?. ?. , ?. @bullet?-t??-b-i,-?-i-s, ?. , ?. ?. , ?. ?@bullet?-?-?-?-t-?-?-t?? et al., ) ???????t??t???s ?? G ?s r?q??r?? ??r t?? ?r????t?? ???? ???????? t?? ??s? ?????t?t???s ?r? ?ss??t????? t?? s??? ?s??? t?? ??s? ??? ?r t?? ?r????t?? ???? s???? ??r t?? s???????t???s? t?? ??r??r ???s?sts ??rt? ?s ??rr??t??? ?r ?? t?? ????rs?r? s????ss????? ???ss?? t?? ?????r?s ??ss??r? ?t?? s?ss??? ?s t??? ??r??? ?s ????r???s???? t??? ?t ?s ?r??t?? t?? r???t t? ????? ??t?r???? ?ts s?ss??? ???? ??t? t??t ?s s??? ?s ? ??rt? ?s ??rr??t??? t?? ????rs?r? ???r?s ?ts ???? ???r? ?st?? ?s ?????? ?r?s?? ?? s??? ? ??s?? t?? t?? ??rt??s r?????? t?? s???? ?????r??? ??str???t?? s?ss??? ???? ??????? ??t??? t??t t?? ????t??????t? ?s ??t ?? ???r?? ?? ?r??????? t?? ??ss??r??s? t? t?? ??rt??????ts? ??? ??ss??r?s ?r? ???s?? ?? t?? ????r?????t ????? t??? ????s t??? t? t?? ??rt??s ?s ????ts? ???s ?? ???r??t??s s???r?t? ???? ?? t?? ??s? ???r? t?? ????st ?????rs ?????t? t?? ?r?t???? ??t? t?? ????r??t ??ss??r?s? ???s ?????s? ??r ??st????? t?? ??s? ???r? ? ?s?r ??st???s ?ts ??ss??r?? ?t ??s? ??????s t??t t?? s???r?t? ?s ?r?s?r??? ??r ??? ??ss??r? ??str???t???s, ) t? S? ?? t??s ?s t?? ?rst ?????ss??? q??r?? ?r ?? t??s ?s t?? s????? ?????ss??? q??r? ??? t??r? ?s ? r???r? (Pj, Pi, pw ? )? t??? r???r? (Pi, Pj, pw) ??? ??r? t??s r???r? ?r?s?? ? ???? r???????? ? q??r? pw ? ) ??t? pw ? = pw? ??? ? ??? sk ? ??s s??t t? Pj? ??? (Pj, Pi, pw) ??s ?r?s? ?t t?? t???? t??? ??t??t (sid, sk ? ) t? Pi? ? ?? ??? ?t??r ??s?? ???? ? ??? r????? ??? sk ? ?? ????t? k ??? s??? (sid, sk ? ) t? Pi? ??t??r ???? ??r? t?? r???r? (Pi, Pj, pw) ?s ??????t??? ???? ?? ??? ??ss??r????s?? ???????????? ????t??????t? FpwKE

?. ??????-pr, ?. , ?. ???, ?. ?. , ?. et al., ?ss t??t ??s ?s?? t? ???r??t t?? ??ss??r?? ??? ??????? t?? ??s? ?? ????? t?? ????rs?r? ?r?????s t?? ?s?r ??t? ?? ???r??t??? ?? t?? ?r??? ??ss??r?? ?? t??s ??s?? t?? s???r?t? ?? t?? ?r?

?. ?-r-t??-????rs?r?-?s-?ss?-?-t??@bullet@bullet?-t-?-???ss-t??, ?. , ?. , ?. , ?. et al., ? ?t?? s?????t?r ??s ???r??? ????? ??ss??r? t? ?s??? ??????r? ??t?s ??? s????s? t??t t?? s?????t?r ??s t? st?rt t??? t?? ????rs?r?? ?s ??s?r???? ?????? ?t r?????rs t?? ??ss??r? ?s?? ?? t?? ????rs?r? ?s s??? ?s t?? ??tt?r ??s s??t ?ts ?????? ??t t??s ?s t?? ??t?? ?? ?t t?r?s ??t t??t t?? ???ss ?? t?? ????rs?r? ?s ????rr??t? t??r? ?s ?? ?r????? t????s t? t?? s???t???ss? ??t ?t??r??s?? t?? s?????t?r ?s st??? ??t??r??t t?? s??? ??ss??r?? ??? ?rst ??? ?s ????r ?s?? ?? t?? r???????? ?? t?? ?r?t????? ???s s????s t?? ?r????? s???? ?? t?? ??? ????? t?? s?????t?r ?s

?. ???, ?. Pj, ?. ?. , I. Vki-)-?-?t, ?. ??@bullet??@bullet??-?????s-t??t-com et al., hkJ; ?, (?I, pw J ), com I )? ???t ?t ?????t?s com J = com?(?J, pw J ; RJ) ??? s???s t?? ??ss????t?s t?? ?r????t??? hp I = ProjKG(hkI; ?, (?J, pw I ), com J )? ???t ?t ?????t?s ?I = Sign(SKI, (com I , com J , hp I , hp J )) ??? s???s t?? ??ss??? (?????t?r??, ?I, hp I ) t? PJ? ?t ?????t?s t?? s?ss??? ??? skI = ProjHash(hp J ; ?, (?I, pw I ), com I ; wI) + Hash(hkI; ?, (?J, pw I ), com J )? ??? ?r?s?s ??? ?r???t? ??t? ?????t pw I ??? skI? ??????? ??? ?????? ??t? ?? ????r?? ?? ???? PJ r??????s ? ??ss??? (?????t?r??, ?I, hp I )? ?t ?????s t??t Ver(VKI, (com I , com J , hp J ), ?I) = 1? ?? ??t? ?t ???rts t?? s?ss??? ??t??tt??? ??t????? ?t??r??s?? ?t ?????t?s ?J = Sign

?. ?@bullet-?-???-?-?r, ?. Pi?-???-?-?-?t-?-?-?-?-?t?s-t??-s?ss?, ?. ???, and =. Hashj, ProjHash I (hp I ; ?, (?J, pw J ), com J ; wJ)? ??t??ts (sid, ssid, skJ)? s?ts t?? s?ss??? ?s ?????t??? ????? ????s ?? ??r? t?????r t??t ?t ?r?s?s ???r?t???? ?????

?. ?. , ?. ?. , ?. ?. , F. , ?. S???-t??t et al., ?r? ?s r?????r??? ????? ?s ??s? ????? ? r????? ???? ????? t??? ???rts ?? (U 5) ?? t?? s????t?r? ?? t?? s?r??r ?s ???????? ?? t?? s?r??r ??s ??rr??t?? ????r? (U 5)? S r?????rs ??s ??ss??r? ??? ???s ????t?? t?? s??? ?s ?r?????s?? ??s?r????? ???s ?s ????st?????s????? ?r?? t?? ??r??r ???? ??? t? t?? ?s?????r???????ss ?? t?? ??s? ????t???? ? ?r?? G 5 ? ?? t?? ??s? ???r? ?????t?? ??s ??t ?r?????????r?t??? S ??tr??ts pw

?. Pr, ?. @bullet, ?. S?-?ss?, ?. T??t, A. et al., pw I ) t? t?? ????t??????t?? ?? t??s ?s ? ??rr??t ???ss? t??? S s?ts t?? ??ss??r? ?? t??s s?r??r s?ss??? t? pw I ? ?t??r??s?? t??s ?s

?. T??-s?-?-??r-(-p-i, ?. , ?. , ?. T??-?t-t??-?-?-?-?-?-t??s-st?, ?. ??-?-?@bullet?s-t??s-?-?-rr? et al., P J , ssid) ?s ? ???r s?ss??? t? (P I , ssid ? ) ?? ssid = ssid ? ? ?? s?ss??? (P I , ssid) ??s ???r P J ? s?ss??? (P J , ssid) ??s ???r P I ? ??? t??s? t?? s?ss???s ???? ????s?t? r???s ??????t /s?r??r?? ?? t?? ???r (com J , VK J ) ?s ??t ?q??? t? t?? ???r, )? ?s ???? ?s t?? s?????? ????r?t?? ??t? SK I t? ?????t? ? I ??? s???s t?? ?????t?r?? ??ss??? (? I , hp I ) t? A ?? ?????? ?? (P I , ssid)?

?. ?t-?s-(-p-i, ?. ?. , ?. , ?. ????, ?. et al., ???r s?ss??? P I ????sts ???? ??s ??rr??t?? s????r ?? t?? ?r?t????? t??? S ????s ?ts ??ss??r? pw I ?????? ??s ?? ??rt?????r ?s?? ?? t??

?. , ?. , ?. , ?. ?-r-t??, ?. ?. et al., I ; ?, (? J , pw I ), com J )? ????? ?? t?? s?r??r r?????s ????st ??t?? (S4)? t?? s?????t?r ?s?s ? ????P?? q??r? t? t?? ????t??????t?? ?? t?? ??s??r ?s ??s ?t??t ?s pw I = pw J ?? ?t ????s ??? t?? s??? r????? ????? ??r ProjHash(hp I ; ?hp J ; ?, (? I , pw I ), com I ; w I ) = Hash(hk J ; ?, (? I , pw J ), com I )? ?t??r??s?? S s?ts sk I

?. ?. ???, ?. @bullet@bullet-?-?s-?r-?-?-t??, ?. , ?. , ?. ?. et al., ??s r?????r?? ? ??ss??r?? t?? s?????t?r ?s?s ? ????P?? q??r? t? t?? ????t??????t?? ?? ?t ?s ??rr??t? t??? ?t ?????t?s ????st?? t?? s?ss??? ??? ?? t?? ?????t? ?t??r??s?? ?r ?? ?t ??s ??t r?????r?? ??? ??ss??r? ?? t?? ??tr??t???? ?t s?ts t?? ????? Hash(hk I ; ?, (? J , pw I ), com J ) ?t r????? ?t?? ??t?r? ??? sk I ???? ?? s?t ?? r???? (U 5)?? ??t? t??t t?? s???t? ??s? ????? ???? ????ss?r??? ?? r????? ?? ???str??t??? ?? t?? ?????s s??t ?? t?? ?????t???

J. Projhash-(-hp-i-;-?, J. , J. ?q??@bullet-t, ?. Hashhk, I. et al., ? I , pw I ), com I ; w I ) = Hash(hk J ; ?, (? I , pw J ), com I )? sk I ??? sk J ?r? t??s ?q???? ?s r?q??r??? ??t? t??t s???? Hash(hk I ; ?hp J ; ?, (? I , pw I ), com I ; w I ) ???s??t ???? t? I , pw J ), com I ) ??? ProjHash(hp I ; ?, J , pw J ), com J ; w J ), issue.5

?. ?. , ?. , ?. S?-??rst?, ?. ?@bullet???-??ts-?-?-rr?-?-t??-??t?r-t??-?????t?, ?. ?? et al., ? t?? s?????t?r ?s?s ? ????P?? q??r? ??r ????? ??t? ????s ??ss??r? t? t?? ????t??????t?? ?? t??? ?r? t?? s???? S r?????rs t?? ??ss??r? ?? ?????? ??? s???? ?t ??s??t r????? ?r?s?? ??r ??t?? ?t ???? ?? ?? ???? t? ?????t? sk I ????t?? ?s t?? ????rs?r? s?

?. ???-t??t-t??-?-@bullet???rs-??t-t??-s?, ?. ???-??-t???-?-?-?-?t-s??r?-t??-s?, ?. , ?. R???t?-??t?-?s-?r?s??-s-?-t??t-t??-????rs?r?-??-?-?-?-t-??r???-?-?-?t??, ?. ??-??-?-?@bullet@bullet??-??-?@bullet???-??ts-?-?-rr? et al., ?ss??r??? ?t??r??s?? ?? t?? s????t?r? ?s ??rr??t ??t t???r ??ss??r?s ?r? ????r??t? t??? ????? ?s ?r?????? ??t? ? r????? ????? ?r????? t??t ??r ??t? ?s s????s?? t? ?? ?r?s??? s? t??t t?? ????rs?r? ?s ??t s????s?? t? ?? ???? t? ??r??? ?t?? ?t??r??s?? ?? t?? s????t?r? ?s ????rr??t? t?? s??

?. , ?. ?. , ?. , and ?. ?-?-???rr??-?-?-?-t??, ?ss??r?s ?r? t?? s???? ??t? t??s? ??t?t???s? t?? i = 1 ??s? ?s ????t?? G 3 ??? i = q s + 1

?. , ,. .. , ?. ?. , ?. ?. , ?. ?? et al., 3) ?? t?? i th s?ss???? ???r?t???? ?s ????t???? ????r? t??s st??? ????? t?? ??rr??t??? ????rs ????r? t??s r????? t?? ?r???????t? t??t t?? ????rs?r? ??rr??ts ? ?????r ?? t?? i th s?ss?

?. T?-t??t-t??-?-?-rr?, ?. , ?. ?. , ?. ??-?-?-?-@bullet@bullet-?-?-t??s-st?-?-?r?-???@bullett-??t?-?s-?-?-t??-?-?-r, ?. et al., P I , ssid)?s ??ss??r? pw I ??? t?? ????? ? I ? t?? ??str???t??? {pk I , com I , ? I , pw I , hp I , Hash(hk I ; ?, (? J , pw I ), com J )} ?s st?t?st?????? ???s? t? t?? ??str???t??? {pk I , com I , ? I , pw I , hp I , z} ???r? z ?s ? r? I ; ?, (? J , pw I ), com J ) ?s ? ????????t ?? t?? s?ss??? ??? sk I ??r (P I , ssid)? t??? t?? s?ss??? ??? ????r?t?? ?s st?t?st?????? ???s? t?, hk

?. ?. , ?. , ?. ?. , ?. T??-??s?-??-?-?t?-?-?-s-s?-?-?s-t??-?-?-??st?-?-???s????@bullet?t?-??t???, ?. G. ???r?-t??t-t??-???s-??r? et al., ? t?? s???t? ?r????t??? ??s? ????t??? Hash ??t? r?s???t t? com J ? ??t? t??t ?? t?? ???r?? ????s? t?? s?ss???s ?r? ?r??r?? ??t? r?s???t t? t?? r????s (S2), S4) ?? t?? s?????t???? ??t? ?? t?? s?r??r ?s ??rr??t?? ??t?r