計畫編號：NSC92-2213-E032-019研究期間：200308~200407研究經費：416,000[[sponsorship]]行政院國家科學委員

黃心嘉

計畫編號：NSC92-2213-E032-019研究期間：200308~200407研究經費：416,000行政院國家科學委員

Tamkang University Institutional Repository

????????????????  ????   ??????????????????????   ?????????? ?????NSC92-2213-E-032-019- ?????92?08?01??93?07?31? ???????????????     ?????????  ??????????  ???     ?????????  ?????????????     ? ? ? ? 93?9?24? ?????????????????????? ???????????????????????????? ?                           ? ?  ?????????????????????? ? ?                           ? ???????????????????????????? ?????5?????  □????? ?????NSC 92-2213-E-032-019- ?????  92? 8? 1?? 93 ? 7? 31?   ?????? ??? ??????? ??? ??????? ??? ??????? ???     ??? ??????? ??? ???????????????? □?????????????? □???????????????? □????????????????????? □?????????????????  ???????????? ? ? ? ? ??? ??????? - 1 - ???????????????????? ?????????????????????? Anonymous Proxy Group-oriented Signature Schemes with Undeniable Agents ?????NSC 92-2213-E-032-019 ?????92? 8? 1?? 93? 7? 31? ???????  ???????  ??? ?????????? ??????? ??? ??? ??????? ??? Email: sjhwang@mail.tku.edu.tw  ??????? ???? ??????????????????????????????????????????????????????????Mambo??????????????????????????????????????????????????????????????????????????????????????????????????????(t, n) ??????????? ???? Actually, in many situations, the proxy signer may want to be anonymous to avoid disturbance.  In our previous project, an anonymous proxy signature scheme with undeniable agents has been proposed.  Except satisfying the seven properties proposed by Mambo et al, the proxy signer in our scheme is anonymous.  When any dispute occurs, the original signers and the trust third party can prove the identity of the proxy signer.  Due to the group-oriented application, based on the prvious scheme, the anonymous proxy multi-signature scheme with undeniable agents and the anonymous proxy (t, n) threshold signature schemes with a mutually trusted party are proposed in this project. ???: proxy signature scheme, proxy multi-signature scheme, proxy threshold signature scheme, digital signature scheme. ??????? ?????????????Mambo?? [14, 15]????????????????????[9-12, 14, 15, 17, 18, 20-21, 23, 24]?????????????????????????????????????????????????????? (NSC90-2213-Z- 032-025)????????????????????????????????????????????????????????????? ?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????[3-5, 19, 22, 25]???????????(t, n) 2 ???????????? n ????????????????????????????????????????????? t ????????????????????????????????? ??????? (?) ??????????  ???? Chaum? van Antwerpen [1]???????????????? p? q ?????????? p= 2q+1. ?ω∈Zp*??????? q???? Bob????? a∈Zq* ?????? β= ωa mod p??? G ?? Zp*???q?????????????M∈G????Bob????????σ= Ma mod p???????????σ? Bob??Bob???? ZP?logωβ= logMσ???????????σ??Bob??Bob??????????ZP? ogωβ≠ logMσ??????? Alice???????? ?? 1: Alice ? Zq*??????? e1 ?e2????? c= σe1βe2 mod p? Bob? ?? 2: Bob???? d= ca-1 mod p? Alice? ?? 3: Alice? d≠ Me1ωe2 mod p?? d? ?? 4: Alice ? Zq*????????? f1? f2????? C= σf1βf2 mod p?Bob? ?? 5: Bob????D= Ca-1 mod p?Alice? ?? 6: Alice ? D≠ Mf1ωf2 mod p?? D? ?? 7: Alice ??σ???????(dω-e2)f1 ≡ (Dω-f2)e1 (mod p). ???σ?????? ZP? logωβ≠ logM??? logωβ= logM? ???????????????????????????????????????????????????????????? ?????? ? p? q ?????????? p= 2q+1. ? g∈Zp*??????? q??? h ???????????? i ? Zq*????????? xi??????? yi= gxi mod p? ?????? ??????? A ????????????? B?????? A ???????k∈Zq*????? H= yBk mod p? r= g-kH mod p??? A?? s= k- rxAh(mw ) mod q???mw???????????????????????????????????????????? A ???????(IDB, (r, s), mw)???(r, s)? mw??????????????? B???????? B?? gs yArh(mw)r≡ (gs yArh(mw))xB (mod p) (1) ??(r, s)? mw????(1)?????????? B??((r, s), mw, α)???α= gs yArh(mw) mod p? ??????????? ????????? B ???? m ??????????? t∈Zq*??? T= αt mod p?????? U?? h(m||r||s)≡ TxB+ tU (mod q)  (2)? ??(T, U)??? m????????((mw, (r, s)), (m, (T, U)))????????α= gs yArh(mw) mod p? H= αr mod p????? m?????(T, U)??????? αh(m||r||s) ≡TUHT (mod p)? (3) ??(T, U)? ????????? ??? m?????(T, U)????????????????? B??????????? A?????? TTP????????3 ? B??????(IDB, (r, s), mw)?????TTP??α= gs yArh(mw) mod p? H = αr mod p??????(3)??(T, U)??????(T, U)???TTP ????????????(common secret exponent validation protocol ? ? ?CSEV)????? loggyB= xB =logαH?? loggyB= xB =logαH?? B?????????????loggyB≠ logαH?? B?????????? ?????????? ??????? g?yB?α?H? xB? ????? loggyB= xB = logαH????? ?? 1: ???? Zq*??????? e1?e2????? c= He1yBe2 mod P????? ?? 2: ????? d=cxB-1 mod p ????? ?? 3: ???? d≡ αe1ge2 (mod P)??d?? d≡ αe1ge2 (mod P)????????? loggyB= xB= logαH? ?? 4: ???? Zq*??????? f1?f2????? c'= Hf1 yBf2 mod P????? ?? 5: ????? D= c'xB-1 mod p????? ?? 6: ???? D≡ αf1gf2 (mod P)??D?? D≡ αf1gf2 (mod P)????????? loggyB= xB= logαH? ?? 7: ????(dg-e2)f1≡(Dg-f2)e1 (mod p) ?? D? d??(dg-e2)f1≡(Dg-f2)e1 (mod p)???? loggyB≠ logαH????????? ??????????? H????????? B????????????????? B????????????????????? H'?  (?) ???????????? ???????????????????????? UB??????????????????????????????? ?????? ? p? q ?????????? p= 2q+1? ? g∈Zp*??????? q??? h ???????????? Ui ? Zq*????????? xi??????? yi= gxi mod p???????? Go= {U1, U2, …, Un}??????????? UB????????????? yG= ∏i=n1yiyi mod p??????? sG= ∑i=n1xiyi mod q? ?????? ????????? Go ?????????????? UB ?????????????? ?? 1: Go???????Ui?Zq*???????? ki? ?? 2: ????? Ui?? Hi= yBki mod p?αi= gki mod p????????????(Hi, αi)????????UB??? Go???? Uj?? j= 1, 2, ..., n? j≠i? ?? 3: ??(Hi, αi)??Uj ???????Ui ??????????????????????????????????????? g(=g)?αi(=yB)?yB(=α)?Hi(= H)????? ki (= xB)??? Uj? Ui ??loggαi= ki= logyBHi? ?? 4: ????Ui??α= ∏i=n1αi mod p= g∑i=n1ki mod p?H= ∏i=n1Hi mod p= yB∑ i=n1ki mod p? R= α-1H mod p?4 ?? Ui?? si= ki-xiyiRh(mw) mod q???????UB?? R? ?? 5: ???? Ui? si? UB ?????? ?? 6: UB?????? Go????????αi ≡ gsi yiyiRh(mw) (mod p)??????????? si? ?? 7: ???? si ??????UB?????? Go ??????? S≡ ∑i=n1si≡ (∑i=n1ki)–Rh(mw)× (∑ i=n1xiyi) (mod q)??????? Ui???????? (IDB, (R, S), mw)? ??????????? ???????????????????????????????????????? UB?? h(m||R||S)≡ TxB + tU (mod q)??? h(m||r||s)≡ TxB+ tU (mod q)????? m??????(T, U)???????((mw, (R, S)), (m, (T, U)))??????α≡ gS× yGRh(mw) (mod p)? H= αR mod p???αh(m||R||S) ≡ TUHT (mod p) ??(T, U)? ????????? ??? m?????(T, U)????????????????? UB??????????? Go?????? TTP????????? UB??????(IDB, (R, S), mw)?????TTP??α= gS×yGRh(mw) mod p? H = αR mod p??? yG= ∏i=n1 yiyi mod p????? TTP?????????????? loggyB= xB =logαH?? loggyB= xB =logαH?? UB????????????? loggyB≠ logαH?? UB????????????????????? H????????? UB????????????????? UB????????????????????? H'? (?) ????????????? ???????????????????????? UB????? n????????? t?? t????????????????????????????????Go= {U1, U2, ..., Un}  ?????? ?????????? Go ????????????? (a trusted key authentication center??? KAC)???KAC????????? p? q??? p= 2q+1?KAC?????? q ??? g∈Zp*??????? Go?KAC? Zq*??????? t-1 ???????f(x)= a0+ a1x+ a2x2+…+ at-1xt-1????????Go ?????? f(0)??? Ui ?????f(IDi)??? IDi??? Ui??????? KAC??????????? YG=gf(0) mod p???????? ypi=gf(IDi) mod p???????Go???? Ui? ?????? ?????? Go?? t ????? D= {U1, U2, …, Ut}?????????????UB??? D?? t????????????? UB??????????? mw??????? mw??? t?????? ?? 1: D ??????? Ui? Zq*??????????? ki?????αi= gki mod p? Hi= yBki mod p??? Ui ???????? (Hi, αi)? UB ? D??????? ?? 2: ??(Hi, αi)???? Uj??????? Ui ???????????????????????????????????????g(=g)?αi(=yB)?yB(=α)?Hi(= H)????? ki (= xB)??? Uj?5 Ui ?? loggαi= ki= logyBHi? ?? 3: D ?????? Ui??α= ∏i=t1αi mod p= g∑i=t1ki mod p? H= ∏i=t1Hi mod p= yB∑ i=t1ki mod p? R= α-1H mod p?????? UB????????? ?? 4: D ?????? Ui ???????? f(IDi)??????????????? mw??? si=(f(IDi)Li+ xiyi)× R× h(mw)- ki mod q???∏≠= −−=tijj jiji IDIDIDL,1mod q? ?? 5: ?? D ?????? Ui?????????? si???????????? UB? ?? 6: ?????? UB? D ?? t ??????????? si?????gsi × αi ≡ ((ypiLi)×(yiyi))Rh(mw) (mod p)?????????? si???yi= gxi mod p? ypi= gf(IDi) mod p? ?? 7: ??????? si????????? UB? D?? t????? S≡ ∑i=t1si ≡ R× h(mw)×∑i=t1 (f(IDi)Li+ xiyi)- ∑i=t1 ki (mod q)????????(mw, (R, S))?D?? t?????????(IDB, (R, S), mw)? ??????????? ?????????????????????????????????? UB??? Zq*???????? t??? T=gt mod p?????? U ?? h(m||R||S)≡ TxB + tU (mod q)????????α= (YGs× yD)Rh(mw) × g-S mod p? H= αR mod p??? YGs= ∏i=t1ypiLi mod p? yD= ∏i=t1yiyi mod p????αh(m||R||S)= TUHT mod p??(T, U)? ????????? ??? m?????(T, U)????????????????? UB ?????? D??????? TTP????????? UB??????(IDB, (R, S), mw)????? TTP??α= gS×yGRh(mw) mod p? H = αR mod p??? yG= ∏i=n1 yiyi mod p????? TTP?????????????? loggyB= xB =logαH??loggyB= xB =logαH?? UB????????????? loggyB≠ logαH?? UB????????????????????? H????????? UB????????????????? UB ????????????????????? H'? ???????? ??????????????????????????????????????????????????????????????????????????(t, n) ???????????? n ????????????????????????????????????????????? t ?????????????????????????????????????????????????????????????????????? ?????? [1] Chaum, D. and Van Heyst, E. V., “Group 6 signatures,” Pre-proceeding of Eurocrypt’91, Lecture Notes in Compute Science, Vol. 547, Springer, Berlin, 1991, pp. 257-265. [2] Harn, L., “Group-oriented (t, n) threshold digital signature scheme and digital multi-signature,” IEE Proceed Computer Digital Technicality, Vol. 141, No. 5, 1994, pp. 307-313. 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[12] Lee, Narn-Yih, Hwang, Tzonelih, and Wang, Chin Hung, “On Zhang’s nonrepudiable proxy signature schemes,” Third Australasian Conference, ACISP ’98, 1998, pp. 415-422. [13] Li, Z. C., Hui, L. C. K., Chow, K. P., Chong, C. F., Tsang, H. H., and Chan, H. W., “Cryptanalysis of Harn digital multi-signature scheme with distinguished signing authorities,” Electronics Letters, Vol. 36, No. 4, 2000, pp. 314- 315. [14] MAMBO, Masahiro, USUDA Keisuke, and OKAMOTO, Eiji, “Proxy signatures: Delegation of the power to sign message,” IEICE. Trans. Fundamentals, E79-A, 9, 1996, pp. 1338-1354. [15] MAMBO, Masahiro, USUDA, Keisuke, and OKAMOTO, Eiji, “Proxy signatures for 7 delegation signing operation,“ Proc. 3nd ACM Conference on Computer and Communication Security, 1996, pp. 48-57. 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[21] Sun, Hung-Min, and Hsieh, Bin-Tsan, “Remark on two nonrepudiable proxy signature schemes,” Proceedings of the Ninth National Conference on Information Security, Taiwan, 1999, pp. 241-246. [22] Sun, Hung-Min, Lee N.-Y., and Hwang, T, “Threshold proxy signatures,” IEE Proceedings-computers & Digital Techniques, Vol. 146, No. 5, September 1999, pp. 259-263. [23] Yen, Sung-Ming, Hung, Chung-Pei, and Lee, Yi-Yuan, “Remarks on some proxy signature schemes,” 2000 International Computer Symposium, Chiayi, Taiwan, R.O.C., Dec. 6-8, 2000, pp. 54-59. [24] Yi, L. Bai, G., and Xiao, G., “Proxy multi-signature scheme: A new type of proxy signature scheme,” Electronics Letters, Vol. 36, No. 6, 2000, pp.527-528. [25] Zhang, K., “Threshold proxy signature schemes,” 1997 Information Security Workshop, Japan, September 1997, pp. 191-197. 

The Design of Proxy Group-Oriented Signature Schemes with Anonymous Proxy Agent

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[[alternative]]The Design of Proxy Group-Oriented Signature Schemes with Anonymous Proxy Agent

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