ࡱ>   !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root EntryS~SummaryInformation(DocumentSummaryInformation80PowerPoint Document(B4 ՜.+,D՜.+,X (0 8 @ HP University of Missouri-Columbia ꁚ[IN (\dlKSOProductBuildVer      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Oh+'0ȉ(4@ T d p|Slide 1Engineering Technical Services_o(u7b137@n@~G_  ]&" WMFCp /Qi_ EMF/ql@u-WPS Office EMF'% % # t;t;; 6=6/=6/6<>% ( _888% # t;t;@> ARLArial% # t;t;@mA  T=<<LTitle: Optimized Implementation of a General Secret Sharing ZkZkZkZZZZZkkZZkZZ}ZZ}kZ}ZZRLArial% ( TTV LP(\RLArial% ( T8 'Lfor audiences with security background)M\M>M>MM\>MM\\RLArial% ( TpM5LXProf. \MMMRLArial% ( T5 L`Lein HarnMMn_888% ( RLArial% (  T/ "LSchool of Computer and Engineering>MMMM\MM>\>RLArial% ( T8j 'LUniversity of Missouri-Kansas City, USA>\>MMMM>\>\M>MMM_888% ( RL_oŖў% ( # t;t;@> A# t;t;# t;t;/Aq=A# t;t;# t;t;( AKBRLArial% ( # t;t;( AKB TJ< L`Abstract k}kZRLTimes New Roman% ( T8RLSecret sharing is one of most popular cryptographic tools which has been proposed ssWsHAdsWHAHdAsAWAdHAHsWAsWHWsHsAHHdAHsAsdAssAWdsARLTimes New Roman% ( TLoriginally in 1979. ShamirWHHsHHAHAAAAsHWRLTimes New Roman% ( TT LP WRLTimes New Roman%&" WMFC / ( TO =Ls threshold secret sharing is the most popular scheme in the dAHWsdHAdssWsHAdsWHAHdAHsAdHAHsWAdsssAHAHsARLTimes New Roman% ( TL|literature. But, ShamirHHHsWsHWsAAAHAAsHWRLTimes New Roman% ( TTS LP WRLTimes New Roman% ( T ILs scheme has a special secret access structure in which (a) any t (i.e., dAdsssAsdAsAdssHsHAdssWsHAssssddAdHWsHWsAHAHsAWsWAsAHAWHAsAAARLTimes New Roman% ( Td(LTthe HsARLTimes New Roman% ( TT~(LP sRLTimes New Roman% ( T( L`thresholdHWsdHRLTimes New Roman% ( TT(LP sRLTimes New Roman% ( T*(JL) or more than t shareholders can recover the secret and (b) fewer than t WAWAWsAHsAHAdsWsHsWdAssAWsssWAHsAdssWsHAsAWWAWssWAHsAHARLTimes New Roman% ( Tp`[Lshareholders cannot recover the secret. A general secret sharing has more general secret dsWsHsWdAssHAWsssWAHsAdssWsHAAAAAssWsHAdssWsHAdsWHAsdAWsAssWsHAdssWsHARLTimes New Roman% ( T"Laccess structure in which (a) any ssssddAdHWsHWsAHAHsAWsWAsARLTimes New Roman% ( TT LP sRLTimes New Roman% ( T Llqualified subsetsHHWHsAddsHRLTimes New Roman% ( TTXLP sRLTimes New Roman&" WMFC /% ( T<(L of shareholders can recover the secret AWAdsWsHsWdAssAWsssWAHsAdssWsHARLTimes New Roman% ( T Ldand (b) any sAWWAsARLTimes New Roman% ( TT LP sRLTimes New Roman% ( TT Lpunqualified subsetsHHWHsAddsHRLTimes New Roman% ( TT LP sRLTimes New Roman% ( T. <L of shareholders cannot recover the secret. Most papers on AWAdsWsHsWdAssHAWsssWAHsAdssWsHAAAdHAssWdAARLTimes New Roman% ( T `L general secret sharing in literature contain only theoretical discussion. In this talk, I will ssWsHAdssWsHAdsWHAHAHHHsWsHWsAsHsHAHAHsWsHHssHAHdsddHAAAWAHHdAHsHAAWAHHHARLTimes New Roman% ( T|@ ]Lintroduce my recent paper to propose a complete implementation of a general secret sharing. HHWssAAWsssHAssWAHAWdsAsAsHsHsAHHssHsHHAWAsAssWsHAdssWsHAdsWHAAARLTimes New Roman% ( TPx VLWe use Boolean logic to characterize a general secret access structure and derive the sAdsAHssAHHsAHAssWssHsWHssAsAssWsHAdssWsHAssssddAdHWsHWsAsAsWHsAHsARLTimes New Roman% ( TdYLminimal positive secret access and the maximal negative secret access subsets. Then, we HHsHAdHHHsAdssWsHAssssddAsAHsAsHsHAssHHsAdssWsHAssssddAddsHdAAAsAAsARLTimes New Roman% ( ThZLuse these two subsets to determine parameters to implement a general secret sharing. Our dsAHsdsAHAddsHdAHAsHsWHsAsWssHsWdAHAHHssHAsAssWsHAdssWsHAdsWHAAAWARL&" WMFC /Times New Roman% ( T FLdesign enables to select optimized parameters and is a general design.sdHAssHsdAHAdsHssHAHHHssAsWssHsWdAsAHdAsAssWsHAsdHARL_oŖў% ( # t;t;( AKB# t;t;# t;t;@XBRLArial% ( # t;t;@XBT< L`BiographyZ}RLArial% ( T L`Lein HarnHHdRLArial% ( TTLPHRLTimes New Roman% ( TLLreceived the B.S. degree in electrical engineering from the National Taiwan WsssHsAHsAAAAsWssAHAsHssHWHssHAsHssWHAWWAHsAsHHsHAsHsARLTimes New Roman% ( Tp[LUniversity in 1977, the M.S. degree in electrical engineering from the State University of HsWdHHAHAAAHsAAAAsWssAHAsHssHWHssHAsHssWHAWWAHsAHsHsAHsWdHHAWARLTimes New Roman% ( TPVLNew York-Stony Brook in 1980, and the Ph.D. degree in electrical engineering from the sAWWHAWAHAAAsAHsAAAAsWssAHAsHssHWHssHAsHssWHAWWAHsARLTimes New Roman% ( TL(ULUniversity of Minnesota in 1984. In 1984, he joined the Department of Electrical and HsWdHHAWAHsdHsAHAAAWAAAsAHHsAHsAssWHsHAWAHssHWHssHAsARLTimes New Roman% ( Td`YLComputer Engineering, University of Missouri- Columbia as an assistant professor, and in HsWAHssWHAAHsWdHHAWAHddWHWAHHsAsdAsAsddHdHsHAWWsddWAAsAHARLTimes New Roman% ( TDTL1986, he moved to Computer Science and Telecommunication Program (CSTP), University AAsAsAHAHsWAsHsssAs&" WMFC /AsHssHssHHAWWsAWWAAHsWdHHARLTimes New Roman% ( TL ULof Missouri, Kansas City (UMKC). While at UMKC, he went on development leave to work WAHddWHAAsdsdAHHAWWAAHHsAsHAAAsAsHAAssHsHAHsssAHAWARLTimes New Roman% ( TP VLin Racal Data Group, Florida for a year. His research interests include cryptography, HAsssHAsHsAWAAHWHsAWWAsAssWAAHdAWsdssWsAHHsWsdHdAHsHsAsWHWsAARLTimes New Roman% ( TD@ TLnetwork security, and wireless communication security. He has published a number of sHWAdssWHHAAsAHWsHsddAsHssHHAdssWHHAAsAsdAHHdsAsAsWAWARLTimes New Roman% ( Thx ZLpapers on digital signature design and applications and wireless and network security. He ssWdAAHHHsHAdHsHWsAsdHAsAsHHssHHdAsAHWsHsddAsAsHWAdssWHHAAsARLTimes New Roman% ( ThZLhas written two books on security. He is currently investigating new ways of using secret sdAWHHHsAHAdAAdssWHHAAsAHdAsWWsHHAHsdHHsHHAsAsdAWAdHAdssWsHARLTimes New Roman% ( T  Lsharing in various applications.dsWHAHAsWHdAsHHssHHdARL_oŖў% ( # t;t;@XB# t;t;_888"% ( # t;t;̬@̬@; 6`66(`66(6<@_888% ( # t;t;'% % ( ;  6  6 C6 <>'% ( ; '6=,6=,46'<>% ( _888% _888"% ( # t;t;@0A; 66%6%6<@_888% ( # t;t;# t;t; AQ8ARLArial% ( # t;t; AQ8ATH<LJune 4, Wednesday, 9:30-11:00ZZZ.ZZZkZRLArial% ( TT&" WMFC o/<LPaRLArial% ( T< L`m, Room ZZZ ZRL[SO% ( Txo<L\IQ5uV[[[@@@@@@@RLArial% ( TT/!<LP ZRLArial% ( Td!<LTA302RL_oŖў% ( # t;t; AQ8A# t;t;# t;t;A@RL>Segoe Print% ( # t;t;A@TLtSeminar Announcement1=t==$==RL_oŖў% ( # t;t;A@# t;t;# t;t;33oB̤A M4<H# ??l(( &" WMFC O/ź¼ž&" WMFC //ǻ¸źĹùúǾºǾ&" WMFC /w{}xrs}x{ƾwoms|utǼķ¸żrij~kssq¸ǽƻʿɽ¹hczh~p}xmj|k}g|i}nzlexn}ewg}ktxgxm{bsdxh}ok~_oWi]qh}qr`tSfavoezkxWfZll~q`rK^cvyfzzbmTipqcqǿI\`tarʿVeRfp&" WMFC /j~J_i~|jxǾO^Xnj|ovL_vBQe{fiJ_QZ_HP}jyp[kpxUWsIN^YZdDBN20A>Jk|nlyhthtWdMZko47R]`sgqt{bncspylyx{ps;:Zcao}IMvS]T`\hM_S`etooq}|tn[pBQA@U58EMQlJQvucqgztUZWYnJJXb_kIDO42?9C\{}zq~kvdpbpcr|trxqq~hunssiygudrqvspyzwuoWh@Jt?@P34?KL]JOogq^l[pX]~VWgQPXWV_JGR65A9?Wwyyqlwuopu{|wtqonTd?GfBCQ,-8IIUMOfajR_]qY]|YZjST[NPWEGS?AM;BZnzrruvutsi]sbxVeAD^:=M**6DCNBGYPVO[^kjh{XYdUR[NKQIHREFVJ=AdJQ`gztz\Zc^Z`OJQQPVDGX;BZ_rurroodyXlEN{WdSb>CW:9H(*1--555=36UIHriiû&" WMFC O/MLRUT]UUZFDMQNWCEVCJaWgty{xlkjTg_q?IqPbN\FG\::D.,5-*2/,425JSNkonzB=?OOTJJNDBKRNVEBRLObNZvx~kj_sI[[k>HmL^KXGG[:;E3/782:(%-;8@]Xhi`eOJLJILLHPDAJNJOA>JHN\DNoqw|tocyO^DTKWBIhM`EQyFEV23@0.6649*)2@JCAHC@J>BSCNji{}|vr`xE>=D;7B8:F;@WXitr}{z}rmYn2@zDP>AVGH^HQ}3:O/0@-05D@ELFJEBE559ihc;7?=:=MFN>=@0/778B99ML[ks|~rsOe3@yIYFDTRScCJn18M))4315::ARMQHGH015z{=:C;9=TOSIDH31811<45EALodxv|{xsKa1CyGTIGTIKZGMh,0C+)0549?>BQLPCADC?>|ux1.7?=CHCITNO>7=50:22@:?[Zjo{wyurL^4?zCOyB@P=6:MS_i|trzorlFY6A{=Jn45F01@04J(+312:45;D@B547,*-93;)+3>=GJHMIFG0-2.-714CDQp_rlns~vn`vDV4Cw8:=7<335645vpq53:*,8<@M??DF@A528(*5,3JKZbte}ry}utod{K](1[=Ih%(7""/*+9+-6317A>A627527@@??8=()3-0A<9DJGH525..6)->?Ov]oaymv}}rxn[qN['/R8Cb!"-&(0(,803:414323547--0UTSf\\0.6(+:=@O::==;=339+-:1=]PfYrd{px~}xwpriMbKZ&.M09T&')2/3?))0-,0734114+.2xss&" WMFC //B9@&'23:L66=97<0.0)*4&/FBU[q`xjtz|xxrod{N^GY%+G)/C!"*).6.2>'&.)(*;8:666323pdh*'2)-><=L.*.3.1/-5&,>;HmWkavgpv~}zsulczJZIZ(+C),;%&0,0;33?((-946102758300¾83:&*749J85:.,-1,4%'41;[J\]qaymrx~~z{rpjbvHZ=Lv),C"$1"$-16?20;)'-512301548<="#,$&049D*-:''+,()=98:8:XWT505(+:7;M--3(&)$!*$*8.8WEUVk^ultuzy{{}zspnkezgh}ReFW-3L',='*3$'17=M(+3%$'4/1>9;756c\^%%-.3D66@$$$ !%&1'/E5CkK`Ukbwkoqxzy|}|vmh{at\kTgObQiZmIZ@N~).?).@*,701=9>K,-3%&'101<89>;;1+2"%289I+)/! 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While at UMKC, he went on development leave to work Times New Roman-2 @Vin Racal Data Group, Florida for a year. His research interests include cryptography, Times New Roman-2 BTnetwork security, and wireless communication security. He has published a number of Times New Roman-2 CZpapers on digital signature design and applications and wireless and network security. He Times New Roman-2 EZhas written two books on security. 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B8hnVZYjޟ%`7Þx+p=|q_x9#rGQ<$&I?)~qVH`c rRwOu};o`jѵHw+iA#ix9&?mұ?iAWR{k] 4鵮6.@n' HF$sǨ>? f4G'9rzb>>+]=/u/rko" -H ~鏼ܦxqqڛ2qx=ooieLnnAQ^}<~9w`F^l$ǷOzzBk=ꕒMKvM>1#~kmU}|ή}Xǃ:9nYMu@- *ظgU\b|Wi_?~k~ջz˵E駓[kl}|m#f@g%T &NUwCZ([1 l2{cv6==Q=׿߭M'>;ϿϯdGW,2#NGLߙ8qU*`c q1/JIY=^;ԛn9oO!br}`01݃'5ApsN=)ěx$0rI'3M7k[O4SQPzQSȻe_? :20 (   H  s B Rectangle 4P@ Title: Optimized Implementation of a General Secret Sharing (for audiences with security background) Prof. Lein Harn School of Computer and Engineering University of Missouri-Kansas City, USA= )   K <"c"'""cc "cJgg*e  \    c : Text Box 5 T    L  c : Text Box 6  Abstract Secret sharing is one of most popular cryptographic tools which has been proposed originally in 1979. Shamir s threshold secret sharing is the most popular scheme in the literature. But, Shamir s scheme has a special secret access structure in which (a) any t (i.e., the  threshold ) or more than t shareholders can recover the secret and (b) fewer than t shareholders cannot recover the secret. A general secret sharing has more general secret access structure in which (a) any  qualified subset of shareholders can recover the secret and (b) any  unqualified subset of shareholders cannot recover the secret. Most papers on general secret sharing in literature contain only theoretical discussion. In this talk, I will introduce my recent paper to propose a complete implementation of a general secret sharing. We use Boolean logic to characterize a general secret access structure and derive the minimal positive secret access and the maximal negative secret access subsets. Then, we use these two subsets to determine parameters to implement a general secret sharing. Our design enables to select optimized parameters and is a g( I / 0DArialD[SO DWingdings0DArial Rounded MT Bold@DTimes New RomanPDBodoni MT Black`DSegoe Print@   @f" dd@O  @@`` (  ,R$#q!yĒs *@?  O  +p` p 80___PPT10  @8 __WPP6pOp   ` 33` Sf3f` 33g` f` www3PP` ZXdbmo` \ғ3y`Ӣ` 3f3ff` 3f3FKf` hk]wwwfܹ` ff>>\`Y{ff` R>&- {p_/̴." d@O,l" d@O   " @ ` ^" d@O   @@``PR    @ ` ` p>> (    s B  Rectangle 2+  b@Click to edit Master title style!b  c <  Rectangle 3+  Click to edit Master text styles Second level Third level Fourth level Fifth level!      c <  Rectangle 4kB  B "   c <  Rectangle 5 B   D "   c <  Rectangle 6 +B  f*& "" N  6 ? 33 Default Design |t (    c <  Rectangle 2/7   V "     c <  Rectangle 3c 7  X "     H  Rectangle 4    H  Rectangle 5 w  Click to edit Master text styles Second level Third level Fourth level Fifth level!    S   s B  Rectangle 6/H   V "     s B  Rectangle 7c H  z*& " "   N  6 ? 33eneral design. `     "c c "*      c : Text Box 7p Biography Lein Harnreceived the B.S. degree in electrical engineering from the National Taiwan University in 1977, the M.S. degree in electrical engineering from the State University of New York-Stony Brook in 1980, and the Ph.D. degree in electrical engineering from the University of Minnesota in 1984. In 1984, he joined the Department of Electrical and Computer Engineering, University of Missouri- Columbia as an assistant professor, and in 1986, he moved to Computer Science and Telecommunication Program (CSTP), University of Missouri, Kansas City (UMKC). While at UMKC, he went on development leave to work in Racal Data Group, Florida for a year. His research interests include cryptography, network security, and wireless communication security. He has published a number of papers on digital signature design and applications and wireless and network security. He has written two books on security. He is currently investigating new ways of using secret sharing in various applications. x    " " " c c "*      Z )Rectangle 8@ T    b  TZ AutoShape 9~N T    b  @ VZ AutoShape 10H T      H Text Box 14@ bfJune 4, Wednesday, 9:30-11:00am, Room IQ5uV[[[ A302~4 cc cccc"F         s D Rectangle 17P (Seminar Announcement. cc    \A 0? qwVGr 11qw.jpg@@0  C  ? 33r@% u4