%!PS-Adobe-2.0 %%Creator: dvips(k) 5.90a Copyright 2002 Radical Eye Software %%Title: CrAM.dvi %%CreationDate: Fri Mar 26 13:22:48 2004 %%Pages: 16 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX12 CMR10 CMR9 CMBX9 CMBX10 CMTI10 CMR7 CMMI10 CMMI7 %%+ CMSS9 CMSY7 CMSY10 CMTT10 CMSS8 CMSY5 CMMI9 CMSY9 CMR6 CMMI6 CMSY6 %%+ CMTT9 CMEX10 CMSSI9 CMTI9 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips.exe CrAM %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2004.03.26:1322 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: texps.pro %! 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 26 /braceleftbigg put dup 80 /summationtext put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF5B8CAC6A7BEB5D02276E511FFAF2AE11910 DE076F24311D94D07CACC323F360887F1EA11BDDA7927FF3325986FDB0ABDFC8 8E4B40E7988921D551EC0867EBCA44C05657F0DC913E7B3004A5F3E1337B6987 FEBC45F989C8DC6DC0AD577E903F05D0D54208A0AE7F28C734F130C133B48422 BED48639A2B74E4C08F2E710E24A99F347E0F4394CE64EACB549576E89044E52 EABE595BC964156D9D8C2BAB0F49664E951D7C1A3D1789C47F03C7051A63D5E8 DF04FAAC47351E82CAE0794AA9692C6452688A74A7A6A7AD09B8A9783C235EC1 EA2156261B8FB331827145DE315B6EC1B3D8B67B3323F761EAF4C223BB214C4C 6B062D1B281F5041D068319F4911058376D8EFBA59884BA3318C5BC95684F281 E0591BC0D1B2A4592A137FF301610019B8AC46AE6E48BC091E888E4487688350 E9AD5074EE4848271CE4ACC38D8CBC8F3DB32813DDD5B341AF9A6601281ABA38 4A978B98483A63FCC458D0E3BCE6FD830E7E09B0DB987A6B63B74638FC9F21A5 8C68479E1A85225670D79CDDE5AC0B77F5A994CA700B5F0FF1F97FC63EFDE023 8135F04A9D20C31998B12AE06676C362141AAAA395CDEF0A49E0141D335965F2 FB4198499799CECCC8AA5D255264784CD30A3E8295888EFBC2060ADDD7BAC45A EEEECDFF7A47A88E69D84C9E572616C1AC69A34B5F0D0DE8EE4EDF9F4ADE0387 680924D8D5B73EF04EAD7F45977CA8AD73D4DD45DE1966A3B8251C0386164C35 5880DD2609C80E96D1AB861C9259748E98F6711D4E241A269ED51FF328344664 3AF9F18DCE671611DB2F5D3EA77EE734D2BED623F973E6840B8DAD1E2C3C2666 DD4DD1C1C9C622FAEAB9D3E54476B49A2A026565F10A840322879C22C6377786 D7BAEC4BF029664ABB5F58EFAB274A348B8B14C598B9468EFFA5B0C8EAA1D961 A101C86EAB7810D83B76BFA4BF0D97BCA4FD9522BD9F4276207A3769E455A54C 4A254D9EEAD12624B9535ABB389D3B0396C2895B42D78371C077832BB3AC7910 E04329A23332C82D01B7992182EAFF2F54B946ED96A9DE254EF20336C6E7D3C7 E6DAFED76C9F6345BC22DCE6BF500BA79D88EFCB3F65BF7D07E4342DE530479D 8481E7CA451F50F5288D782A460752BD401D7F211F5945F32118AA0FA598AD65 85184F1B0856B236BA08D285BF9D9C9C748D24435AC34F54E03156817F23A9C8 EF5E6FABC86B19B051AD2B8675920B7A94B310FDBB5EB7789091029807AB8A8A 3C9B07998C7DBAF2BFC9C02C93D890A5112E60B3EF55C70B0CE875C5C6D158FB A818488C41B43B0D768F0FA6B46A26DF05E05E0BC7BAF1C288B1DF2099CBC06D EED60C15ACC767369BF407B7BC4DE5A773B55D0BA00AA30A91F3D437FDCB0A38 0D350D857E06577866FB189B9041529D5D82A4C5588A1432F1D4042CF39AB59B A9A3D2289E7A24FF9CAF13F557DC875CB21BF78FDCC346F708D363CF5E75313A CEA441D1FC00AB8C14EBFEA8063C2CCF8BD68863BA1B60B43C3AA379771A5CA0 78B33A0848DEEF841200A64C6E899259F5F477680ACE901BAFC65DB679C2AD1B B30A7228BDFB82C0AE 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTT9 %!PS-AdobeFont-1.1: CMTT9 1.0 %%CreationDate: 1991 Aug 20 16:46:24 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 89 /Y put dup 90 /Z put readonly def /FontBBox{-6 -233 542 698}readonly def /UniqueID 5000831 def currentdict end currentfile eexec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2B4A4A54E387836F244D9769AF9D8A270AA6E79620A80B448843FAA1D1EB2006 0AB405A84D594AC53295734BAE32C0D99447CEB1EB264467C714488896ED4A53 0A7286F6EAE165837DCB80A3C7BF7745E1D9DE1C08106042D077E89C2A760C84 30BEB7E8D52950037A9B65D4FEC418375E921DE619780F814999C62CEFCE5737 99C6569B8CDD90 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 48 /prime put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 75 /K put dup 101 /e put dup 104 /h put dup 105 /i put dup 107 /k put dup 110 /n put dup 112 /p put dup 115 /s put dup 116 /t put dup 118 /v put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 61 /equal put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY9 %!PS-AdobeFont-1.1: CMSY9 1.0 %%CreationDate: 1991 Aug 15 07:22:27 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 37 /arrownortheast put dup 38 /arrowsoutheast put dup 50 /element put dup 54 /negationslash put dup 55 /mapsto put dup 59 /emptyset put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put readonly def /FontBBox{-30 -958 1146 777}readonly def /UniqueID 5000819 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 1 /Delta put dup 23 /nu put dup 26 /rho put dup 27 /sigma put dup 58 /period put dup 59 /comma put dup 61 /slash put dup 67 /C put dup 75 /K put dup 79 /O put dup 80 /P put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 121 /y put readonly def /FontBBox{-29 -250 1075 750}readonly def /UniqueID 5087384 def currentdict end currentfile eexec 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY5 %!PS-AdobeFont-1.1: CMSY5 1.0 %%CreationDate: 1991 Aug 15 07:21:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /prime put readonly def /FontBBox{21 -944 1448 791}readonly def /UniqueID 5000815 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSS8 %!PS-AdobeFont-1.1: CMSS8 1.0 %%CreationDate: 1991 Aug 20 17:34:12 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 45 /hyphen put dup 48 /zero put dup 49 /one put dup 50 /two put dup 52 /four put dup 65 /A put dup 68 /D put dup 69 /E put dup 75 /K put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 99 /c put dup 101 /e put dup 105 /i put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 116 /t put dup 121 /y put readonly def /FontBBox{-65 -250 1062 761}readonly def /UniqueID 5000801 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTT10 %!PS-AdobeFont-1.1: CMTT10 1.00B %%CreationDate: 1992 Apr 26 10:42:42 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /asteriskmath put dup 48 /prime put dup 121 /dagger put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSS9 %!PS-AdobeFont-1.1: CMSS9 1.0 %%CreationDate: 1991 Aug 20 17:34:24 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 39 /quoteright put dup 43 /plus put dup 45 /hyphen put dup 48 /zero put dup 49 /one put dup 50 /two put dup 52 /four put dup 53 /five put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 72 /H put dup 75 /K put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 121 /y put dup 122 /z put readonly def /FontBBox{-63 -250 1027 760}readonly def /UniqueID 5000802 def currentdict end currentfile eexec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3B2132F0151E229D7B2FD62C56EF88C19ABEE2B8B5D510AE41B110D00F224352 D1157E46F6E89B761D6DDB3CAE9455B5A7EA7413D2F49B0C9B58DD8C01218939 7E07AA503ACFCA9EE5E205688744638E7411F3384815B73B0843D04AC54340B2 4D67FBF0E318DFD2F312AA80BF651E94630810486794C223BBD5CD127A53151E E73AFBDCDF67B4DE8FCD7601696E4CDE4C6903D7E02F618A100D83C819DA20C9 59F60AF9C07BFBCD8A99944A4670074B4F766F05ADC0A0CD8330747C528BEF9E 7CC63DBBFC24DEFEB21FCAD58C4D19AE26B6765AC41E1F7E27685A85286069FC 4FFE27CF3D15ACCB624919F577A91578B560CE47D6DCB6BAA50351186BABBF2B 2FA419E8A24529BE16C9258D63204D92D50B314E4ECFA0B3EFFAC55FAF1F24B0 85E0D315CF2AE71ED058313A93607D46642EE7AF58608D92831739553DC2AD13 DDD64DDF668CC0FFBAC7728A910924BAFFA98C46E7601C72788717CF83791FEB E303C0349FC60712E9814D8AD9688367A756EE1B89F3158D38B086EA7D9ADFDC 78E24CB74F0DFDE588D9AD564B15EED0A5BE1694A309B0ECCC1D8A7E98B68D6E 3AB34AE5BA3F19C8841D36709B4045FB2CB8301CF116F045F5FBFD4A09FCD3A1 BB5A051C1F7A244E24EB72EFC962FF21A2BE73CF42F34947BFCDCA8E86BAF9B9 492C0EB839A300B6A536EC1236D38D051AB628D76406DD553F62F5738BC086D2 81FBB29763938E88C5BDEEBA0AE1007D8F59FA52070C03B9DA7AFBB75F822DE2 1FD2077529981CE65FD5DB0230EF1F2C1F4F1071D3C10F412D6B3587F5133834 453F0195D4 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 84 /T put dup 110 /n put dup 115 /s put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 23 /nu put dup 26 /rho put dup 27 /sigma put dup 58 /period put dup 59 /comma put dup 61 /slash put dup 75 /K put dup 77 /M put dup 79 /O put dup 80 /P put dup 84 /T put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 104 /h put dup 107 /k put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 118 /v put dup 120 /x put dup 121 /y put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec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All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 43 /plus put dup 49 /one put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 65 /A put dup 67 /C put dup 76 /L put dup 77 /M put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 65 /A put dup 67 /C put dup 69 /E put dup 70 /F put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put dup 123 /endash put readonly def /FontBBox{-301 -250 1164 946}readonly 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All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 65 /A put dup 67 /C put dup 73 /I put dup 77 /M put dup 80 /P put dup 82 /R put dup 84 /T put dup 86 /V put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 121 /y put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 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%!PS-AdobeFont-1.1: CMBX9 1.0 %%CreationDate: 1991 Aug 20 16:36:25 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 46 /period put dup 65 /A put dup 97 /a put dup 98 /b put dup 99 /c put dup 114 /r put dup 115 /s put dup 116 /t put readonly def /FontBBox{-58 -250 1195 750}readonly def /UniqueID 5000767 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F0364CD5660F74BEE96790DE35AFA90CCF712 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 19 /acute put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 61 /equal put dup 63 /question put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 127 /dieresis put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 34 /quotedblright put dup 35 /numbersign put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 87 /W put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 96 /quoteleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 124 /emdash put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F 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4[15 3[27 1[27 15[34 40 1[39 46 3[43 5[37 45 2[41 12[31 1[31 31 31 2[21 45[{}22 58.1154 /CMSS8 rf /Fl 134[44 2[44 44 44 44 44 44 44 44 44 1[44 2[44 44 44 44 44 44 44 44 44 13[44 44 1[44 44 44 44 1[44 5[44 44 1[44 44 19[44 44 44[{}33 83.022 /CMTT10 rf /Fm 134[37 14[23 28[100 21[0 4[55 11[83 83 1[42 42 83 29[42 2[65{}12 83.022 /CMSY10 rf /Fn 134[30 72[19 44[34 3[{}3 58.1154 /CMSY7 rf /Fo 133[33 35 2[35 40 28 29 26 1[40 38 40 61 18 38 20 18 40 38 23 34 40 34 40 37 10[51 1[52 43 50 1[49 57 54 67 1[53 2[54 2[46 56 49 51 51 11[38 38 1[38 38 38 2[26 1[60 3[21 39[{}46 74.7198 /CMSS9 rf /Fp 140[31 4[41 25[39 84[{}3 58.1154 /CMMI7 rf /Fq 134[41 47 1[40 1[30 39 37 1[42 40 50 73 1[43 2[48 2[39 43 36 1[44 12[49 3[53 63 1[81 1[71 13[42 1[23 23 30[47 43 2[41 23[{}27 83.022 /CMMI10 rf /Fr 206[33 5[51 43[{}2 58.1154 /CMR7 rf /Fs 134[40 39 55 38 45 28 34 35 1[42 42 47 68 21 38 25 25 42 38 25 38 42 38 38 42 12[59 6[74 52 8[59 1[62 18[25 30 25 31[47 12[{}33 83.022 /CMTI10 rf /Ft 132[48 1[50 50 2[53 37 38 39 1[53 48 53 80 27 2[27 53 48 29 44 53 42 53 46 12[66 53 72 1[65 72 75 91 6[60 63 1[69 1[72 10[48 48 48 48 48 48 2[27 46[{}39 83.022 /CMBX10 rf /Fu 134[59 3[62 44 44 46 1[62 56 62 93 31 2[31 62 56 34 51 62 50 62 54 10[85 1[78 1[84 1[77 2[106 3[42 5[81 1[85 12[56 56 56 56 49[{}31 99.6264 /CMBX12 rf /Fv 139[34 35 36 14[39 49 43 31[67 18[25 46[{}8 74.7198 /CMBX9 rf /Fw 128[38 3[38 34 41 41 55 41 43 30 30 30 1[43 38 43 64 21 41 23 21 43 38 23 34 43 34 43 38 3[21 1[21 47 58 1[79 58 58 55 43 57 1[52 60 58 70 48 60 39 28 58 60 50 52 59 55 54 58 1[36 1[60 2[21 38 38 38 38 38 38 38 38 38 38 38 21 26 21 60 1[30 30 20[38 6[43 45 11[{}76 74.7198 /CMR9 rf /Fx 131[83 42 37 44 44 60 44 46 32 33 33 44 46 42 46 69 23 44 25 23 46 42 25 37 46 37 46 42 23 2[23 1[23 51 2[85 1[62 60 46 61 1[57 65 62 76 52 65 43 30 62 65 54 57 63 60 59 62 3[65 1[23 23 42 42 42 42 42 42 42 42 42 42 42 23 28 23 65 1[32 32 23 3[69 42 20[46 46 48 11[{}79 83.022 /CMR10 rf /Fy 134[71 4[52 53 55 1[75 67 75 4[37 75 67 1[61 1[60 75 65 12[94 6[128 9[97 1[102 65[{}18 119.552 /CMBX12 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: A4 end %%EndSetup %%Page: 1 1 TeXDict begin 1 0 bop 851 448 a Fy(The)44 b(Cryptographic)h(Abstract)g (Mac)l(hine)1324 737 y Fx(Dean)27 b(Rosenzw)n(eig)f(and)i(Da)n(v)n(or)e (Runje)1620 911 y Fw(Univ)n(ersit)n(y)f(of)h(Zagreb)759 1217 y Fv(Abstract.)43 b Fw(The)17 b(Cryptographic)h(Abstract)e(Mac)n (hine)i(is)g(an)f(executional)h(mo)r(del)759 1308 y(of)23 b(cryptographic)e(actions,)i(indep)r(enden)n(t)e(of)h(the)f(concrete)h (cryptographic)g(pro-)759 1399 y(cedures)k(emplo)n(y)n(ed,)f(ev)n(en)g (of)i(the)e(abstraction)i(lev)n(el)e(of)i(the)e(underlying)g(mo)r(del) 759 1491 y(of)c(cryptograph)n(y)-6 b(.)19 b(This)h(is)g(motiv)l(ated)g (b)r(oth)f(b)n(y)g(a)h(theoretical)h(purp)r(ose)f(of)g(relat-)759 1582 y(ing)i(the)g(dynamics)f(of)i(proto)r(col)g(executions)e(at)h (di\013eren)n(t)g(lev)n(els)g(of)g(abstraction,)759 1673 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b(translation)f(of)h(pro)r(ofs)f(for)h(the)g (abstract)f(cryptograph)n(y)e(mo)r(del)k(in)n(to)e(pro)r(ofs)h(for)523 2085 y(di\013eren)n(t)36 b(computational)f(mo)r(dels,)g(with)h(target)f (theorems)g(of)h(form:)f(abstractly)f(safe)523 2184 y(proto)r(col)i(+)i (computationally)e(safe)i(algorithms)e(=)h(computationally)g(safe)g (proto)r(col,)523 2284 y(for)e(di\013eren)n(t)g(notions)g(of)h (`computationally)e(safe'.)h(It)h(seems)f(that)h(the)g(prop)r(erties)e (of)523 2383 y(abstract)28 b(cryptograph)n(y)e(used)i(in)h(a)g(formal)f (pro)r(of,)g(together)g(with)h(the)g(computational)523 2483 y(securit)n(y)19 b(criterion)g(desired,)h(will)h(largely)d (dictate)j(the)f(computational)g(securit)n(y)f(assump-)523 2583 y(tions)28 b(on)h(algorithms)e(needed.)i(W)-7 b(e)29 b(see)f(this)h(future)g(w)n(ork)e(as)h(direct)g(con)n(tin)n(uation)g (and)523 2682 y(application)e(of)g([AR02)o(,MW03])g(for)g(analysis)f (of)h(static)g(messages)f(and)h([MW03)o(,W)-7 b(ar03)o(])523 2782 y(for)28 b(dynamic)f(proto)r(col)g(execution.)h(The)g(CrAM)g (seems)g(to)g(b)r(e)g(the)h(righ)n(t)e(setting,)h(since)523 2882 y(it)g(pro)n(vides)f(a)g(simple)h(and)g(precise)f(w)n(a)n(y)f(of)i (sa)n(ying)e(that)j(cryptographic)c(agen)n(ts)i(at)h(dif-)523 2981 y(feren)n(t)c(abstraction)f(lev)n(els)g(`do)h(the)h(same':)f(they) g(execute)g(the)h(same)e(CrAM)i(program)d(in)523 3081 y(di\013eren)n(t)28 b(en)n(vironmen)n(ts.)648 3193 y(This)f(pap)r(er)g (in)n(tends)h(to)f(realize)g(most)g(\(though)h(not)g(all\))f(of)h(aims) f(2)g(and)h(4.)648 3305 y(W)-7 b(e)30 b(start,)g(in)g(section)g(1,)g(b) n(y)g(la)n(ying)f(do)n(wn)g(the)i(v)n(o)r(cabulary)d(and)i(the)h (assumptions)523 3405 y(common)c(to)h(all)f(abstraction)f(lev)n(els)h (w)n(e)g(rely)g(on)h(throughout)e(the)i(pap)r(er.)648 3517 y(In)h(section)g(2)g(w)n(e)g(revisit)f(the)i(message)e(pattern)h (language)f(of)h([RRS03)o(])h(in)f(order)f(to)523 3617 y(allo)n(w)j(di\013eren)n(t)h(mo)r(dels)g(of)g(cryptograph)n(y)-7 b(,)30 b(at)i(di\013eren)n(t)g(lev)n(els)g(of)g(abstraction,)f(to)h(b)r (e)523 3716 y(plugged)27 b(in)n(to)g(patterns.)g(F)-7 b(or)27 b(the)h(purp)r(ose)f(of)h(this)g(pap)r(er,)f(w)n(e)g(in)n(ten)n (tionally)g(disregard)523 3816 y(in)n(terpretations)22 b(of)h(cryptographic)e(ob)5 b(jects,)23 b(and)g(place)g(a)g(minimal)g (set)h(of)f(assumptions)523 3916 y(on)36 b(a)f(mo)r(del)h(of)g (cryptograph)n(y)e(needed)i(to)f(pro)n(v)n(e)g(equiv)-5 b(alence)35 b(of)h(message)e(patterns)523 4015 y(and)23 b(CrAM)h(programs.)d(The)i(mo)r(di\014ed)h(language)e(of)i(message)e (patterns)h(recaptures)f(the)523 4115 y(univ)n(ersalit)n(y)34 b(prop)r(erties)h(of)h(patterns)g(wrt)g(the)g(mo)r(del)g(of)g(abstract) f(cryptograph)n(y)e(of)523 4214 y([RRS03)o(].)648 4327 y(The)28 b(main)g(result)g(of)h(this)f(pap)r(er)g(is)g(generation)f(of) h(pro)n(v)-5 b(ably)27 b(correct)g(implemen)n(ta-)523 4426 y(tion)i(of)g(a)f(pattern{based)g(proto)r(col)g(description)g(for) g(a)h(giv)n(en)f(programming)f(language)523 4526 y(and)36 b(a)g(cryptographic)e(programming)g(library)-7 b(.)35 b(This)h(is)g(accomplished)g(b)n(y)f(compiling)523 4625 y(patterns)27 b(to)g(CrAM)g(co)r(de,)g(in)h(a)f(pro)n(v)-5 b(ably)26 b(correct)f(and)j(complete)f(w)n(a)n(y)-7 b(.)26 b(In)h(view)g(of)h(the)523 4725 y(represen)n(tation)21 b(of)j(proto)r(col)e(roles)g(of)h([RRS03)o(])g(as)g(sequences)f(of)h (matc)n(h{create)f(pairs)g(of)523 4825 y(patterns,)29 b(w)n(e)h(obtain)f(compilation)g(of)h(proto)r(col)e(roles)g(to)i(CrAM)g (co)r(de)f(automatically)-7 b(,)523 4924 y(b)n(y)27 b(pasting)g(and)h (glueing)f(with)h(instructions)f(for)g(input{output.)1943 5173 y(2)p eop end %%Page: 3 3 TeXDict begin 3 2 bop 648 448 a Fx(The)36 b(in)n(tuition)g(of)g(a)g (proto)r(col)f(role)g(as)g(an)h(in)n(teractiv)n(e)f(mac)n(hine)h(with)g (input)h(and)523 548 y(output)f(of)f(messages)e(gets)i(a)g(concrete)f (form)h(in)h(the)f(CrAM,)g(whic)n(h)g(is)h(no)n(w)e(also)g(de-)523 648 y(coupled)d(from)f(an)n(y)g(sp)r(eci\014c)h(mo)r(del)g(of)g (encryption,)g(and)f(w)n(orks)g(with)h(an)n(y)f(reasonable)523 747 y(mo)r(del)e(supp)r(orted)f(b)n(y)h(the)g(v)n(o)r(cabulary)d(and)j (assumptions.)648 847 y(W)-7 b(e)33 b(sho)n(w)e(that)i(b)r(oth)g (compilation)f(algorithms)g(are)f(b)r(oth)i(correct)f(and)g(complete,) 523 946 y(whic)n(h)37 b(means)f(that)h(CrAM)f(programs)e(are)i(at)g (least)h(as)e(strong)h(as)g(patterns,)g(in)h(an)n(y)523 1046 y(sp)r(eci\014c)28 b(incarnation)e(of)i(b)r(oth.)648 1146 y(In)d(section)f(3)h(w)n(e)g(de\014ne)g(the)g(CrAM,)g(and)g(in)g (section)g(4)f(w)n(e)h(de\014ne)g(the)h(compilation.)523 1245 y(Pro)r(ofs)37 b(of)h(securit)n(y)g(for)g(pattern{based)f(proto)r (col)g(descriptions,)h(to)g(b)r(e)h(done)f(in)h(the)523 1345 y(completion)21 b(of)g(aim)g(2)g(indicated)g(ab)r(o)n(v)n(e,)f (will)i(comp)r(ose)e(with)i(our)e(correctness)g(and)h(com-)523 1445 y(pleteness)f(pro)r(ofs)f(presen)n(ted)h(here)f(so)h(as)f(to)h (pro)n(v)n(e)f(securit)n(y)g(of)h(CrAM{implemen)n(tations)523 1544 y(of)25 b(proto)r(cols.)e(A)i(CrAM{implemen)n(tation)f(b)r(ecomes) h(a)f(real)g(implemen)n(tation)h(either)f(b)n(y)523 1644 y(in)n(terpreting)e(the)h(CrAM)g(directly)f(\(one)h(w)n(a)n(y)e(of)i (doing)f(that)h(is)g(AsmL)f(co)r(de)h(to)g(b)r(e)g(found)523 1743 y(at)28 b([W)-7 b(eb)q(]\),)28 b(or)g(b)n(y)g(expanding)f(CrAM)i (programs)d(in)n(to)i(programs)e(of)i(the)h(target)e(imple-)523 1843 y(men)n(tation)h(language)e(in)i(a)f(pro)n(v)-5 b(ably)26 b(correct)h(w)n(a)n(y)-7 b(.)26 b(The)i(latter)f(p)r (ossibilit)n(y)h(is)f(the)h(only)523 1943 y(really)19 b(practical)f(one,)h(but)h(conceptually)f(it)h(is)g Fs(deja)j(vu)p Fx(,)d(and)f(is)h(skipp)r(ed)f(here)g(to)h(conserv)n(e)523 2042 y(some)29 b(space.)g(In)h(view)g(of)g(our)f(tec)n(hnical)g(framew) n(ork,)f(that)i(of)g(ASMs)g(as)f(implemen)n(ted)523 2142 y(in)e(AsmL,)g(it)g(is)f(rather)g(straigh)n(tforw)n(ard)d(to)k(expand)f (CrAM)g(co)r(de)h(to)f(pro)n(v)-5 b(ably)25 b(correct)523 2242 y(co)r(de)g(in)g(an)n(y)f(language)g(with)h(a)g(w)n(ell)g (de\014ned)g(ASM)h(seman)n(tics,)e(suc)n(h)h(as)f(C,)h(C++,)f(Ja)n(v)-5 b(a)523 2341 y([GH93,HS00)o(,W)e(al95)o(,SSB01)o(].)648 2441 y(The)36 b(results)f(presen)n(ted)g(here)h(are)e(in)j(a)e(sense)g (indep)r(enden)n(t)i(of)f(the)g(ASM)h(frame-)523 2540 y(w)n(ork.)26 b(The)h(justi\014cation)g(for)g(relying)f(on)g(ASMs)i (and)f(AsmL)g(\(if)h(one)e(is)h(still)h(needed\))f(is)523 2640 y(threefold:)575 2804 y Ft({)41 b Fx(The)28 b(framew)n(ork)d(supp) r(orts)j(our)e(mo)r(del)i(of)g(abstract)e(cryptograph)n(y)f([RRS03])j (w)n(ell.)575 2904 y Ft({)41 b Fx(Main)27 b(results)f(of)h(this)h(pap)r (er)e(are)g(essen)n(tially)g(on)h(compiler)f(correctness/complete-)664 3003 y(ness,)d(and)f(ASMs)i(are)e(a)g(pro)n(v)n(en)f(time{tested)i(to)r (ol)g([BR94)o(,BD96)o(,GZ00)o(,SSB01])g(for)664 3103 y(that.)575 3202 y Ft({)41 b Fx(The)32 b(thrust)g(of)g(our)f(program)e (is)j(ab)r(out)g(relating)f(di\013eren)n(t)h(lev)n(els)f(of)g (abstraction,)664 3302 y(and)d(this)g(is)f(the)h(core)e(business)i(of)f (the)h(ASM)g(metho)r(dology)-7 b(.)523 3466 y(F)g(or)41 b(ASM)g(metho)r(dology)-7 b(,)41 b(our)f(results)h(then)h(just)f(op)r (en)h(another)e(application)g(area,)523 3566 y(in)33 b(a)f(w)n(a)n(y)g(somewhat)g(di\013eren)n(t)h(from)f(that)h(of)g([BR97) o(,BR98)o(])g(|)g(w)n(e)f(in)n(tend)i(not)e(only)523 3665 y(to)41 b(use)f(ASMs)h(in)g(order)f(to)g(pro)n(v)n(e)f(proto)r (cols)h(correct,)f(but)i(also)f(to)h(generate)e(their)523 3765 y(implemen)n(tations)23 b(in)g(a)g(uniform)g(w)n(a)n(y)-7 b(.)22 b(F)-7 b(ormal)22 b(ASM)h(mo)r(dels)g(for)g(patterns,)f(CrAM)h (and)523 3865 y(the)28 b(compilation,)f(in)h(form)f(of)h(executable)f (AsmL)h(co)r(de,)f(can)g(b)r(e)h(found)g(at)g([W)-7 b(eb].)523 4129 y Fu(1)112 b(V)-9 b(o)s(cabulary)38 b(and)h(Assumptions)523 4327 y Fx(An)n(y)26 b(instance)h(of)f(the)h(CrAM)f(is)h(de\014ned)f (wrt)h(the)g(follo)n(wing)e(basic)h(univ)n(erses:)f(univ)n(erse)523 4426 y Fq(M)36 b Fx(of)28 b(enco)r(ded)f(messages,)f(and)i(univ)n(erse) e Fq(O)31 b Fx(of)c(abstract)g(cryptographic)e(ob)5 b(jects.)648 4526 y(The)35 b(distinction)g(b)r(et)n(w)n(een)g Fq(M)43 b Fx(and)35 b Fq(O)j Fx(is)c(real)g(in)h(concrete)f(cryptographic)f (APIs:)523 4625 y(ev)n(ery)h(API)g(the)i(authors)d(kno)n(w)h(ab)r(out)h (needs)g(to)g(represen)n(t)f(a)g(k)n(ey)g(in)n(ternally)g(b)r(efore)523 4725 y(accessing)j(it)i(for)f(encryption,)g(it)h(is)f(accessible)f(for) h(encryption)g(only)g(in)h(form)f(of)g(an)523 4825 y(abstract)18 b(ob)5 b(ject,)18 b(sa)n(y)g(a)h(handle)f(in)h(old{fashioned)f(APIs,)g (an)h Fq(O)r Fx(,)g(distinct)h(from)e(the)i(b)n(yte{)523 4924 y(arra)n(y)f(represen)n(tation)g(of)i(the)h(k)n(ey)-7 b(,)20 b(an)h Fq(M)30 b Fx(used)21 b(for)g(comm)n(unicating)f(it)i (externally)-7 b(.)20 b(Ev)n(en)1943 5173 y(3)p eop end %%Page: 4 4 TeXDict begin 4 3 bop 523 448 a Fx(plain)27 b(b)n(yte{ob)5 b(jects,)26 b(suc)n(h)g(as)h(nonces)f(and)h(hashes,)f(are)g(t)n (ypically)g(stored)h(in)n(ternally)f(in)523 548 y(an)i(in)n(ternal)f (form,)h(as)f(an)g Fq(O)r Fx(,)i(distinct)g(in)f(general)e(from)i(the)g (format)g(used)f(for)h(external)523 648 y(comm)n(unication,)f(that)h (of)f Fq(M)9 b Fx(,)28 b(sa)n(y)e(PK)n(CS)h(#7)g([PK)n(C93)n(])h(or)e (PGP)h(messages.)648 747 y(W)-7 b(e)20 b(assume)f(the)h(univ)n(erse)f Fq(O)j Fx(to)e(b)r(e)g(split)g(in)n(to)g(a)f(\014nite)i(set)f(of)f (pairwise)g(disjoin)n(t)h(t)n(yp)r(es)523 847 y Fq(T)572 859 y Fr(1)609 847 y Fq(;)14 b(:)g(:)g(:)f(;)h(T)842 859 y Fp(n)887 847 y Fx(.)21 b(F)-7 b(or)21 b(eac)n(h)f(t)n(yp)r(e)h Fq(T)32 b Fx(w)n(e)21 b(will)g(use,)g(b)r(oth)h(in)f(patterns)g(and)g (in)g(the)h(CrAM,)f(t)n(yp)r(ed)523 947 y(v)-5 b(ariables)29 b Fq(v)913 916 y Fp(T)995 947 y Fx(to)h(range)f(o)n(v)n(er)f Fq(T)12 b Fx(.)30 b(W)-7 b(e)30 b(shall)g(also)f(use)h Fs(r)l(aw)i(variables)p Fx(,)g(whic)n(h)e(will)g(range)523 1046 y(o)n(v)n(er)37 b(ra)n(w)g(messages)g(from)h Fq(M)9 b Fx(,)38 b(with)h(meta)n(v)-5 b(ariable)37 b Fq(r)r Fx(,)i(as)f(w)n(ell)g(as)g(meta)n(v)-5 b(ariables)37 b Fq(o)p Fx(,)523 1146 y Fq(m)31 b Fx(for)g(ob)5 b(jects)31 b(from)g Fq(O)r Fx(,)h Fq(M)41 b Fx(resp)r(ectiv)n(ely)-7 b(,)30 b(and)h(meta)n(v)-5 b(ariable)30 b Fq(v)35 b Fx(for)c(arbitrary) e(ob)5 b(ject)523 1245 y(v)-5 b(ariables.)648 1345 y(Eac)n(h)30 b(t)n(yp)r(e)i(is)f(asso)r(ciated)f(with)j(one)e(or)f(more)h(of)h Fs(kinds)39 b Fx(suc)n(h)31 b(as)g Fo(Nonce)p Fx(,)i Fo(Hash)p Fx(,)f Fo(En-)523 1445 y(cryptionKey)q Fx(,)i(etc.)e(The)g (table)g(b)r(ello)n(w)g(lists)g(the)h(kinds,)f(together)f(with)i(a)e (meta)n(v)-5 b(ariable)523 1544 y(asso)r(ciated)26 b(with)i(eac)n(h)f (kind,)h(to)g(denote)f(v)-5 b(ariables)26 b(to)i(range)e(o)n(v)n(er)g (t)n(yp)r(es)h(of)h(that)g(kind.)881 1722 y Fq(K)62 b Fo(PrivateKey)260 b Fq(h)87 b Fo(Hash)588 b Fq(e)96 b Fo(Encryption)881 1822 y Fq(k)90 b Fo(PublicKey)288 b Fq(c)99 b Fo(PrimitiveV)n(alue)283 b Fq(sk)53 b Fo(SigningKey)881 1921 y Fq(sh)46 b Fo(Sha)n(redKey)269 b Fq(cr)62 b Fo(CreatableObject) 232 b Fq(s)96 b Fo(Signature)881 2021 y Fq(n)83 b Fo(Nonce)409 b Fq(ek)53 b Fo(EncryptionKey)281 b Fq(v)s(k)49 b Fo(V)n(erifyingKey) 881 2120 y Fq(a)89 b Fo(AgentName)232 b Fq(dk)49 b Fo(DecryptionKey)277 b Fq(t)105 b Fo(T)-6 b(uple)523 2299 y Fx(The)28 b(names)f(of)h(the)g (kinds)g(listed)g(ab)r(o)n(v)n(e)f(are)g(at)g(this)h(lev)n(el)g(only)f (a)h(heuristic)f(indication)523 2399 y(of)g(our)g(in)n(ten)n(tions;)g (ev)n(ery)f(incarnation)h(of)g(the)h(CrAM)f(m)n(ust)h(pro)n(vide)e(its) i(meanings)f(for)523 2499 y(them)h(b)n(y)g(pro)n(viding)e(the)i(asso)r (ciated)e(concrete)h(t)n(yp)r(es.)648 2598 y(The)34 b(t)n(yp)r(e)h Fo(RSAES-O)n(AEP-DecryptionKey-1024)g Fx(is)g(an)f(example)g(of)g(suc)n (h)g(a)g(concrete)523 2698 y(t)n(yp)r(e)43 b(of)f(the)h(kind)g Fo(PrivateKey)r Fx(,)f(em)n(b)r(o)r(dying)g(a)h(concrete)e (cryptographic)g(decryption)523 2798 y(primitiv)n(e)28 b(RSADP)h(\(using)f(default)g(hash)g(function)h(and)f(mask)f (generation)g(algorithm:)523 2897 y(SHA-1\),)g(with)f(a)g(concrete)f (enco)r(ding)h(metho)r(d)h(EME-O)n(AEP)-7 b(,)24 b(according)g(to)i(PK) n(CS)f(#1)523 2997 y(standard)j([PK)n(C02)n(],)i(and)f(sp)r(eci\014c)g (k)n(ey)g(material)f(|)i(1024)d(bit)j(long)f(RSA)h(priv)-5 b(ate)29 b(k)n(ey)-7 b(.)523 3097 y(Univ)n(erse)21 b Fq(M)31 b Fx(of)21 b(a)h(CrAM)g(instance)f(with)i(this)f(t)n(yp)r(e)g (m)n(ust)g(also)f(include)h(enco)r(dings)f(of)h(all)523 3196 y(messages)28 b(encrypted)h(with)g(RSAES-O)n(AEP)f(using)h(1024)e (bit)j(long)e(priv)-5 b(ate)29 b(RSA)h(k)n(eys,)523 3296 y(together)d(with)h(enco)r(dings)f(of)g(all)h(1024)d(bit)k(long)d(priv) -5 b(ate)28 b(and)f(public)h(RSA)g(k)n(eys.)648 3396 y(W)-7 b(e)28 b(assume)e(the)i(follo)n(wing)f(relationships)f(b)r(et)n (w)n(een)i(kinds:)558 3562 y(1.)41 b(Eac)n(h)27 b(t)n(yp)r(e)h(of)g (kind)h Fo(PrivateKey)h Fx(or)d Fo(Sha)n(redKey)h Fx(is,)g(nonexclusiv) n(ely)-7 b(,)27 b(a)h Fo(DecryptionKey)664 3662 y Fx(t)n(yp)r(e)c(or)g (a)f Fo(SigningKey)j Fx(t)n(yp)r(e;)e(on)g(the)g(other)g(hand)g(eac)n (h)f Fo(DecryptionKey)i Fx(or)e Fo(SigningKey)664 3761 y Fx(t)n(yp)r(e)28 b(is)f(either)h(a)f Fo(PrivateKey)j Fx(t)n(yp)r(e)d(or)g(a)g Fo(Sha)n(redKey)h Fx(t)n(yp)r(e;)558 3861 y(2.)41 b(Eac)n(h)25 b Fo(PublicKey)i Fx(or)e Fo(Sha)n(redKey)i Fx(t)n(yp)r(e)f(is,)g(nonexclusiv)n(ely)-7 b(,)25 b(an)g Fo(EncryptionKey)j Fx(t)n(yp)r(e)e(or)664 3961 y(a)e Fo(V)n(erifyingKey)k Fx(t)n(yp)r(e;)d(on)g(the)g(other)f(hand)g(eac)n (h)g Fo(EncryptionKey)i Fx(t)n(yp)r(e)f(or)f Fo(V)n(erifyingKey)664 4060 y Fx(t)n(yp)r(e)k(is)f(either)h(a)f Fo(PublicKey)i Fx(or)e(a)g Fo(Sha)n(redKey)h Fx(t)n(yp)r(e;)558 4160 y(3.)41 b(the)c Fo(CreatableObject)g Fx(t)n(yp)r(es)g(are)f(exactly)g (all)g Fo(Nonce)i Fx(t)n(yp)r(es,)f Fo(PrivateKey)h Fx(t)n(yp)r(es)f (and)664 4260 y Fo(Sha)n(redKey)28 b Fx(t)n(yp)r(es.)523 4426 y(The)i Fo(PrimitiveV)n(alue)h Fx(t)n(yp)r(es)f(are)e(understo)r (o)r(d)i(to)f(consist)g(of)h(b)r(o)r(oleans,)f(b)n(ytes)g(and)h(other) 523 4526 y(primitiv)n(e)f(v)-5 b(alues)28 b(needed.)h(The)g(t)n(yp)r(e) g Fo(RSAES-O)n(AEP-DecryptionKey-1024)i Fx(from)d(the)i(ex-)523 4625 y(ample)c(ab)r(o)n(v)n(e)g(has)g(the)h(follo)n(wing)e(kinds)i (asso)r(ciated)e(with)i(it:)g Fo(PrivateKey)r Fq(;)14 b Fo(DecryptionKey)523 4725 y Fx(and)27 b Fo(CreatableObject)p Fx(.)648 4825 y(The)g(v)n(o)r(cabulary)f(con)n(tains)h(the)h(pro)r (cedure)f(signatures)f(listed)i(in)g(the)g(follo)n(wing)e(ta-)523 4924 y(ble,)g(asso)r(ciated)f(to)h(eac)n(h)f(t)n(yp)r(e)h Fq(T)38 b Fx(of)26 b(appropriate)e(kind)i(\(with)h(signatures)e(in)h (terse,)f(but)1943 5173 y(4)p eop end %%Page: 5 5 TeXDict begin 5 4 bop 523 448 a Fx(understandable)27 b(programming)e(st)n(yle\):)679 629 y(kind)j(of)f Fq(T)394 b Fx("shared)26 b(in)n(terface")242 b("ob)5 b(ject)26 b(in)n(terface")679 829 y(an)n(y)594 b Fq(T)29 b Fo(deco)r(de)1704 841 y Fp(T)1756 829 y Fx(\()p Fq(M)9 b Fx(\))1910 799 y Fn(y)2302 829 y Fq(M)27 b Fo(enco)r(de)2632 841 y Fp(T)2684 829 y Fx(\()p Fq(T)12 b Fx(\))679 946 y Fo(T)-6 b(uple)546 b Fq(T)29 b Fo(createT)-6 b(uple)1852 965 y Fp(T)1905 946 y Fx(\()1937 889 y Fm(\000)-58 b(!)1937 946 y Fq(M)9 b Fx(\))2059 916 y Fn(y)2302 889 y Fm(\000)-59 b(!)2302 946 y Fq(M)27 b Fo(analyzeT)-6 b(uple)2822 965 y Fp(T)2874 946 y Fx(\()p Fq(T)12 b Fx(\))679 1046 y Fo(CreatableObject)208 b Fq(T)29 b Fo(create)1675 1058 y Fp(T)1727 1046 y Fx(\(\))1791 1015 y Fn(\003)679 1145 y Fo(Hash)564 b Fq(M)27 b Fo(hash)1657 1157 y Fp(T)1709 1145 y Fx(\()p Fq(M)9 b Fx(\))679 1245 y Fo(PrivateKey)1274 b Fq(T)2363 1215 y Fn(0)2403 1245 y Fo(op)2481 1257 y Fp(T)2534 1245 y Fx(\()p Fq(T)12 b Fx(\))679 1345 y Fo(EncryptionKey)1156 b Fq(M)27 b Fo(encrypt)2647 1364 y Fp(T)2699 1345 y Fx(\()p Fq(T)7 b(;)14 b(M)9 b Fx(\))2946 1315 y Fn(\003y)679 1446 y Fo(DecryptionKey)1152 b Fq(M)27 b Fo(decrypt)2647 1464 y Fp(T)2699 1446 y Fx(\()p Fq(T)7 b(;)14 b(M)9 b Fx(\))2946 1415 y Fn(y)679 1546 y Fo(SigningKey)1266 b Fq(M)27 b Fo(sign)2535 1565 y Fp(T)2588 1546 y Fx(\()p Fq(T)7 b(;)14 b(M)9 b Fx(\))2835 1516 y Fn(\003y)679 1646 y Fo(V)n(erifyingKey)1220 b Fx(Bo)r(olean)26 b Fo(verify)2794 1665 y Fp(T)2846 1646 y Fx(\()p Fq(T)7 b(;)14 b(M)t(;)g(M)9 b Fx(\))3215 1616 y Fn(y)523 1824 y Fx(where)23 b(the)i(pro)r(cedures)d(mark)n(ed)h (with)i Fm(\003)e Fx(can)h(b)r(e)g(nondeterministic,)g(and)g(those)f (mark)n(ed)523 1936 y(with)39 b Fm(y)f Fx(migh)n(t)h(fail,)f(sa)n(y)f (in)i(case)e(of)i(unexp)r(ected)g(format)e(of)i(an)f(argumen)n(t;)3141 1879 y Fm(\000)-58 b(!)3141 1936 y Fq(M)47 b Fx(is)38 b(a)523 2035 y(shorthand)27 b(for)g Fl(Seq)42 b(of)h(M)27 b Fx(of)h(AsmL.)648 2135 y(The)41 b(in)n(tended)i(in)n(terpretation)d (of)i Fo(enco)r(de)2059 2147 y Fp(T)2112 2135 y Fq(=)p Fo(deco)r(de)2376 2147 y Fp(T)2470 2135 y Fx(is)f(enco)r(ding/deco)r (ding)g(b)r(e-)523 2234 y(t)n(w)n(een)27 b(ob)5 b(jects)27 b(of)h(t)n(yp)r(e)f Fq(T)39 b Fx(and)27 b(enco)r(ded)h(messages,)e (according)f(to)j(a)f(formatting)g(stan-)523 2334 y(dard)32 b(carried)f(b)n(y)h Fq(T)12 b Fx(.)32 b(Deco)r(ding)h(migh)n(t)f(fail,) h(since)f(the)h(message)e(ma)n(y)h(not)h(b)r(e)g(a)f(v)-5 b(alid)523 2434 y(enco)r(ding)27 b(of)h(some)f Fq(T)12 b Fx(.)27 b(Th)n(us,)g(giv)n(en)g(a)g(t)n(yp)r(e)h Fq(T)39 b Fx(and)27 b(an)h(enco)r(ded)f(message)g Fq(m)c Fm(2)g Fq(M)9 b Fx(,)27 b(w)n(e)523 2533 y(either)g(ha)n(v)n(e)g Fo(enco)r(de)1172 2545 y Fp(T)1224 2533 y Fx(\()p Fo(deco)r(de)1479 2545 y Fp(T)1531 2533 y Fx(\()p Fq(m)p Fx(\)\))d(=)f Fq(m)p Fx(,)k(or)g Fo(deco)r(de)2259 2545 y Fp(T)2339 2533 y Fx(fails)h(at)f Fq(m)p Fx(.)648 2633 y(Ha)n(ving)e(the)h(same)f (enco)r(ding)h(is)g(the)g(only)g(criterion)f(of)h(ob)5 b(ject)25 b(iden)n(tit)n(y)h(used)g(in)h(the)523 2733 y(CrAM.)648 2832 y(It)39 b(w)n(ould)f(b)r(e)h(a)f(nice)g(prop)r(ert)n (y)g(of)h(enco)r(dings)e(that)i(the)g(domains)f(of)h Fo(deco)r(de)3247 2844 y Fp(T)3338 2832 y Fx(of)523 2932 y(di\013eren)n(t)24 b(t)n(yp)r(es)f(b)r(e)h(disjoin)n(t;)g(this)f(w)n (ould)g(th)n(w)n(art)g(t)n(yp)r(e-\015a)n(w)g(attac)n(ks)f(on)h(proto)r (cols,)f(and)523 3031 y(it)38 b(is)g(usually)f(ac)n(hiev)n(ed)f(b)n(y)h (t)n(yp)r(e-tagging)f(the)i(enco)r(dings.)f(F)-7 b(or)37 b(the)h(purp)r(ose)f(of)h(this)523 3131 y(pap)r(er,)27 b(w)n(e)g(do)h(not)f(mak)n(e)g(an)n(y)g(suc)n(h)g(assumptions.)648 3231 y(T)n(yp)r(es)20 b(of)i(kind)f Fo(T)-6 b(uple)21 b Fx(represen)n(t)f(di\013eren)n(t)i(metho)r(ds)f(of)g(enco)r (ding/deco)r(ding)f(of)h(mes-)523 3330 y(sage)36 b(tuples,)h(of)g (\014xed)g(or)f(b)r(ounded)i(or)e(arbitrary)f(arit)n(y)-7 b(.)36 b(Enco)r(ding)g(of)h(a)g(tuple)g(with)523 3430 y Fo(createT)-6 b(uple)894 3449 y Fp(T)966 3430 y Fx(can)18 b(fail,)i(sa)n(y)e(if)h(an)g(input)h(sequence)f(is)g(of)g(wrong)f (length.)h(Giv)n(en)g(a)g(tuple)h(ob-)523 3530 y(ject)25 b Fq(t)f Fx(of)f(t)n(yp)r(e)i(T,)f(w)n(e)f(assume)h Fo(enco)r(de)1738 3542 y Fp(T)1790 3530 y Fx(\()p Fo(createT)-6 b(uple)2193 3548 y Fp(T)2246 3530 y Fx(\()p Fo(analyzeT)g(uple)2691 3548 y Fp(T)2743 3530 y Fx(\()p Fq(t)p Fx(\)\)\))24 b(=)f Fo(enco)r(de)3235 3542 y Fp(T)3287 3530 y Fx(\()p Fq(t)p Fx(\).)523 3629 y(Notice)j(the)g(use)f(of)h Fo(enco)r(de)1379 3641 y Fp(T)1457 3629 y Fx(for)g(establishing)f(equalit)n(y)g(of)g (abstract)g(ob)5 b(jects)25 b(of)h(t)n(yp)r(e)g Fq(T)12 b Fx(.)648 3729 y(T)n(yp)r(es)28 b(of)g(kind)h Fo(CreatableObject)p Fx(,)g(those)f(of)g(nonces,)g(priv)-5 b(ate)29 b(and)f(shared)f(k)n (eys,)h(also)523 3828 y(ha)n(v)n(e)e(a)i Fo(create)977 3840 y Fp(T)1029 3828 y Fx(\(\))g(metho)r(d)h(attac)n(hed,)e(returning) f(a)i(presumably)e(fresh)i(ob)5 b(ject.)648 3928 y(An)30 b(ob)5 b(ject)29 b(of)g(t)n(yp)r(e)h Fq(T)41 b Fx(of)29 b(kind)h Fo(Hash)g Fx(carries)e(a)h(concrete)g(hashing)g(algorithm)f (used)523 4028 y(in)35 b Fo(hash)773 4040 y Fp(T)825 4028 y Fx(.)g(Di\013eren)n(t)g(t)n(yp)r(es)g(ma)n(y)f(carry)f (di\013eren)n(t)i(algorithms,)e(sa)n(y)g(t)n(yp)r(es)i Fo(SHA-1)g Fx(and)523 4127 y Fo(MD5)30 b Fx(carry)f(SHA-1)h([FIP95)o(]) h(and)f(MD5)g([Riv92)o(])h(cryptographic)d(hash)i(algorithms)f(re-)523 4227 y(sp)r(ectiv)n(ely)-7 b(.)648 4327 y(The)33 b(same)g(holds)g(for)g (ob)5 b(jects)33 b(of)g(k)n(ey{t)n(yp)r(es,)g(but)h(they)-7 b(,)34 b(in)f(addition)h(to)f(carrying)523 4426 y(an)k(algorithm,)f (also)g(carry)g(a)g(concrete)h(k)n(ey)f(to)h(b)r(e)h(used)f(in)g Fo(encrypt)2811 4445 y Fp(T)2864 4426 y Fq(;)14 b Fo(decrypt)3138 4445 y Fp(T)3190 4426 y Fq(;)g Fo(sign)3353 4445 y Fp(T)523 4526 y Fx(and)32 b Fo(verify)862 4545 y Fp(T)915 4526 y Fx(.)g(F)-7 b(or)32 b(example,)g(an)h(ob)5 b(ject)32 b(of)g(t)n(yp)r(e)h Fo(RSAES-O)n(AEP-Decrypt-1024)g Fx(carries)d(a)523 4625 y(1024)f(bit)i(long)f(RSA)h(priv)-5 b(ate)30 b(k)n(ey)-7 b(,)30 b(while)h Fo(decrypt)2143 4644 y Fk(RSAES-O)n(AEP-Decrypt-1024) 2914 4625 y Fx(is)g(exactly)f(the)523 4725 y(pro)r(cedure)d Fl(RSAES-OAEP-Decr)o(ypt)21 b Fx(from)27 b([PK)n(C02)n(].)648 4825 y(F)-7 b(or)34 b(eac)n(h)g(t)n(yp)r(e)h Fq(T)46 b Fx(of)35 b(kind)g Fo(PrivateKey)i Fx(w)n(e)d(also)g(ha)n(v)n(e)g(a)g (function)h Fo(op)2957 4837 y Fp(T)3010 4825 y Fx(,)g(returning)523 4924 y(an)27 b(ob)5 b(ject)26 b(of)h(attac)n(hed)g(t)n(yp)r(e)g Fq(T)1568 4894 y Fn(0)1590 4924 y Fx(,)g(whic)n(h)g(has)g(to)f(b)r(e)i (of)f(kind)g Fo(PublicKey)q Fx(.)g(Extending)g(the)1943 5173 y(5)p eop end %%Page: 6 6 TeXDict begin 6 5 bop 523 448 a Fx(previous)38 b(example,)g(the)h(t)n (yp)r(e)g Fo(RSAES-O)n(AEP-EncryptionKey-1024)h Fx(of)e(kinds)h Fo(PublicKey)523 548 y Fx(and)27 b Fo(EncryptionKey)r Fx(,)h(is)f(the)h(co)r(domain)f(of)g Fo(op)1979 560 y Fk(RSAES-O)n(AEP-DecryptionKey-1024)2896 548 y Fx(.)648 649 y(W)-7 b(e)38 b(also)e(assume)h(that)h(deco)r(dings)f(of)h(the)g (co)r(domain)f(of)g Fo(encrypt)2840 668 y Fp(T)2930 649 y Fx(b)r(elong)h(to)f(an)523 749 y Fo(Encryption)42 b Fx(t)n(yp)r(e,)g(and)g(that)g(deco)r(dings)g(of)f(the)i(co)r(domain)e (of)h(a)f Fo(sign)2874 768 y Fp(T)2968 749 y Fx(b)r(elong)h(to)f(a)523 849 y Fo(Signature)27 b Fx(t)n(yp)r(e.)648 950 y(This)f(is)h(all)f (that)h(w)n(e)g(ha)n(v)n(e)e(to)i(assume)f(of)g(k)n(ey)g(and)h(hash)f (t)n(yp)r(es)h(for)f(the)h(purp)r(oses)f(of)523 1050 y(this)i(pap)r(er.)f(It)h(is)g(our)e(understanding)h(that)h(also)575 1223 y Ft({)41 b Fx(either)28 b Fo(encrypt)1137 1241 y Fp(T)1185 1225 y Fj(0)1211 1223 y Fx(\()p Fo(op)1322 1235 y Fp(T)1374 1223 y Fx(\()p Fq(K)6 b Fx(\))p Fq(;)14 b(m)p Fx(\)\))28 b(fails,)575 1324 y Ft({)41 b Fx(or)27 b Fo(decrypt)1003 1343 y Fp(T)1055 1324 y Fx(\()p Fq(K)q(;)14 b Fo(encrypt)1433 1343 y Fp(T)1481 1326 y Fj(0)1508 1324 y Fx(\()p Fo(op)1618 1336 y Fp(T)1671 1324 y Fx(\()p Fq(K)6 b Fx(\))p Fq(;)14 b(m)p Fx(\)\))23 b(=)g Fq(m)p Fx(,)523 1496 y(and)34 b(lik)n(ewise)f(for)g Fo(verify)1308 1514 y Fp(T)1361 1496 y Fq(=)p Fo(sign)1528 1514 y Fp(T)1614 1496 y Fx(and)h(for)f(shared)g(k)n(eys,)g(but)i(w)n(e)e(do)h(not)g(use) f(suc)n(h)h(as-)523 1595 y(sumptions)28 b(in)f(this)h(pap)r(er.)648 1697 y(It)35 b(is)f(also)g(common)g(to)h(assume)f(that)g(created)g(ob)5 b(jects)35 b(are)e("fresh",)h(encryptions)523 1796 y(are)g("hard)h(to)g (break",)f(signatures)g(are)g("hard)h(to)g(forge",)f(and)h(hashes)f (are)h("hard)f(to)523 1896 y(in)n(v)n(ert".)20 b(But)h(w)n(e)f(cannot)g (ev)n(en)h Fs(say)28 b Fx(on)21 b(this)g(lev)n(el)f(of)h(abstraction)e (what)i(exactly)f("fresh",)523 1995 y("hard",)33 b("break",)g("forge")g (or)h("in)n(v)n(ert")f(mean,)i(since)f(CrAM)h(instances)f(at)h (di\013eren)n(t)523 2095 y(lev)n(els)22 b(of)h(abstraction,)e(and)h (di\013eren)n(t)h(instances)f(at)h(the)g(same)f(lev)n(el)g(of)g (abstraction,)g(will)523 2195 y(in)32 b(general)e(in)n(terprete)h (these)h(notions)f(di\013eren)n(tly)-7 b(.)32 b(In)g([RRS03)o(])g(w)n (e)g(pro)n(vide)e(one)h(suc)n(h)523 2294 y(in)n(terpretation)k(in)i (the)f(con)n(text)g(of)h(abstract)e(encryption,)h(where)f(i.e.)i ("hard")d(means)523 2394 y(imp)r(ossible)29 b(and)g("in)n(v)n(ert")e (means)i(in)n(v)n(ert.)f(In)h(more)g(concrete)f(instances)h(of)g(the)g (CrAM)523 2494 y(these)g(notions)g(will)g(obtain)g(di\013eren)n(t)g (probabilistic)f(p)r(olytime)h(in)n(terpretations.)f(It)h(is)g(a)523 2593 y(primary)k(purp)r(ose)i(of)f(the)h(CrAM)g(to)f(facilitate)h (relating)f(proto)r(col)f(executions)h(under)523 2693 y(di\013eren)n(t)28 b(in)n(terpretations.)523 2951 y Ft(Notation)j(and)i(Mapping)e(to)h(OOP)523 3126 y Fx(In)37 b(the)g(sequel)f(w)n(e)h(use)f(an)h(OOP)e(notation)h(for)h(the)g(ab)r (o)n(v)n(e)e(v)n(o)r(cabulary)-7 b(,)35 b(in)i(order)e(to)523 3225 y(minimize)26 b(the)g(distance)f(b)r(et)n(w)n(een)h(notation)f (and)g(the)h(AsmL)g(mo)r(del.)g(In)f(the)h(signatures)523 3325 y(of)e(the)f(third)h(column)g(of)f(the)h(ab)r(o)n(v)n(e)e(table,)i (the)g("ob)5 b(ject)22 b(in)n(terface",)h(the)h(\014rst)f(argumen)n(t) 523 3425 y(is)31 b(alw)n(a)n(ys)f(of)i(t)n(yp)r(e)f Fq(T)12 b Fx(.)31 b(It)h(is)f(common)g(in)h(OOP)e(to)i(suppress)e(suc)n(h)h(an) h(argumen)n(t,)e(and)523 3524 y(see)39 b(it)h(as)f(the)h("metho)r(d)f (sub)5 b(ject")39 b(or)g("message)e(receiv)n(er".)h(The)h(t)n(yp)r (e{subscript)g(is)523 3624 y(also)32 b(sup)r(er\015uous,)h(since)f(the) i(t)n(yp)r(e)f(is)g(implicit)h(in)f(the)h(sub)5 b(ject.)33 b(Th)n(us)g(w)n(e)g(shall)f(write)523 3724 y Fq(x:)p Fo(encrypt)q Fx(\()p Fq(m)p 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Fw(\))21 b Fh(&)g Fi(\033)2899 2531 y Fe(00)2939 2562 y Fi(;)13 b(\032)3013 2531 y Fe(00)p 571 2594 2534 4 v 1369 2662 a Fi(\033)n(;)g(\032;)g(e)21 b Fw(:)g(E)q(\()p Fi(k)r(p;)12 b(p)p Fw(\))p Fi(;)h(m)21 b Fh(&)g Fi(\033)2152 2640 y Fe(00)2192 2662 y Fi(;)13 b(\032)2266 2640 y Fe(00)3191 2611 y Fi(e)30 b(=)-47 b Fh(2)22 b Fi(\033)523 2935 y(v)560 2944 y Ff(k)598 2935 y Fi(;)14 b(\033)n(;)f(\027)26 b Fh(&)850 2943 y Ff(K)930 2935 y Fi(\033)s Fw(\()p Fi(v)1044 2944 y Ff(k)1082 2935 y Fw(\))p Fi(;)13 b(\033)854 b(v)2081 2944 y Ff(k)2140 2935 y Fh(2)22 b Fi(\033)n(;)13 b(v)2326 2944 y Ff(k)2386 2935 y Fw(=)21 b Fi(K)q(;)13 b(k)r(;)h(sh)523 3051 y(k)24 b Fw(:)d(op\()p Fi(K)5 b Fw(\))p Fi(;)13 b(\033)n(;)h(\027)26 b Fh(&)1092 3059 y Ff(K)1172 3051 y Fi(o)1209 3060 y Ff(k)1247 3051 y Fi(;)13 b(\033)20 b Fw(+)d Fh(f)p Fi(k)24 b Fh(7!)d Fi(o)1659 3060 y Ff(k)1697 3051 y Fh(g)309 b Fi(k)32 b(=)-47 b Fh(2)22 b Fi(\033)n(;)39 b(K)26 b Fh(2)c Fi(\033)n(;)13 b(o)2559 3060 y Ff(k)2619 3051 y Fw(=)21 b Fi(\033)s Fw(\()p Fi(K)5 b Fw(\))p Fi(:)p Fo(op)p Fw(\(\))523 3167 y Fi(k)24 b Fw(:)d(k)n(eyOf)o(\()p Fi(a)p Fw(\))p Fi(;)13 b(\033)n(;)g(\027)27 b Fh(&)1178 3175 y Ff(K)1257 3167 y Fi(o)1294 3176 y Ff(k)1333 3167 y Fi(;)13 b(\033)19 b Fw(+)e Fh(f)p Fi(k)24 b Fh(7!)d Fi(o)1744 3176 y Ff(k)1783 3167 y Fh(g)223 b Fi(k)32 b(=)-47 b Fh(2)22 b Fi(\033)n(;)39 b(a)21 b Fh(2)g Fi(\033)n(;)14 b(o)2530 3176 y Ff(k)2589 3167 y Fw(=)21 b Fi(k)r(:)p Fo(deco)r(de)q Fw(\()p Fi(\027)5 b Fw(\()p Fi(\033)s Fw(\()p Fi(a)p Fw(\))p Fi(:)p Fo(enco)r(de)o Fw(\(\)\)\))1263 3420 y Ft(Fig.)15 b(2.)27 b Fx(Matc)n(hing)g(patterns)g(to)h(messages) 558 3717 y(1.)41 b(the)e(v)-5 b(ariables)38 b(are)g(no)n(w)g(t)n(yp)r (ed)h(according)f(to)g(the)i(v)n(o)r(cabulary)-7 b(,)37 b(denoted)h(in)i(the)664 3816 y(syn)n(tax)27 b(b)n(y)g(corresp)r (onding)f(meta)n(v)-5 b(ariables)26 b(of)h(appropriate)f(kind;)558 3920 y(2.)41 b(the)21 b(encryption)e(v)-5 b(ariable)20 b(of)g([RRS03)o(])h(has)e(mo)n(v)n(ed)h(up)g(fron)n(t,)g(and)g (obtained)g(another)664 4020 y(role,)h(additional)h(to)g(that)g(of)g (recording)e(an)i(encryption)g(seen/created:)e(its)i(t)n(yp)r(e)h(no)n (w)664 4119 y(determines)38 b(ho)n(w)f(to)h(deco)r(de)g(an)g (encryption)f(from)h(an)g(external)f(to)h(an)g(in)n(ternal)664 4219 y(represen)n(tation,)26 b(from)h(an)h Fq(M)36 b Fx(to)27 b(an)h Fq(O)r Fx(;)558 4323 y(3.)41 b(eac)n(h)24 b(comp)r(ound)g(pattern)h(has)f(b)r(een)h(decorated)e(with)i(an)f (appropriate)f(v)-5 b(ariable)24 b(for)664 4422 y(the)k(same)f(purp)r (ose;)558 4526 y(4.)41 b(patterns)22 b Fq(k)j Fx(:)f(k)n(eyOf)o(\()p Fq(a)p Fx(\))p Fq(;)14 b(h)23 b Fx(:)g(H\()p Fq(r)r Fx(\))p Fq(;)14 b(s)25 b Fx(:)e(S\()p Fq(k)s(ey)s(P)12 b(at;)i(r)r Fx(\))22 b(ha)n(v)n(e)e(b)r(een)j(added)e(to)h(deal)f(with)664 4626 y(agen)n(t)27 b(names,)g(hashes)g(and)g(signatures)g(resp)r(ectiv) n(ely)-7 b(.)648 4825 y(P)n(atterns)32 b(can)i(no)n(w)g(matc)n(h)g (messages)f(from)h Fq(M)9 b Fx(,)34 b(and)g(come)g(with)g(a)g(storage)f (split)523 4924 y(in)n(to)27 b(the)h(follo)n(wing)f(stores:)1943 5173 y(8)p eop end %%Page: 9 9 TeXDict begin 9 8 bop 575 448 a Ft({)41 b Fs(obje)l(ct)31 b(stor)l(e)j Fq(\033)s Fx(,)28 b(a)f(\014nite)h(map)g(of)f(ob)5 b(ject)27 b(v)-5 b(ariables)27 b(\(v)-5 b(ariable{ob)5 b(jects\))26 b(to)h Fq(O)r Fx(;)575 545 y Ft({)41 b Fs(message)31 b(stor)l(e)i Fq(\032)p Fx(,)28 b(a)f(\014nite)i(map)e(of)h(ra)n(w)e(v) -5 b(ariables)26 b(to)i Fq(M)9 b Fx(;)575 643 y Ft({)41 b Fs(c)l(erti\014c)l(ate)h(stor)l(e)48 b Fq(\027)5 b Fx(,)41 b(a)g(\014nite)h(map)f(of)g(enco)r(dings)f(of)h(agen)n(t)f (names)h(\(ob)5 b(jects)41 b(of)664 742 y Fo(AgentName)28 b Fx(t)n(yp)r(es\))g(to)g(enco)r(dings)f(of)g(public)h(k)n(eys)f(\(ob)5 b(jects)27 b(of)h Fo(PublicKey)h Fx(t)n(yp)r(es\).)523 899 y(P)n(attern)37 b(matc)n(hing)g(is)h(de\014ned)g(with)h(a)e (relation)g Fq(\033)n(;)14 b(\032;)g(\027)q(;)g(p;)g(m)40 b Fm(&)h Fq(\033)2800 868 y Fn(0)2824 899 y Fq(;)14 b(\032)2904 868 y Fn(0)2927 899 y Fx(,)38 b(where)f Fq(m)h Fx(is)523 998 y(a)f(message)f(and)h Fq(p)g Fx(is)g(a)g(pattern.)h(When)f Fq(\027)43 b Fx(is)37 b(understo)r(o)r(d)g(from)g(con)n(text,)g(w)n(e)g (write)523 1098 y Fq(\033)n(;)14 b(\032;)g(p;)g(m)38 b Fm(&)g Fq(\033)1046 1068 y Fn(0)1069 1098 y Fq(;)14 b(\032)1149 1068 y Fn(0)1172 1098 y Fx(.)37 b(The)f(relation)g(is)g (de\014ned)h(b)n(y)f(deduction)g(rules,)g(v)n(ery)g(similar)f(to)523 1197 y(those)27 b(of)h([RRS03)o(],)g(with)g(the)g(follo)n(wing)f(mo)r (di\014cations:)558 1351 y(1.)41 b(new)28 b(rules)f(ha)n(v)n(e)f(b)r (een)i(added)g(for)f(the)h(new)f(constructs;)558 1448 y(2.)41 b Fo(enco)r(de)23 b Fx(and)f Fo(deco)r(de)g Fx(m)n(ust)g (mediate)g(b)r(et)n(w)n(een)h(in)n(ternal)e(and)h(external)f(forms)h (of)g(cryp-)664 1548 y(tographic)k(ob)5 b(jects;)558 1645 y(3.)41 b(equalit)n(y)27 b(of)h(ob)5 b(jects)27 b(is)g(determined)h(only)f(b)n(y)h(their)f(external)g(represen)n (tations;)558 1742 y(4.)41 b(rules)f(are)f(adapted)g(to)h(rely)g(only)f (on)h(the)g(functionalit)n(y)g(pro)n(vided)f(b)n(y)h(t)n(yp)r(es)g(of) 664 1842 y(cryptographic)26 b(ob)5 b(jects)27 b(and)g(v)-5 b(ariables)27 b(used;)g(and)558 1939 y(5.)41 b(the)19 b(nondeterministic)f(rule)g(for)g(matc)n(hing)g(tuples)h(has)f(b)r(een) g(replaced)g(b)n(y)g(its)g(leftmost{)664 2039 y(deterministic)23 b(instance)f(for)h(simplicit)n(y)-7 b(,)22 b(since)h(this)g(do)r(esn't) g(a\013ect)f(the)i(univ)n(ersalit)n(y)664 2138 y(results)j(of)h([RRS03) o(].)523 2295 y(The)d(rules)f(are)g(giv)n(en)g(in)h(\014gure)f(2,)h (together)f(with)h(side)g(conditions)f(on)h(their)g(applicabil-)523 2394 y(it)n(y)-7 b(.)648 2494 y(Creating)25 b(messages)g(b)n(y)h (patterns)g(is)h(de\014ned)f(b)n(y)h(deduction)f(rules)g(as)g(w)n(ell,) h(pro)n(ving)523 2594 y(statemen)n(ts)g(of)h(form)1664 2693 y Fq(p;)14 b(\033)n(;)g(\032;)g(\027)28 b Fm(\045)c Fq(m;)14 b(\033)2241 2659 y Fn(0)523 2835 y Fx(When)23 b Fq(\032;)14 b(\027)27 b Fx(are)21 b(understo)r(o)r(d)g(from)h(con)n (text,)g(w)n(e)f(write)h Fq(p;)14 b(\033)n(;)g(\032)23 b Fm(\045)g Fq(m;)14 b(\033)2789 2805 y Fn(0)2835 2835 y Fx(or)21 b Fq(p;)14 b(\033)n(;)g Fm(\045)23 b Fq(m;)14 b(\033)3358 2805 y Fn(0)3382 2835 y Fx(.)648 2935 y(The)38 b(rules,)g(giv)n(en)g(in)h(\014gure)f(3,)g(are)g(adapted)g(from)g(the)h (corresp)r(onding)e(rules)h(of)523 3034 y([RRS03)o(])28 b(in)g(v)n(ery)e(m)n(uc)n(h)i(the)g(same)f(w)n(a)n(y)f(as)h(the)h(matc) n(hing)f(rules)g(ab)r(o)n(v)n(e.)523 3274 y Ft(2.2)95 b(Recapturing)31 b(the)h(Relation)f(to)g(Abstract)j(Encryption)523 3430 y Fx(In)g(order)e(to)h(recapture)g(the)h(univ)n(ersalit)n(y)e (prop)r(erties)g(that)i(the)g(patterns)f(of)g([RRS03])523 3530 y(ha)n(v)n(e)38 b(wrt)h(the)h(mo)r(del)g(of)f(abstract)f (encryption)h(explained)g(there,)g(w)n(e)g(only)g(ha)n(v)n(e)f(to)523 3629 y(describ)r(e)33 b(the)h(t)n(yp)r(es)f(used.)g(T)-7 b(o)33 b(k)n(eep)g(things)g(simple,)h(w)n(e)f(shall)g(not)g(extend)g (the)h(t)n(yp)r(es)523 3729 y(of)27 b(abstract)f(messages)f(of)h ([RRS03])h(here)f(\(whic)n(h)h(is)g(straigh)n(tforw)n(ard)c(to)k(do\);) g(w)n(e)f(shall,)523 3828 y(for)k(sak)n(e)f(of)i(this)g(argumen)n(t,)e (suppress)h(the)h(new)f(constructs)g(\(signatures,)f(hashes)h(and)523 3928 y(agen)n(t)d(names\))g(from)g(patterns)h(instead.)648 4028 y(Both)34 b(univ)n(erses)f Fq(O)k Fx(and)d Fq(M)43 b Fx(will)35 b(coincide)e(with)i(the)g(t)n(yp)r(e)g Fl(Message)c Fx(of)j([RRS03].)523 4127 y(The)39 b(t)n(yp)r(es)g(of)g(kinds)g Fo(PublicKey)q Fx(,)h Fo(PrivateKey)q Fx(,)g Fo(Sha)n(redKey)p Fx(,)f Fo(Nonce)q Fx(,)g Fo(Encryption)p Fx(,)g Fo(Byte)h Fx(or)523 4227 y Fo(Bo)r(olean)q Fx(,)h Fo(T)-6 b(uple)41 b Fx(\(w)n(e)f(do)h(not)g(need)g(an)n(y)f(others\))g(will)h(b)r(e)g Fl(PublicKey)l Fx(,)g Fl(PrivateKey)l Fx(,)523 4327 y Fl(SharedKey,)e(Encryption,)h(Nonce,)h(Byte)28 b Fx(or)h Fl(Boolean)m Fx(,)i Fl(MessageSeq)26 b Fx(resp)r(ectiv)n(ely)-7 b(.)523 4426 y Fl(PrivateKey)17 b Fx(and)k Fl(SharedKey)c Fx(t)n(yp)r(es)k(will)g(b)r(e)h(of)f Fo(DecryptionKey)h Fx(kind,)f(while)h Fl(PublicKey)523 4526 y Fx(and)27 b Fl(SharedKey)d Fx(t)n(yp)r(es)k(will)g(b)r(e)g(of)f Fo(EncryptionKey)i Fx(kind.)648 4625 y(In)n(terpretation)18 b(of)i Fo(enco)r(de)1485 4637 y Fp(T)1557 4625 y Fx(will)g(b)r(e)h (iden)n(tit)n(y)f(of)g Fq(T)12 b Fx(,)19 b(while)h Fo(deco)r(de)2733 4637 y Fp(T)2785 4625 y Fx(\()p Fq(m)p Fx(\))g(will)h(b)r(e)f(either) 523 4725 y Fq(m)30 b Fx(for)f Fq(m)h Fx(of)g(t)n(yp)r(e)g Fq(T)41 b Fx(\(since)30 b Fq(M)35 b Fx(=)27 b Fq(O)32 b Fx(no)n(w\),)e(or)f(failing)h(otherwise.)f(Th)n(us)g Fo(deco)r(de)3194 4737 y Fp(T)3276 4725 y Fx(will)523 4825 y(act)23 b(as)g(a)g(t)n(yp)r(e{c)n(hec)n(k)n(er.)e(In)j(case)e(of) i(t)n(yp)r(e)f Fl(MessageSeq)p Fx(,)c Fo(createT)-6 b(uple)24 b Fx(is)f(the)h Fl(MessageSeq)523 4924 y Fx(constructor)i(while)i Fo(analyzeT)-6 b(uple)28 b Fx(extracts)f(the)h(sequence)f(from)g(a)g Fl(MessageSeq)d Fx(ob)5 b(ject.)1943 5173 y(9)p eop end %%Page: 10 10 TeXDict begin 10 9 bop 575 527 a Fi(v)s(;)13 b(\033)24 b Fh(\045)d Fi(\033)s Fw(\()p Fi(v)s Fw(\))p Fi(:)p Fo(enco)r(de)p Fw(\(\))p Fi(;)13 b(\033)575 643 y(cr)n(;)g(\033)24 b Fh(\045)d Fi(o:)p Fo(enco)r(de)q Fw(\(\))p Fi(;)12 b(\033)20 b Fw(+)d Fh(f)p Fi(cr)24 b Fh(7!)d Fi(o)p Fh(g)709 b Fi(cr)32 b(=)-47 b Fh(2)22 b Fi(\033)n(;)13 b(o)22 b Fw(=)f Fi(cr)n(:)p Fo(create)p Fw(\(\))575 760 y Fi(r)n(;)13 b(\033)23 b Fh(\045)f Fi(\032)p Fw(\()p Fi(r)r Fw(\))p Fi(;)12 b(\033)575 876 y(c)21 b Fw(:)h Fi(C)q(;)13 b(\033)24 b Fh(\045)d Fi(C)q(:)p Fo(enco)r(de)q Fw(\(\))p Fi(;)13 b(\033)19 b Fw(+)e Fh(f)p Fi(c)22 b Fh(7!)f Fi(C)5 b Fh(g)617 b Fi(c)30 b(=)-46 b Fh(2)21 b Fi(\033)575 992 y(k)i Fw(:)f(op\()p Fi(K)5 b Fw(\))p Fi(;)13 b(\033)24 b Fh(\045)d Fi(o)1129 1001 y Ff(k)1168 992 y Fi(:)p Fo(enco)r(de)p Fw(\(\))p Fi(;)13 b(\033)20 b Fw(+)d Fh(f)p Fi(k)23 b Fh(7!)f Fi(o)1883 1001 y Ff(k)1921 992 y Fh(g)409 b Fi(k)32 b(=)-46 b Fh(2)21 b Fi(\033)n(;)14 b(o)2618 1001 y Ff(k)2677 992 y Fw(=)21 b Fi(\033)s Fw(\()p Fi(K)5 b Fw(\))p Fi(:)p Fo(op)p Fw(\(\))585 1112 y Fi(k)23 b Fw(:)f(op\()p Fi(K)5 b Fw(\))p Fi(;)13 b(\033)20 b Fw(+)d Fh(f)p Fi(K)27 b Fh(7!)21 b Fi(K)q(:)p Fo(create)q Fw(\(\))p Fh(g)g(\045)g Fi(m;)13 b(\033)1952 1080 y Fe(0)p 585 1143 1390 4 v 882 1211 a Fi(k)24 b Fw(:)d(op\()p Fi(\033)s Fw(\()p Fi(K)5 b Fw(\)\))p Fi(;)13 b(\033)24 b Fh(\045)d Fi(m;)13 b(\033)1655 1190 y Fe(0)2368 1161 y Fi(k)32 b(=)-46 b Fh(2)21 b Fi(\033)n(;)39 b(K)c(=)-46 b Fh(2)21 b Fi(\033)575 1327 y(k)i Fw(:)f(k)n(eyOf)o(\()p Fi(a)p Fw(\))p Fi(;)13 b(\033)24 b Fh(\045)d Fi(m)1246 1336 y Ff(k)1284 1327 y Fi(;)13 b(\033)20 b Fw(+)c Fh(f)p Fi(k)24 b Fh(7!)d Fi(k)r(:)p Fo(deco)r(de)q Fw(\()p Fi(m)2042 1336 y Ff(k)2080 1327 y Fw(\))p Fh(g)220 b Fi(k)32 b(=)-46 b Fh(2)21 b Fi(\033)n(;)14 b(m)2649 1336 y Ff(k)2708 1327 y Fw(=)21 b Fi(\027)5 b Fw(\()p Fi(\033)s Fw(\()p Fi(a)p Fw(\))p Fi(:)p Fo(enco)r(de)o Fw(\(\)\))854 1447 y Fi(k)r(p;)13 b(\033)n(;)h(\027)26 b Fh(\045)1187 1455 y Ff(K)1266 1447 y Fi(o)1303 1456 y Ff(k)1342 1447 y Fi(;)13 b(\033)1423 1415 y Fe(0)1522 1447 y Fi(p;)f(\033)1641 1415 y Fe(0)1685 1447 y Fh(\045)21 b Fi(m;)12 b(\033)1931 1415 y Fe(00)p 585 1478 1657 4 v 636 1546 a Fi(e)21 b Fw(:)h(E\()p Fi(k)r(p;)13 b(p)p Fw(\))p Fi(;)f(\033)24 b Fh(\045)d Fi(m)1269 1554 y Ff(e)1302 1546 y Fi(;)14 b(\033)1384 1525 y Fe(00)1441 1546 y Fw(+)j Fh(f)p Fi(e)k Fh(7!)g Fi(e:)p Fo(deco)r(de)q Fw(\()p Fi(m)2089 1554 y Ff(e)2122 1546 y Fw(\))p Fh(g)2368 1495 y Fi(e)30 b(=)-47 b Fh(2)22 b Fi(\033)n(;)13 b(m)2642 1503 y Ff(e)2697 1495 y Fw(=)21 b Fi(o)2815 1504 y Ff(k)2853 1495 y Fi(:)p Fo(encrypt)p Fw(\()p Fi(m)p Fw(\))1103 1657 y Fi(k)r(p;)13 b(\033)n(;)g(\027)26 b Fh(\045)1435 1665 y Ff(K)1515 1657 y Fi(o)1552 1666 y Ff(k)1590 1657 y Fi(;)13 b(\033)1671 1626 y Fe(0)p 585 1689 1627 4 v 636 1756 a Fi(s)21 b Fw(:)h(S)o(\()p Fi(k)r(p;)13 b(r)r Fw(\))p Fi(;)g(\033)24 b Fh(\045)d Fi(m)1258 1764 y Ff(s)1291 1756 y Fi(;)13 b(\033)1372 1735 y Fe(0)1411 1756 y Fw(+)k Fh(f)p Fi(s)k Fh(7!)h Fi(s:)p Fo(deco)r(de)p Fw(\()p Fi(m)2059 1764 y Ff(s)2092 1756 y Fw(\))p Fh(g)2368 1706 y Fi(s)30 b(=)-47 b Fh(2)22 b Fi(\033)n(;)13 b(m)2642 1714 y Ff(s)2696 1706 y Fw(=)21 b Fi(o)2814 1715 y Ff(k)2853 1706 y Fi(:)p Fo(sign)q Fw(\()p Fi(\032)p Fw(\()p Fi(r)r Fw(\)\))575 1872 y Fi(h)g Fw(:)h(H\()p Fi(r)r Fw(\))p Fi(;)12 b(\033)24 b Fh(\045)d Fi(m)1105 1881 y Ff(h)1145 1872 y Fi(;)14 b(\033)19 b Fw(+)e Fh(f)p Fi(h)22 b Fh(7!)f Fi(h:)p Fo(deco)r(de)q Fw(\()p Fi(m)1908 1881 y Ff(h)1948 1872 y Fw(\))p Fh(g)352 b Fi(h)30 b(=)-46 b Fh(2)21 b Fi(\033)n(;)14 b(m)2651 1881 y Ff(h)2712 1872 y Fw(=)21 b Fi(h:)p Fo(hash)p Fw(\()p Fi(\032)p Fw(\()p Fi(r)r Fw(\)\))991 1985 y Fi(:)13 b(:)g(:)39 b(p)1158 1993 y Ff(i)1184 1985 y Fi(;)13 b(\033)1262 1993 y Ff(i)p Fe(\000)p Fg(1)1388 1985 y Fh(\045)21 b Fi(m)1554 1993 y Ff(i)1580 1985 y Fi(;)13 b(\033)1658 1993 y Ff(i)1723 1985 y Fi(:)g(:)g(:)p 585 2016 1634 4 v 636 2084 a(t)21 b Fw(:)h([)p Fi(p)788 2092 y Fg(1)822 2084 y Fi(;)13 b(:)h(:)f(:)g(;)g(p)1032 2092 y Ff(n)1074 2084 y Fw(])p Fi(;)g(\033)24 b Fh(\045)d Fi(o)1332 2092 y Ff(t)1361 2084 y Fi(:)p Fo(enco)r(de)p Fw(\(\))p Fi(;)13 b(\033)1742 2092 y Ff(n)1801 2084 y Fw(+)k Fh(f)p Fi(t)22 b Fh(7!)f Fi(o)2101 2092 y Ff(t)2129 2084 y Fh(g)2368 2033 y Fi(t)30 b(=)-47 b Fh(2)22 b Fi(\033)n(;)13 b(\033)2610 2041 y Fg(0)2666 2033 y Fw(=)21 b Fi(\033)n(;)13 b(\032)2863 2041 y Fg(0)2919 2033 y Fw(=)21 b Fi(\032;)2368 2124 y(o)2405 2132 y Ff(t)2454 2124 y Fw(=)h Fi(t:)p Fo(createT)-6 b(uple)p Fw(\()2986 2092 y Fh(\000)-60 b(!)2991 2124 y Fi(m)s Fw(\))636 2244 y Fi(p)675 2252 y Fg(1)709 2244 y Fi(;)13 b(\033)n(;)h Fh(\045)21 b Fi(m)986 2213 y Fe(0)1008 2244 y Fi(;)13 b(\033)1089 2213 y Fe(0)1111 2244 y Fi(;)64 b(p)1235 2252 y Fg(2)1270 2244 y Fi(;)13 b(\033)1351 2213 y Fe(0)1373 2244 y Fi(;)g(\032)j Fw(+)h Fh(f)p Fi(r)24 b Fh(7!)d Fi(m)1803 2213 y Fe(0)1825 2244 y Fh(g)h(\045)f Fi(m)2051 2213 y Fe(00)2091 2244 y Fi(;)13 b(\033)2172 2213 y Fe(00)p 585 2276 1679 4 v 949 2343 a Fw(let)26 b Fi(r)d Fw(=)e Fi(p)1238 2351 y Fg(1)1298 2343 y Fw(in)26 b Fi(p)1427 2351 y Fg(2)1461 2343 y Fi(;)13 b(\033)n(;)g Fh(\045)22 b Fi(m)1738 2322 y Fe(00)1778 2343 y Fi(;)13 b(\033)1859 2322 y Fe(00)2368 2293 y Fi(r)32 b(=)-47 b Fh(2)22 b Fi(\032)608 2617 y(v)645 2626 y Ff(k)684 2617 y Fi(;)13 b(\033)n(;)g(\027)26 b Fh(\045)935 2625 y Ff(K)1015 2617 y Fi(\033)s Fw(\()p Fi(v)1129 2626 y Ff(k)1167 2617 y Fw(\))p Fi(;)13 b(\033)775 b(v)2087 2626 y Ff(k)2147 2617 y Fw(=)21 b Fi(K)q(;)13 b(k)r(;)h(sh)608 2733 y(v)645 2742 y Ff(k)684 2733 y Fi(;)f(\033)n(;)g(\027)26 b Fh(\045)935 2741 y Ff(K)1015 2733 y Fi(o;)13 b(\033)20 b Fw(+)d Fh(f)p Fi(v)1302 2742 y Ff(k)1362 2733 y Fh(7!)k Fi(o)p Fh(g)527 b Fi(o)21 b Fw(=)h Fi(v)2239 2742 y Ff(k)2277 2733 y Fi(:)p Fo(create)q Fw(\(\))p Fi(;)12 b(v)2622 2742 y Ff(k)2682 2733 y Fw(=)21 b Fi(K)q(;)13 b(sh)988 2853 y(K)q(;)h(\033)n(;)f(\027)26 b Fh(\045)1306 2861 y Ff(K)1386 2853 y Fi(o)1423 2861 y Ff(K)1482 2853 y Fi(;)13 b(\033)1563 2821 y Fe(0)p 618 2884 1338 4 v 669 2952 a Fi(k)24 b Fw(:)e(op\()p Fi(K)5 b Fw(\))p Fi(;)13 b(\033)n(;)g(\027)26 b Fh(\045)1238 2960 y Ff(K)1318 2952 y Fi(o)1355 2961 y Ff(k)1393 2952 y Fi(;)13 b(\033)1474 2930 y Fe(0)1514 2952 y Fw(+)j Fh(f)p Fi(k)24 b Fh(7!)d Fi(o)1827 2961 y Ff(k)1866 2952 y Fh(g)2062 2901 y Fi(k)32 b(=)-47 b Fh(2)22 b Fi(\033)n(;)13 b(o)2311 2910 y Ff(k)2371 2901 y Fw(=)21 b Fi(o)2489 2909 y Ff(K)2548 2901 y Fi(:)p Fo(op)p Fw(\(\))608 3068 y Fi(k)j Fw(:)d(k)n(eyOf\()p Fi(a)p Fw(\))p Fi(;)12 b(\033)n(;)i(\027)26 b Fh(\045)1263 3076 y Ff(K)1342 3068 y Fi(o)1379 3077 y Ff(k)1418 3068 y Fi(;)13 b(\033)20 b Fw(+)c Fh(f)p Fi(k)24 b Fh(7!)d Fi(o)1829 3077 y Ff(k)1868 3068 y Fh(g)156 b Fi(k)32 b(=)-47 b Fh(2)22 b Fi(\033)n(;)13 b(o)2311 3077 y Ff(k)2371 3068 y Fw(=)21 b Fi(\027)5 b Fw(\()p Fi(\033)s Fw(\()p Fi(a)p Fw(\))p Fi(:)p Fo(enco)r(de)o Fw(\(\)\))p Fi(:)p Fo(deco)r(de)p Fw(\(\))1171 3321 y Ft(Fig.)14 b(3.)27 b Fx(Creating)g(messages)f(through)h(patterns)648 3602 y(The)32 b Fo(create)h Fx(metho)r(ds,)g(where)f(they)h(are)f(needed)g (\(in)h(cases)f(of)g(t)n(yp)r(es)h Fl(PrivateKey)l Fx(,)523 3702 y Fl(SharedKey)24 b Fx(and)j Fl(Nonce)n Fx(\))h(are)f(implemen)n (ted)h(b)n(y)f(appropriate)f(default)i(constructors.)648 3801 y(Under)h(these)g(pro)n(visos,)e(as)h(the)h(reader)f(can)h(easily) f(c)n(hec)n(k,)g(the)i(presen)n(t)e(rules)g(w)n(ork)523 3901 y(exactly)38 b(lik)n(e)h(the)h(rules)e(of)h([RRS03],)g(if)g(w)n(e) g(disregard)e(the)j(nondeterminism)f(of)g(the)523 4001 y(tuple{matc)n(hing)27 b(rule)g(there,)h(whic)n(h)f(is)h(not)f(needed)h (for)f(the)h(results)f(of)h([RRS03)o(].)523 4259 y Fu(3)112 b(The)38 b(Cryptographic)g(Abstract)f(Mac)m(hine)523 4452 y Fx(The)25 b(Cryptographic)d(Abstract)i(Mac)n(hine)g(is)h(a)f (simple)g(mac)n(hine)h(with)g(a)f(program,)e(stor-)523 4551 y(age,)29 b(accum)n(ulator,)g(input)i(and)f(output.)h(Its)f (storage)e(is)j(decomp)r(osed)e(in)n(to)h(stores)f Fq(\033)s Fx(,)i Fq(\032)523 4651 y Fx(and)c Fq(\027)5 b Fx(.)648 4750 y(More)26 b(formally)-7 b(,)27 b(a)g(Cryptographic)f(Abstract)h (Mac)n(hine)g(is)h(a)f(tuple)1334 4924 y Fm(M)c Fx(=)g(\()p Fo(p)n(rog)q Fq(;)32 b Fo(p)r(c)p Fq(;)g(\033)n(;)h(\032;)g(\027)q(;)14 b Fo(in)o Fq(;)32 b Fo(out)p Fq(;)h Fo(acc)p Fx(\))1922 5173 y(10)p eop end %%Page: 11 11 TeXDict begin 11 10 bop 523 527 a Fw(instruction)437 b(up)r(date)25 b(set)1193 b(condition)523 760 y Fd(INPUT)605 b Fh(f)p Fo(in)22 b Fw(:=)f Fo(null)p Fi(;)13 b Fo(acc)22 b Fw(:=)f Fi(in)p Fh(g)836 b Fo(in)21 b Fh(6)p Fw(=)g Fo(null)523 876 y Fd(OUTPUT)566 b Fh(f)p Fo(out)21 b Fw(:=)h Fo(acc)p Fh(g)1134 b Fo(out)21 b Fw(=)g Fo(null)523 992 y Fd(LOAD)27 b Fi(r)582 b Fh(f)p Fo(acc)22 b Fw(:=)f Fi(\032)p Fw(\()p Fi(r)r Fw(\))p Fh(g)523 1108 y Fd(STORE)27 b Fi(r)543 b Fh(f)p Fi(\032)p Fw(\()p Fi(r)r Fw(\))21 b(:=)g Fo(acc)p Fh(g)523 1225 y Fd(STORE)40 b(CONST)27 b Fi(c)f(C)229 b Fh(f)p Fi(\033)s Fw(\()p Fi(c)p Fw(\))21 b(:=)h Fi(C)5 b Fh(g)523 1341 y Fd(DECODE)27 b Fi(v)502 b Fh(f)p Fi(\033)s Fw(\()p Fi(v)s Fw(\))21 b(:=)g Fi(v)s(:)p Fo(deco)r(de)q Fw(\()p Fo(acc)p Fw(\))p Fh(g)523 1457 y Fd(ENCODE)27 b Fi(v)502 b Fh(f)p Fo(acc)22 b Fw(:=)f Fi(\033)s Fw(\()p Fi(v)s Fw(\))p Fi(:)p Fo(enco)r(de)p Fw(\(\))p Fh(g)523 1573 y Fd(CREATE)27 b Fi(cr)471 b Fh(f)p Fi(\033)s Fw(\()p Fi(cr)r Fw(\))21 b(:=)g Fi(cr)n(:)p Fo(create)q Fw(\(\))p Fh(g)523 1689 y Fd(ANALYZE)41 b(TUPLE)27 b Fi(t)1112 1657 y Fh(\000)-60 b(!)1132 1689 y Fi(r)156 b Fh(f)p Fi(\032)p Fw(\()p Fi(r)1466 1697 y Ff(i)1492 1689 y Fw(\))21 b(:=)g Fi(\033)s Fw(\()p Fi(t)p Fw(\))p Fi(:)p Fo(analyzeT)-6 b(uple)p Fw(\(\)\()p Fi(i)p Fw(\))26 b Fh(j)g Fi(r)2467 1697 y Ff(i)2514 1689 y Fh(2)2586 1657 y(\000)-60 b(!)2606 1689 y Fi(r)22 b Fh(g)523 1806 y Fd(CREATE)41 b(TUPLE)26 b Fi(t)1073 1774 y Fh(\000)-60 b(!)1093 1806 y Fi(r)195 b Fh(f)p Fi(\033)s Fw(\()p Fi(t)p Fw(\))21 b(:=)g Fi(t:)p Fo(createT)-6 b(uple)p Fw(\([)p Fi(\032)p Fw(\()p Fi(r)2195 1814 y Ff(i)2221 1806 y Fw(\))25 b Fh(j)h Fi(r)2358 1814 y Ff(i)2406 1806 y Fh(2)2478 1774 y(\000)-60 b(!)2498 1806 y Fi(r)22 b Fw(])p Fh(g)523 1922 y Fd(OPPOSITE)27 b Fi(K)k(k)325 b Fh(f)p Fi(\033)s Fw(\()p Fi(k)r Fw(\))21 b(:=)h Fi(\033)s Fw(\()p Fi(K)5 b Fw(\))p Fi(:)p Fo(op)p Fw(\(\))p Fh(g)523 2038 y Fd(KEY)40 b(OF)565 b Fh(f)p Fo(acc)22 b Fw(:=)f Fi(\027)5 b Fw(\()p Fo(acc)p Fw(\))p Fh(g)523 2154 y Fd(MATCH)27 b Fi(r)543 b Fh(;)1507 b Fo(acc)21 b Fw(=)g Fi(\032)p Fw(\()p Fi(r)r Fw(\))523 2271 y Fd(ENCRYPT)27 b Fi(ek)424 b Fh(f)p Fo(acc)22 b Fw(:=)f Fi(\033)s Fw(\()p Fi(ek)r Fw(\))p Fi(:)p Fo(encrypt)p Fw(\()p Fo(acc)p Fw(\))p Fh(g)523 2387 y Fd(DECRYPT)27 b Fi(dk)420 b Fh(f)p Fo(acc)22 b Fw(:=)f Fi(\033)s Fw(\()p Fi(dk)r Fw(\))p Fi(:)p Fo(decrypt)p Fw(\()p Fo(acc)p Fw(\))p Fh(g)523 2503 y Fd(SIGN)27 b Fi(sk)541 b Fh(f)p Fo(acc)22 b Fw(:=)f Fi(\033)s Fw(\()p Fi(sk)r Fw(\))p Fi(:)p Fo(sign)q Fw(\()p Fo(acc)p Fw(\))p Fh(g)523 2619 y Fd(VERIFY)27 b Fi(v)s(k)h(r)396 b Fh(;)1507 b Fi(\033)s Fw(\()p Fi(v)s(k)r Fw(\))p Fi(:)p Fo(verify)q Fw(\()p Fi(\032)p Fw(\()p Fi(r)r Fw(\))p Fi(;)12 b Fo(acc)q Fw(\))523 2736 y Fd(HASH)27 b Fi(h)573 b Fh(f)p Fo(acc)22 b Fw(:=)f Fi(h:)p Fo(hash)p Fw(\()p Fo(acc)p Fw(\))p Fh(g)1483 2989 y Ft(Fig.)14 b(4.)27 b Fx(CrAM)h(instructions)523 3264 y(where)g(the)h(stores)f Fq(\033)n(;)14 b(\032;)g(\027)35 b Fx(are)28 b(as)g(in)h(Section)f(2.1,)h Fo(p)r(c)f Fx(is)h(a)f (program)f(coun)n(ter)h(holding)g(a)523 3363 y(nonnegativ)n(e)d(in)n (teger,)g Fo(acc)i Fx(holds)e(a)h(message,)f(and)h Fo(in)p Fq(;)14 b Fo(out)26 b Fx(hold)g(either)g(messages)e(or)i(the)523 3463 y(n)n(ull)21 b(ob)5 b(ject)21 b Fo(null)p Fx(.)g(The)g(program)d Fo(p)n(rog)k Fx(is)f(a)f(sequence)h(of)f(instructions)h(de\014ned)g(in) g(\014gure)f(4.)523 3563 y(Most)29 b(instructions)g(address)f(v)-5 b(ariables)28 b(of)h(some)g(concrete)g(t)n(yp)r(e,)g(what)h(pro)n (vides)d(them)523 3662 y(with)37 b(a)g(sp)r(eci\014c)g(seman)n(tics.)f (It)h(is)g(through)f(the)i(c)n(hoice)e(of)h(concrete)f(t)n(yp)r(es)g (that)i(the)523 3762 y(domains)d(of)h(cryptographic)d(ob)5 b(jects)35 b(and)h(messages)e(pro)r(cessed)g(b)n(y)h(the)h(mac)n(hine,) g(as)523 3861 y(w)n(ell)26 b(as)f(cryptographic)f(algorithms)h(used,)g (are)g(determined:)i(w)n(e)e(can)h(\(and)g(do\))g(run)g(the)523 3961 y(same)34 b(CrAM)h(programs)d(b)r(oth)j(with)g(the)g(en)n(tirely)f (abstract)g(mo)r(del)g(of)h(encryption)f(of)523 4061 y([RRS03)o(],)28 b(and)g(with)g(concrete)f(cryptographic)e(APIs,)i(see) h([W)-7 b(eb].)648 4160 y(Executing)26 b(an)i(instruction,)f(if)h(p)r (ossible,)g(transforms)1334 4326 y Fm(M)23 b Fx(=)g(\()p Fo(p)n(rog)q Fq(;)32 b Fo(p)r(c)p Fq(;)g(\033)n(;)h(\032;)g(\027)q(;)14 b Fo(in)o Fq(;)32 b Fo(out)p Fq(;)h Fo(acc)p Fx(\))523 4493 y(to)28 b(some)1216 4659 y Fm(M)1316 4624 y Fn(0)1362 4659 y Fx(=)23 b(\()p Fo(p)n(rog)p Fq(;)33 b Fo(p)r(c+1)p Fq(;)f(\033)1957 4624 y Fn(0)1981 4659 y Fq(;)g(\032)2079 4624 y Fn(0)2103 4659 y Fq(;)g(\027)q(;)14 b Fo(in')p Fq(;)32 b Fo(out')p Fq(;)h Fo(acc')p Fx(\))523 4825 y(b)n(y)38 b(executing)f(the)h(up)r(dates)g(asso)r(ciated)f(to)g(eac)n(h)g (instruction)h(b)r(elo)n(w.)f(There)h(are)e(no)523 4924 y(branc)n(hes)f(or)g(jumps)i(in)f(the)h(CrAM,)f(since)g(it)g(is)g (concerned)f(just)i(with)f(analysis)f(and)1922 5173 y(11)p eop end %%Page: 12 12 TeXDict begin 12 11 bop 523 448 a Fx(syn)n(thesis)34 b(of)g(messages.)e(If)j(needed,)f(they)h(can)e(b)r(e)i(easily)e(added)h (to)h(the)f(mac)n(hine,)g(or)523 548 y(the)j(mac)n(hine)e(as)h (de\014ned)g(here)g(can)g(b)r(e)g(used)g(as)g(a)f(submac)n(hine)h(of)g (a)g(mac)n(hine)f(with)523 648 y(some)e(con)n(trol)f(\015o)n(w)g(mec)n (hanisms.)h(Note)g(that)h(there)f(is)g(no)g Fq(\027)2555 617 y Fn(0)2579 648 y Fx(:)g(in)h(our)e(presen)n(t)h(mo)r(del)523 747 y(the)28 b(certi\014cate)f(store)g(is)g(constan)n(t.)648 847 y(Executing)f(an)i(instruction)f(can)g(b)r(e)h(imp)r(ossible)g(for) f(one)g(of)h(the)g(follo)n(wing)e(reasons:)558 1005 y(1.)41 b(An)28 b(explicit)g(side)g(condition)f(of)h(the)g(instruction)f(do)r (es)g(not)h(hold.)558 1104 y(2.)41 b(An)30 b(expression)e(o)r(ccurring) g(in)i(the)g(up)r(dates)g(or)e(in)i(the)g(side)f(conditions)h(cannot)f (b)r(e)664 1203 y(executed)f(b)r(ecause)f(a)g(metho)r(d)h(is)g(not)f (de\014ned)h(at)g(an)f(argumen)n(t.)523 1363 y(In)h(an)n(y)f(of)h (these)f(cases)g(w)n(e)g(imagine)g(the)h(mac)n(hine)g(has)f(failed,)h (ab)r(orted)f(\(in)h(our)f(imple-)523 1463 y(men)n(tation)g(w)n(e)h (raise)e(an)h(exception\).)648 1562 y(The)39 b(fact)g(that)g(one)g (step)g(of)g(execution)g(successfully)f(transforms)g Fm(M)h Fx(to)g Fm(M)3269 1532 y Fn(0)3331 1562 y Fx(as)523 1662 y(ab)r(o)n(v)n(e)25 b(will)h(b)r(e)h(denoted)f(b)n(y)g Fm(M)d(!)g(M)1779 1632 y Fn(0)1802 1662 y Fx(;)k(the)f(re\015exiv)n(e)f (transitiv)n(e)h(closure)f(of)h Fm(!)g Fx(will)h(b)r(e)523 1762 y(denoted)h(b)n(y)976 1715 y Fn(\003)952 1762 y Fm(!)p Fx(.)648 1861 y(Since)37 b(some)g(of)g(the)g(op)r(erations)f (used)i(in)f(the)h(seman)n(tics)e(of)h(CrAM)g(instructions)523 1961 y(can)32 b(b)r(e)h(nondeterministic,)g Fm(!)g Fx(and)1766 1914 y Fn(\003)1741 1961 y Fm(!)g Fx(are)f(not)h(functions,)g(they)g (are)e(in)i(general)e(just)523 2061 y(relations.)648 2160 y(In)26 b(the)g Fs(initial)36 b Fx(state)26 b(of)g(a)g(CrAM)g(w)n (e)g(ha)n(v)n(e)f Fo(p)r(c)e Fx(=)g(0;)i(it)i(is)f Fs(terminate)l(d)35 b Fx(if)27 b Fo(p)r(c)c Fx(=)f Fm(j)p Fo(p)n(rog)q Fm(j)p Fx(,)523 2260 y(i.e.)h(it)f(has)g(executed)h(its)f(en)n(tire)g(program) f(without)i(failure.)f(A)g(CrAM)h(in)f(an)h(initial)f(state)523 2359 y Fs(terminates)34 b Fx(if)27 b(there)f(is)h(a)f(terminated)h (CrAM)f Fm(M)2158 2329 y Fn(0)2208 2359 y Fx(suc)n(h)g(that)h Fm(M)2720 2312 y Fn(\003)2696 2359 y Fm(!)c(M)2902 2329 y Fn(0)2925 2359 y Fx(;)k(w)n(e)f(shall)g(sa)n(y)523 2459 y(that)34 b(it)h(terminates)e(with)i Fq(m)1485 2429 y Fn(0)1508 2459 y Fq(;)14 b(\033)1595 2429 y Fn(0)1618 2459 y Fq(;)g(\032)1698 2429 y Fn(0)1755 2459 y Fx(if)35 b(the)f(v)-5 b(alue)34 b(stored)f(in)h(the)h(accum)n(ulator)d(is)i Fq(m)3359 2429 y Fn(0)3382 2459 y Fx(,)523 2559 y(and)29 b(the)g(ob)5 b(ject)29 b(store)f(and)g(the)i(message)d(store)h(of)h Fm(M)2316 2529 y Fn(0)2368 2559 y Fx(are)f(resp)r(ectiv)n(ely)g Fq(\033)3012 2529 y Fn(0)3035 2559 y Fq(;)14 b(\032)3115 2529 y Fn(0)3138 2559 y Fx(.)29 b(When)523 2658 y Fq(m)596 2628 y Fn(0)647 2658 y Fx(is)e(not)h(of)g(in)n(terest,)f(it)h(will)g(b) r(e)g(skipp)r(ed.)648 2758 y(The)j(syn)n(tax)g(and)g(the)h(seman)n (tics)f(of)h(individual)g(instructions)f(is)g(displa)n(y)n(ed)g(in)h (\014g-)523 2858 y(ure)j(4,)g(where)g(the)g(\014rst)g(column)h(pro)n (vides)d(the)j(syn)n(tax,)e(the)i(second)f(column)g(the)h(se-)523 2957 y(man)n(tics)f(of)g(instruction)g(execution,)g(giv)n(en)f(b)n(y)h (a)g(set)g(of)g(ASM)g(up)r(dates,)h(in)f(terms)g(of)523 3057 y Fq(\033)n(;)14 b(\032;)g(\027)q(;)g Fo(in)p Fq(;)g Fo(out)p Fq(;)g Fo(acc)p Fx(,)27 b(and)h(the)f(third)h(column)f(the)h (explicit)g(side)f(condition,)g(if)h(an)n(y)-7 b(,)27 b(under)523 3156 y(whic)n(h)h(the)g(instruction)f(can)g(execute.)523 3416 y Fu(4)112 b(Compiling)39 b(Message)g(P)m(atterns)e(to)g(CrAM)523 3609 y Fx(In)c(this)g(section)g(w)n(e)g(sho)n(w)f(ho)n(w)g(to)h (compile)g(message)e(patterns)i(to)f(CrAM)h(programs,)523 3709 y(b)r(oth)j(for)g(matc)n(hing)f(and)h(for)f(creation.)g(In)h(view) f(of)h(the)g(represen)n(tation)e(of)i(proto)r(col)523 3809 y(roles)25 b(of)h([RRS03)o(])g(as)f(sequences)g(of)h(matc)n (h{create)e(pairs)h(of)h(patterns,)g(w)n(e)f(obtain)h(com-)523 3908 y(pilation)32 b(of)f(proto)r(col)g(roles)g(to)g(CrAM)h(co)r(de)f (automatically)-7 b(,)31 b(b)n(y)h(pasting)f(and)h(glueing)523 4008 y(with)c(instructions)f(for)g(input{output.)648 4108 y(The)g(in)n(tuition,)h(expressed)f(in)h([RRS03)o(])g(b)n(y)f(sa)n (ying)664 4266 y(A)k(role)f(can)g(b)r(e)i(seen)e(as)g(an)g(in)n (teractiv)n(e)g(mac)n(hine)g(with)i(input)f(and)g(output)g(of)664 4366 y(messages,)19 b(with)i(a)g(program)d(giv)n(en)i(b)n(y)h(a)f (sequence)g(of)h(actions.)e(A)i(con\014guration)664 4465 y(consists)32 b(of)g(state)g(of)h(memory)e(\(assignmen)n(t\))h(and)g (program)f(coun)n(ter)g(\(action)664 4565 y(index\).)523 4725 y(gets)22 b(a)h(concrete)f(form)g(in)i(the)f(CrAM,)g(whic)n(h)g (is)f(no)n(w)h(also)e(decoupled)i(from)g(an)n(y)f(sp)r(eci\014c)523 4825 y(mo)r(del)36 b(of)f(encryption,)g(and)g(w)n(orks)f(with)i(an)n(y) f(reasonable)e(mo)r(del)j(supp)r(orted)f(b)n(y)h(the)523 4924 y(v)n(o)r(cabulary)26 b(and)h(assumptions.)1922 5173 y(12)p eop end %%Page: 13 13 TeXDict begin 13 12 bop 551 527 a Fw(pattern)511 b(instructions)551 643 y Fi(v)54 b Fw(\()p Fi(v)24 b Fh(2)d Fi(\033)s Fw(\))428 b([)12 b Fd(STORE)26 b Fi(r)1601 612 y Ff(s)1634 643 y Fi(;)13 b Fd(ENCODE)27 b Fi(v)s(;)13 b Fd(MATCH)27 b Fi(r)2262 612 y Ff(s)2307 643 y Fw(])551 760 y Fi(v)54 b Fw(\()p Fi(v)32 b(=)-46 b Fh(2)21 b Fi(\033)s Fw(\))428 b([)12 b Fd(DECODE)26 b Fi(v)15 b Fw(])551 876 y Fi(r)53 b Fw(\()p Fi(r)23 b Fh(2)e Fi(\032)p Fw(\))441 b([)12 b 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b(denoted)523 4625 y(in)h(the)f(co)r(de)h(b)n(y)f Fq(r)1100 4595 y Fp(s)1136 4625 y Fx(.)g(By)g(con)n(v)n(en)n(tion,)f(ev)n(ery)g (o)r(ccurrence)g(of)i(a)f(scratc)n(h)f(v)-5 b(ariable)24 b(is)h(fresh,)523 4725 y(o)r(ccurring)f(no)n(where)g(in)h(the)h (pattern,)f(and)g(no)n(where)g(else)f(in)i(the)g(compiled)f(co)r(de)g (except)523 4825 y(for)31 b(the)g(places)g(indicated.)g(This)h(ensures) e(that)h(scratc)n(h)f(v)-5 b(ariables)30 b(in)n(v)n(ok)n(ed)g(for)h(a)f (part)523 4924 y(of)e(a)f(pattern)g(cannot)g(in)n(terfere)g(with)h (compilation)f(or)g(in)n(terpretation)g(of)g(other)g(parts.)1922 5173 y(13)p eop end %%Page: 14 14 TeXDict begin 14 13 bop 523 833 a Fw(pattern)347 b(instructions)523 950 y Fi(v)54 b Fw(\()p Fi(v)24 b Fh(2)e Fi(\033)s Fw(\))274 b([)p Fd(ENCODE)28 b Fi(v)s Fw(])523 1066 y Fi(cr)53 b Fw(\()p Fi(cr)32 b(=)-47 b Fh(2)22 b Fi(\033)s Fw(\))214 b([)p Fd(CREATE)28 b Fi(cr)r(;)13 b Fd(ENCODE)27 b Fi(cr)r Fw(])523 1182 y Fi(r)53 b Fw(\()p Fi(r)23 b Fh(2)f Fi(\033)s 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Fa(Pr)l(o)l(c)l(e)l(e)l(ding)30 b(of)d(13th)h(IEEE)f(CSFW)p Fw(,)f(2000.)523 1727 y(DMP03.)75 b(Nancy)30 b(Durgin,)g(John)h(Mitc)n(hell,)h(and)f(Dusk)n(o)f(P)n(a)n (vlo)n(vic.)50 b(A)30 b(comp)r(ositional)j(logic)876 1818 y(for)26 b(proto)r(col)h(correctness.)36 b Fa(Journal)28 b(of)f(Computer)i(Se)l(curity)p Fw(,)e(11,)g(2003.)523 1910 y(FHG99.)88 b(F.)32 b(Ja)n(vier)h(Tha)n(y)n(er)f(F\023)-38 b(abrega,)33 b(Jonathan)g(C.)f(Herzog,)h(and)f(Josh)n(ua)h(D.)f (Guttman.)876 2001 y(Strand)24 b(spaces:)i(Pro)n(ving)f(securit)n(y)g (proto)r(cols)i(correct.)34 b Fa(Journal)27 b(of)g(Computer)h(Se-)876 2092 y(curity)p Fw(,)e(7\(2/3\),)i(1999.)523 2183 y(FIP95.)126 b(NIST.)25 b(Secure)g(Hash)h(Standard.)34 b Fa(FIPS)27 b(PUB)g(180-1)p Fw(,)g(1995.)523 2275 y(GH93.)138 b(Y.)31 b(Gurevic)n(h)g(and)g(J.)h(Huggins.)52 b(The)32 b(Seman)n(tics)g(of)g (the)f(C)h(Programming)h(Lan-)876 2366 y(guage.)i(In)25 b Fa(CSL)i(92)p Fw(,)g(v)n(olume)e(702)i(of)g Fa(LNCS)p Fw(,)f(pages)g(274{309.)j(Springer,)d(1993.)523 2457 y(GZ00.)149 b(G.)30 b(Go)r(os)i(and)e(W.)h(Zimmermann.)49 b(V)-6 b(eri\014ying)30 b(Compilers)i(and)e(ASMs.)48 b(In)30 b Fa(ASM)876 2549 y(2000)p Fw(,)c(v)n(olume)g(1912)h(of)f Fa(LNCS)p Fw(.)h(Springer-V)-6 b(erlag,)26 b(2000.)523 2640 y(HS00.)155 b(J.)20 b(Huggins)g(and)g(W.)g(Shen.)k(The)c(Static)h (and)e(Dynamic)h(Seman)n(tics)g(of)h(C.)k(T)-6 b(ec)n(hnical)876 2731 y(Rep)r(ort)25 b(CPSC-2000-4,)j(Kettering)e(Univ)n(ersit)n(y)-6 b(,)24 b(2000.)523 2823 y(Lo)n(w96.)117 b(Ga)n(vin)24 b(Lo)n(w)n(e.)33 b(Breaking)25 b(and)g(\014xing)f(the)g(Needham-Sc)n (hro)r(eder)f(public-k)n(ey)g(proto-)876 2914 y(col)j(using)g(FDR.)34 b(In)25 b Fa(Pr)l(o)l(c)l(e)l(e)l(dings)k(of)f(T)-6 b(A)n(CAS,)27 b Fw(v)n(olume)e(1055)i(of)i Fa(LNCS)p Fw(,)d(1996.)523 3005 y(MW03.)107 b(D.)36 b(Micciancio)i(and)e(B.)g(W)-6 b(arinsc)n(hi.)66 b(Completeness)37 b(theorems)g(for)g(the)f(Abadi-)876 3097 y(Roga)n(w)n(a)n(y)18 b(logic)i(of)f(encrypted)e(expressions.)23 b Fa(Journal)e(of)f(Computer)i(Se)l(curity)p Fw(,)e(2003.)523 3188 y(PK)n(C93.)91 b(RSA)24 b(Lab)r(oratories.)36 b Fa(PK)n(CS)28 b(#7,)f(V)-6 b(ersion)28 b(2.10)p Fw(,)e(No)n(v)n(em)n(b) r(er,)f(1993.)523 3279 y(PK)n(C02.)91 b(RSA)24 b(Lab)r(oratories.)36 b Fa(PK)n(CS)28 b(#1,)f(V)-6 b(ersion)28 b(2.1)p Fw(,)e(June,)g(2002.) 523 3371 y(Riv92.)137 b(R.)25 b(Riv)n(est.)34 b(The)26 b(MD5)g(message{digest)i(algorithm.)36 b Fa(RF)n(C)27 b(1321)p Fw(,)g(1992.)523 3462 y(RRS03.)99 b(D.)31 b(Rosenzw)n(eig,)i (D.)e(Runje,)g(and)g(N.)g(Slani.)52 b(Priv)l(acy)-6 b(,)31 b(abstract)h(encryption)e(and)876 3553 y(proto)r(cols:)i(an)e(ASM)g(mo) r(del)g({)h(P)n(art)g(I.)47 b(In)30 b Fa(ASM)h(2003,)h Fw(v)n(olume)e(2589)i(of)g Fa(LNCS)p Fw(.)876 3645 y(Springer-V)-6 b(erlag,)26 b(2003.)523 3736 y(SSB01.)116 b(R.)31 b(St\177)-38 b(ark,)31 b(J.)h(Sc)n(hmid,)f(and)g(E.)g(B\177)-38 b(orger.)53 b Fa(Java)34 b(and)f(the)g(Java)h(Virtual)f(Machine:)876 3827 y(De\014nition,)27 b(V)-6 b(eri\014c)l(ation,)28 b(V)-6 b(alidation)p Fw(.)35 b(Springer-V)-6 b(erlag,)26 b(2001.)523 3919 y(W)-6 b(al95.)124 b(C.)29 b(W)-6 b(allace.)45 b(The)29 b(Seman)n(tics)g(of)h(the)e(C++)h(Programming)i(Language.)44 b(In)28 b Fa(Sp)l(e)l(c-)876 4010 y(i\014c)l(ation)k(and)h(V)-6 b(alidation)32 b(Metho)l(ds)p Fw(,)g(pages)g(131{164.)i(Oxford)c(Univ)n (ersit)n(y)g(Press,)876 4101 y(1995.)523 4193 y(W)-6 b(ar03.)115 b(B.)28 b(W)-6 b(arinsc)n(hi.)40 b(A)27 b(computational)i (analysis)f(of)h(the)e(Needham-Sc)n(hro)r(eder\(-Lo)n(w)n(e\))876 4284 y(proto)r(col.)35 b(In)25 b Fa(Pr)l(o)l(c)l(e)l(e)l(dings)30 b(of)d(16th)i(IEEE)e(CSFW)p Fw(.)e(A)n(CM)h(Press,)h(2003.)523 4375 y(W)-6 b(eb.)182 b(h)n(ttp://www.fsb.hr/matematik)l (a/index.php?ulaz=proto)r(cols.)1922 5173 y Fx(16)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF