stte v therml cvty" Chnese Physcs vol. 7 p [6] Z. Z-Yun L. Y-Mn Z. Xue-Qn Z. Wen nd Z. Zhn-Jun "Trnsformton opertor nd crteron for perfectly teleportng rtrry three-qut stte wth 6

17 sx-qut chnnel nd ell-stte mesurement" Chnese Physcs Letters vol. 6 p [7] C.-W. Ts nd T. Hwng "Teleportton of pure EPR stte v GHZ-lke stte" nterntonl Journl of Theoretcl Physcs vol. 49 pp [8] M. Hllery V. užek nd A. erthume "Quntum secret shrng" Physcl Revew A vol. 59 p [9] L. Xo G. L. Long F. G. Deng nd J. W. Pn "Effcent multprty quntum-secret-shrng schemes" Physcl Revew A vol. 69 My 004. [0] Z. J. Zhng nd Z. X. Mn "Multprty quntum secret shrng of clsscl messges sed on entnglement swppng" Physcl Revew A vol. 7 Aug 005. [] F. G. Deng G. L. Long nd H. Y. Zhou "An effcent quntum secret shrng scheme wth Ensten-Podolsky-Rosen prs" Physcs Letters A vol. 340 pp Jun [] F. G. Deng H. Y. Zhou nd G. L. Long "Crculr quntum secret shrng" Journl of Physcs -Mthemtcl nd Generl vol. 39 pp Nov [3] L. F. Hn Y. M. Lu J. Lu nd Z. J. Zhng "Multprty quntum secret shrng of secure drect communcton usng sngle photons" Optcs Communctons vol. 8 pp My 008. [4] F. G. Deng X. H. L nd H. Y. Zhou "Effcent hgh-cpcty quntum secret shrng wth two-photon entnglement" Physcs Letters A vol. 37 pp Mr [5] Y. Sun Q. Y. Wen F. Go X.. Chen nd F. C. Zhu "Multprty quntum secret shrng sed on ell mesurement" Optcs Communctons vol. 8 pp Sep 009. [6] R.-h. Sh L.-s. Hung W. Yng nd H. Zhong "Multprty quntum secret shrng wth ell sttes nd ell mesurements" Optcs Communctons vol. 83 pp [7] K. ostrom nd T. Felnger "Determnstc secure drect communcton usng entnglement" Physcl Revew Letters vol. 89 Oct [8] F.-G. Deng G. L. Long nd X.-S. Lu "Two-step quntum drect communcton protocol usng the Ensten-Podolsky-Rosen pr lock" Physcl Revew A vol. 68 p [9] Z. X. Mn Z. J. Zhng nd Y. L "Determnstc secure drect communcton y usng swppng quntum entnglement nd locl untry opertons" Chnese Physcs Letters vol. pp. 8- Jn

18 [0] Y.-. Zhn L.-L. Zhng nd Q.-Y. Zhng "Quntum secure drect communcton y entngled qutrts nd entnglement swppng" Optcs Communctons vol. 8 pp [] C. TSA nd T. HWANG "Fult tolernt two-step quntum secure drect communcton protocol gnst collectve noses" Scence Chn Physcs Mechncs & Astronomy 0. [] S.-L. Hung T. Hwng nd P. Gope "Mult-prty quntum prvte comprson wth n lmost-dshonest thrd prty" Quntum nformton Processng vol. 4 pp [3] W.-W. Zhng nd K.-J. Zhng "Cryptnlyss nd mprovement of the quntum prvte comprson protocol wth sem-honest thrd prty" Quntum nformton processng vol. pp [4] M. oyer D. Kengserg nd T. Mor "Quntum key dstruton wth clsscl o" n Quntum Nno nd Mcro Technologes 007. CQNM'07. Frst nterntonl Conference on 007 pp [5] M. oyer R. Gelles D. Kengserg nd T. Mor "Semquntum key dstruton" Physcl Revew A vol. 79 p [6] J.-W. Pn D. ouwmeester H. Wenfurter nd A. Zelnger "Expermentl entnglement swppng: Entnglng photons tht never ntercted" Physcl Revew Letters vol. 80 p [7] M. Zukowsk A. Zelnger M. Horne nd A. Ekert "" Event-redy-detectors" ell experment v entnglement swppng" Physcl Revew Letters vol. 7 pp [8] F. Go F.-Z. Guo Q.-Y. Wen nd F.-C. Zhu "Comment on Expermentl demonstrton of quntum protocol for yzntne greement nd lr detecton " Physcl revew letters vol. 0 p [9] C.-W. Yng T. Hwng nd Y.-P. Luo "Enhncement on quntum lnd sgnture sed on two-stte vector formlsm " Quntum nformton processng vol. pp [30] F.-G. Deng P. Zhou X.-H. L C.-Y. L nd H.-Y. Zhou "Roustness of two-wy quntum communcton protocols gnst Trojn horse ttck" rxv preprnt qunt-ph/ [3] Q.-Y. C "Evesdroppng on the two-wy quntum communcton protocols wth nvsle photons" Physcs Letters A vol. 35 pp [3] F.-G. Deng X.-H. L H.-Y. Zhou nd Z.-j. Zhng "mprovng the securty of multprty quntum secret shrng gnst Trojn horse ttck" Physcl Revew A vol. 7 p [33] X.-H. L F.-G. Deng nd H.-Y. Zhou "mprovng the securty of secure drect 8

19 communcton sed on the secret trnsmttng order of prtcles" Physcl Revew A vol. 74 p [34] Shh-Mn Hung nd Tzonelh Hwng Multprty Quntum Prvte Comprson wth ndvdully dshonest Thrd Prtes for strngers rxv: