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cleartomark
%%EndFont 
%%BeginFont: MSAM10
%!PS-AdobeFont-1.1: MSAM10 2.1
%%CreationDate: 1993 Sep 17 09:05:00
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSAM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSAM10 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 /square put
readonly def
/FontBBox{8 -463 1331 1003}readonly def
/UniqueID 5031981 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 14 /delta put
dup 15 /epsilon1 put
dup 61 /slash put
dup 96 /lscript put
dup 97 /a put
dup 106 /j put
dup 107 /k put
readonly def
/FontBBox{11 -250 1241 750}readonly def
/UniqueID 5087381 def
currentdict end
currentfile eexec
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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: CMSS12
%!PS-AdobeFont-1.1: CMSS12 1.0
%%CreationDate: 1991 Aug 20 17:33:47
% 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 (CMSS12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMSS12 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 78 /N put
readonly def
/FontBBox{-62 -251 978 758}readonly def
/UniqueID 5000804 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
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dup 15 /epsilon1 put
dup 61 /slash put
dup 79 /O put
dup 107 /k put
dup 110 /n put
dup 111 /o put
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readonly def
/FontBBox{-32 -250 1048 750}readonly def
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currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR12
%!PS-AdobeFont-1.1: CMR12 1.0
%%CreationDate: 1991 Aug 20 16:38:05
% 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 (CMR12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR12 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 2 /Theta put
dup 8 /Phi put
dup 10 /Omega put
dup 33 /exclam put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus 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
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dup 82 /R put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 98 /b put
dup 100 /d put
dup 103 /g put
dup 105 /i put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 126 /tilde put
readonly def
/FontBBox{-34 -251 988 750}readonly def
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currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI12
%!PS-AdobeFont-1.1: CMMI12 1.100
%%CreationDate: 1996 Jul 27 08:57:55
% 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 (CMMI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI12 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 /alpha put
dup 12 /beta put
dup 14 /delta put
dup 15 /epsilon1 put
dup 17 /eta put
dup 20 /kappa put
dup 21 /lambda put
dup 26 /rho put
dup 27 /sigma put
dup 28 /tau put
dup 30 /phi put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 65 /A put
dup 66 /B put
dup 68 /D put
dup 69 /E put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 83 /S put
dup 85 /U put
dup 86 /V put
dup 89 /Y put
dup 90 /Z put
dup 96 /lscript put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d 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 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 126 /vector put
readonly def
/FontBBox{-30 -250 1026 750}readonly def
/UniqueID 5087386 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. 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 0 /parenleftbig put
dup 1 /parenrightbig put
dup 16 /parenleftBig put
dup 17 /parenrightBig put
dup 22 /floorleftbigg put
dup 23 /floorrightbigg put
dup 26 /braceleftbigg put
dup 27 /bracerightbigg put
dup 80 /summationtext put
dup 81 /producttext put
dup 88 /summationdisplay put
dup 112 /radicalbig put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSY8
%!PS-AdobeFont-1.1: CMSY8 1.0
%%CreationDate: 1991 Aug 15 07:22:10
% 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 (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY8 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 1 /periodcentered put
dup 3 /asteriskmath put
dup 18 /reflexsubset put
dup 21 /greaterequal put
dup 48 /prime put
dup 50 /element put
dup 98 /floorleft put
dup 99 /floorright put
dup 102 /braceleft put
dup 103 /braceright put
dup 106 /bar put
dup 112 /radical put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueID 5000818 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 51 /three 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: CMMI8
%!PS-AdobeFont-1.1: CMMI8 1.100
%%CreationDate: 1996 Jul 23 07:53:54
% 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 (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI8 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 /alpha put
dup 14 /delta put
dup 15 /epsilon1 put
dup 27 /sigma put
dup 28 /tau put
dup 58 /period put
dup 59 /comma put
dup 61 /slash put
dup 65 /A put
dup 66 /B put
dup 69 /E put
dup 79 /O put
dup 84 /T put
dup 86 /V put
dup 96 /lscript put
dup 97 /a put
dup 98 /b put
dup 100 /d put
dup 102 /f put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 109 /m put
dup 110 /n put
dup 112 /p put
dup 116 /t put
dup 120 /x put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 def
currentdict end
currentfile eexec
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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. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 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 1 /periodcentered put
dup 2 /multiply put
dup 3 /asteriskmath put
dup 8 /circleplus put
dup 17 /equivalence put
dup 18 /reflexsubset put
dup 20 /lessequal put
dup 21 /greaterequal put
dup 24 /similar put
dup 33 /arrowright put
dup 41 /arrowdblright put
dup 50 /element put
dup 52 /triangle put
dup 54 /negationslash put
dup 56 /universal put
dup 69 /E put
dup 73 /I put
dup 75 /K put
dup 80 /P put
dup 82 /R put
dup 89 /Y put
dup 94 /logicaland put
dup 100 /ceilingleft put
dup 101 /ceilingright put
dup 102 /braceleft put
dup 103 /braceright put
dup 106 /bar put
dup 112 /radical put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueID 5000820 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40
% 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 (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 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 2 /Theta put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus 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 61 /equal put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 103 /g put
dup 108 /l put
dup 109 /m put
dup 120 /x put
dup 126 /tilde put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec
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%%BeginFont: CMSY7
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%%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
readonly def
/FontBBox{-15 -951 1252 782}readonly def
/UniqueID 5000817 def
currentdict end
currentfile eexec
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124 V 260 w(Ref)p 1572 124 V 224 w(2)32 b(DB)p 1981 124
V 184 w(3)h(DB)p 2389 124 V 158 w(4)g(DB)p 2747 124 V
433 w Fu(k)j Fv(DB)p 3710 124 V 188 127 3524 4 v 188
144 V 186 266 4 123 v 309 230 a Fu(k)s Fv(th)d(ro)s(ot)p
783 266 V 169 w(Th)g(3.2)p 1164 266 V 178 w([23])p 1572
266 V 178 w(no)f(PIR)p 1981 266 V 100 w(no)h(PIR)p 2389
266 V 145 w Fu(n)2544 193 y Fs(1)p Fq(=)p Fs(2)p 2747
266 V 3048 230 a Fu(k)25 b Fr(\001)d Fu(n)3232 193 y
Fs(1)p Fq(=)p Fs(lg)13 b Fq(k)p 3710 266 V 188 269 3524
4 v 186 391 4 123 v 238 355 a Fv(Co)m(v.)45 b(Co)s(des)p
783 391 V 100 w(Th)33 b(3.3)p 1164 391 V 178 w([23])p
1572 391 V 248 w Fu(n)1752 319 y Fs(1)p Fq(=)p Fs(3)p
1981 391 V 2032 355 a Fv(no)g(PIR)p 2389 391 V 145 w
Fu(n)2544 319 y Fs(1)p Fq(=)p Fs(4)p 2747 391 V 2799
355 a Ft(\()p Fu(k)19 b Ft(lg)f Fu(k)s Ft(\))p Fu(n)3151
319 y Fs(1)p Fq(=)p Fs(\(lg)c Fq(k)r Fs(+lg)e(lg)h Fq(k)r
Fs(\))3616 355 y Fv(?)p 3710 391 V 188 394 3524 4 v 186
517 4 123 v 265 480 a(p)s(oly)32 b(in)m(ter.)p 783 517
V 1164 517 V 587 w([22])p 1572 517 V 248 w Fu(n)1752
444 y Fs(1)p Fq(=)p Fs(2)p 1981 517 V 2103 480 a Fu(n)2161
444 y Fs(1)p Fq(=)p Fs(3)p 2389 517 V 2486 480 a Fu(n)2544
444 y Fs(1)p Fq(=)p Fs(4)p 2747 517 V 2953 480 a Ft(\()p
Fu(k)3045 444 y Fs(2)3101 480 y Ft(log)18 b Fu(k)s Ft(\))p
Fu(n)3394 444 y Fs(1)p Fq(=k)p 3710 517 V 188 520 3524
4 v 186 648 4 128 v 407 612 a Fv(Rec)p 783 648 V 269
w(Th)33 b(3.7)p 1164 648 V 202 w([2])p 1572 648 V 273
w Fu(n)1752 575 y Fs(1)p Fq(=)p Fs(3)p 1981 648 V 2103
612 a Fu(n)2161 575 y Fs(1)p Fq(=)p Fs(5)p 2389 648 V
2486 612 a Fu(n)2544 575 y Fs(1)p Fq(=)p Fs(7)p 2747
648 V 2991 612 a Ft(2)3040 575 y Fq(k)3079 552 y Fp(2)3117
612 y Fu(n)3175 575 y Fs(1)p Fq(=)p Fs(\(2)p Fq(k)r Fo(\000)p
Fs(1\))p 3710 648 V 188 651 3524 4 v 186 773 4 123 v
259 737 a Fv(Linear)f(Alg)p 783 773 V 1164 773 V 580
w([41])p 1572 773 V 248 w Fu(n)1752 701 y Fs(1)p Fq(=)p
Fs(3)p 1981 773 V 2103 737 a Fu(n)2161 701 y Fs(1)p Fq(=)p
Fs(5)p 2389 773 V 2486 737 a Fu(n)2544 701 y Fs(1)p Fq(=)p
Fs(7)p 2747 773 V 3014 737 a Fu(k)s Ft(!)p Fu(n)3153
701 y Fs(1)p Fq(=)p Fs(\(2)p Fq(k)r Fo(\000)p Fs(1\))p
3710 773 V 188 776 3524 4 v 186 898 4 123 v 259 862 a
Fv(Linear)g(Alg)p 783 898 V 1164 898 V 501 w([40,)h(10)o(])p
1572 898 V 170 w Fu(n)1752 826 y Fs(1)p Fq(=)p Fs(3)p
1981 898 V 2103 862 a Fu(n)2161 826 y Fs(1)p Fq(=)p Fs(5)p
2389 898 V 2486 862 a Fu(n)2544 826 y Fs(1)p Fq(=)p Fs(7)p
2747 898 V 3008 862 a Fu(k)3062 826 y Fs(3)3101 862 y
Fu(n)3159 826 y Fs(1)p Fq(=)p Fs(\(2)p Fq(k)r Fo(\000)p
Fs(1\))p 3710 898 V 188 902 3524 4 v 186 1024 4 123 v
255 988 a Fv(p)s(oly-hea)m(vy)p 783 1024 V 1164 1024
V 576 w([12])p 1572 1024 V 248 w Fu(n)1752 952 y Fs(1)p
Fq(=)p Fs(3)p 1981 1024 V 2057 988 a Fu(n)2115 952 y
Fs(1)p Fq(=)p Fs(5)p Fq(:)p Fs(25)p 2389 1024 V 2441
988 a Fu(n)2499 952 y Fs(1)p Fq(=)p Fs(7)p Fq(:)p Fs(87)p
2747 1024 V 2961 988 a Fu(n)3019 952 y Fq(O)r Fs(\(lg)13
b(lg)g Fq(k)r(=k)g Fs(lg)f Fq(k)r Fs(\))p 3710 1024 V
188 1027 3524 4 v 59 1295 a Fv(T)-8 b(able)32 b(1:)43
b Fn(Summary)37 b(of)h(Information)e(Theoretic)g(Sc)m(hemes,)h(up)h(to)
f(a)h(constan)m(t)f(factor.)0 1575 y(KEY)f(IDEA:)g(View)h(the)g
(database)i(as)f(a)1809 1503 y Fr(p)p 1892 1503 59 4
v 72 x Fu(n)22 b Fr(\002)2072 1503 y(p)p 2155 1503 V
72 x Fu(n)38 b Fn(bit)e(arra)m(y)i(and)g(use)g(prop)s(erties)f(of)g
Fr(\010)p Fn(.)0 1767 y Fm(Pr)-5 b(o)g(of.)48 b Fv(W)-8
b(e)36 b(do)f(the)h Fu(k)f Ft(=)d(4)j Fv(case)h(and)f(lea)m(v)m(e)h
(the)f(generalization)e(to)i(the)h(reader.)51 b(Eac)m(h)36
b(index)g(of)f(the)0 1887 y(database)c(is)f(represen)m(ted)j(as)e(an)g
(ordered)g(pair)f Ft(\()p Fu(i)1889 1902 y Fs(1)1929
1887 y Fu(;)17 b(i)2006 1902 y Fs(2)2045 1887 y Ft(\))p
Fv(,)31 b(where)h Fu(i)2454 1902 y Fs(1)2524 1887 y Fv(and)f
Fu(i)2745 1902 y Fs(2)2816 1887 y Fv(are)f(written)h(in)f(base)h
Fr(d)3687 1816 y(p)p 3770 1816 V 71 x Fu(n)q Fr(e)p Fv(.)0
2008 y(The)i(databases)h(are)e(lab)s(eled)g Fu(D)s(B)1300
2023 y Fs(00)1374 2008 y Fv(,)h Fu(D)s(B)1592 2023 y
Fs(01)1666 2008 y Fv(,)g Fu(D)s(B)1884 2023 y Fs(10)1991
2008 y Fv(and)g Fu(D)s(B)2339 2023 y Fs(11)2413 2008
y Fv(.)0 2152 y Fn(4-DB,)k Fu(O)s Ft(\()443 2080 y Fr(p)p
526 2080 V 72 x Fu(n)p Ft(\))p Fn(-bit,)g(Information)f(Theoretic)g
(PIR)g(Sc)m(heme)119 2369 y Fv(1.)49 b(Alice)31 b(w)m(an)m(ts)j(to)e
(kno)m(w)i(bit)e Fu(x)1348 2384 y Fq(i)1372 2393 y Fp(1)1407
2384 y Fq(;i)1451 2393 y Fp(2)1489 2369 y Fv(.)119 2570
y(2.)49 b(Alice)31 b(generates)j Fu(\033)n(;)17 b(\034)39
b Fr(2)29 b(f)p Ft(0)p Fu(;)17 b Ft(1)p Fr(g)1434 2486
y Fo(p)p 1491 2486 43 3 v 1491 2533 a Fq(n)1538 2570
y Fv(.)119 2770 y(3.)49 b(Alice)21 b(then)i(generates)h(t)m(w)m(o)f
(additional)1735 2698 y Fr(p)p 1818 2698 59 4 v 72 x
Fu(n)g Fv(bits)f(strings)g(from)f(the)i(\034rst)f(t)m(w)m(o)h(strings:)
39 b Fu(\033)3534 2734 y Fo(0)3585 2770 y Ft(=)27 b Fu(\033)5
b Fr(\010)q Fu(i)3859 2785 y Fs(1)244 2891 y Fv(and)33
b Fu(\034)487 2854 y Fo(0)538 2891 y Ft(=)28 b Fu(\034)33
b Fr(\010)23 b Fu(i)850 2906 y Fs(2)889 2891 y Fv(.)119
3091 y(4.)49 b(Alice)32 b(sends)j(t)m(w)m(o)f(strings)f(to)g(eac)m(h)h
(database.)46 b Fu(D)s(B)2199 3106 y Fs(00)2307 3091
y Fv(receiv)m(es)35 b Fu(\033)n(;)17 b(\034)11 b Fv(.)46
b Fu(D)s(B)3047 3106 y Fs(01)3155 3091 y Fv(receiv)m(es)35
b Fu(\033)i Fv(and)c Fu(\034)3849 3055 y Fo(0)3873 3091
y Fv(.)244 3212 y Fu(D)s(B)402 3227 y Fs(10)509 3212
y Fv(receiv)m(es)h Fu(\033)926 3175 y Fo(0)982 3212 y
Fv(and)f Fu(\034)11 b Fv(.)43 b Fu(D)s(B)1453 3227 y
Fs(11)1560 3212 y Fv(receiv)m(es)35 b Fu(\033)1978 3175
y Fo(0)2033 3212 y Fv(and)e Fu(\034)2276 3175 y Fo(0)2300
3212 y Fv(.)119 3412 y(5.)49 b Fu(D)325 3427 y Fs(00)432
3412 y Fv(sends)34 b Fr(\010)770 3428 y Fq(\033)r Fs(\()p
Fq(j)868 3437 y Fp(1)904 3428 y Fs(\)=1)p Fq(;\034)8
b Fs(\()p Fq(j)1136 3437 y Fp(2)1171 3428 y Fs(\)=1)1293
3412 y Fu(x)1348 3427 y Fq(j)1377 3436 y Fp(1)1411 3427
y Fq(;j)1460 3436 y Fp(2)1498 3412 y Fv(.)43 b Fu(D)1649
3427 y Fs(01)1757 3412 y Fv(sends)34 b Fr(\010)2095 3428
y Fq(\033)r Fs(\()p Fq(j)2193 3437 y Fp(1)2229 3428 y
Fs(\)=1)p Fq(;\034)2405 3409 y Fe(0)2427 3428 y Fs(\()p
Fq(j)2483 3437 y Fp(2)2518 3428 y Fs(\)=1)2640 3412 y
Fu(x)2695 3427 y Fq(j)2724 3436 y Fp(1)2758 3427 y Fq(;j)2807
3436 y Fp(2)2845 3412 y Fv(.)244 3533 y Fu(D)325 3548
y Fs(10)432 3533 y Fv(sends)g Fr(\010)770 3548 y Fq(\033)812
3529 y Fe(0)836 3548 y Fs(\()p Fq(j)892 3557 y Fp(1)926
3548 y Fs(\)=1)p Fq(;\034)8 b Fs(\()p Fq(j)1158 3557
y Fp(2)1193 3548 y Fs(\)=1)1315 3533 y Fu(x)1370 3548
y Fq(j)1399 3557 y Fp(1)1434 3548 y Fq(;j)1483 3557 y
Fp(2)1520 3533 y Fv(.)44 b Fu(D)1672 3548 y Fs(11)1779
3533 y Fv(sends)34 b Fr(\010)2117 3548 y Fq(\033)2159
3529 y Fe(0)2183 3548 y Fs(\()p Fq(j)2239 3557 y Fp(1)2273
3548 y Fs(\)=1)p Fq(;\034)2449 3529 y Fe(0)2472 3548
y Fs(\()p Fq(j)2528 3557 y Fp(2)2563 3548 y Fs(\)=1)2684
3533 y Fu(x)2739 3548 y Fq(j)2768 3557 y Fp(1)2803 3548
y Fq(;j)2852 3557 y Fp(2)2890 3533 y Fv(.)119 3733 y(6.)49
b(Alice)32 b(X)m(ORs)i(the)g(four)f(bits.)45 b(Since)33
b Fu(x)1694 3748 y Fq(i)1718 3757 y Fp(1)1753 3748 y
Fq(;i)1797 3757 y Fp(2)1869 3733 y Fv(is)g(the)h(only)e(bit)h(that)g
(app)s(eared)g(an)h(o)s(dd)f(n)m(um)m(b)s(er)g(of)244
3854 y(times,)f(the)h(result)f(is)g Fu(x)1124 3869 y
Fq(i)1148 3878 y Fp(1)1183 3869 y Fq(;i)1227 3878 y Fp(2)1265
3854 y Fv(.)146 4071 y(Note)h(that)f(the)h(n)m(um)m(b)s(er)g(of)f(bits)
g(sen)m(t)i(is)e Ft(8)1768 3999 y Fr(p)p 1851 3999 V
72 x Fu(n)22 b Ft(+)g(4)p Fv(.)p 3829 4071 4 66 v 3833
4008 59 4 v 3833 4071 V 3891 4071 4 66 v 0 4358 a Fk(3.2)130
b(A)45 b Fj(k)t Fk(-DB,)e Fj(O)s Fi(\(\()p Fj(k)23 b
Fi(lg)e Fj(k)t Fi(\))p Fj(n)1388 4315 y Fh(1)p Fg(=)p
Fh(lg)13 b Fg(k)s Fh(+lg)h(lg)g Fg(k)1869 4358 y Fi(\))p
Fk(\(?\)-bit)45 b(PIR)e(Sc)l(heme)0 4543 y Fv(The)31
b(PIR)f(sc)m(hemes)i(in)d(this)g(section)h(are)g(from)f(Chor)h(et)g
(al.)f([23].)42 b(W)-8 b(e)30 b(sho)m(w)h(a)f(2-DB)g
Fu(O)s Ft(\()p Fu(n)3398 4507 y Fs(1)p Fq(=)p Fs(3)3507
4543 y Ft(\))p Fv(-bit)f(PIR)0 4663 y(sc)m(heme,)j(whic)m(h)f(con)m
(tains)f(most)f(of)h(the)h(ideas.)42 b(W)-8 b(e)31 b(will)d(then)j(sk)m
(etc)m(h)h(a)e Fu(k)s Fv(-DB)g(case,)i(whic)m(h)f(is)e(similar)0
4784 y(but)k(whose)h(bit)d(complexit)m(y)h(dep)s(ends)i(on)f(op)s(en)f
(questions)i(in)m(v)m(olving)d(co)m(v)m(ering)i(sets.)146
4904 y(In)42 b(the)f(PIR)g(sc)m(heme)i(from)c(Theorem)j(3.2,)h(Alice)d
(sends)i(man)m(y)f(more)f(bits)h(than)g(the)h(database)0
5025 y(sends.)91 b(By)48 b(making)f(the)h(databases)h(send)g(a)e
(comparable)g(n)m(um)m(b)s(er)h(of)f(bits)h(as)g(Alice,)i(the)f(total)0
5145 y(n)m(um)m(b)s(er)33 b(of)f(bits)g(comm)m(unicated)g(b)s(et)m(w)m
(een)i(Alice)e(and)g(the)h(databases)h(can)e(b)s(e)h(reduced.)0
5340 y Fn(Theorem)k(3.3.)42 b Fm([23)o(])35 b(Ther)-5
b(e)34 b(is)h(a)f(a)h(2-DB)f Fu(O)s Ft(\()p Fu(n)1875
5304 y Fs(1)p Fq(=)p Fs(3)1984 5340 y Ft(\))p Fm(-bit)h(PIR)f(scheme.)p
eop end
%%Page: 6 6
TeXDict begin 6 5 bop 0 100 a Fn(KEY)44 b(IDEA:)g(T)-9
b(w)m(o)44 b(databases)j(can)e(do)h(the)f(w)m(ork)f(of)h(eigh)m(t.)72
b(Co)m(v)m(ering)44 b(co)s(des)i(help)e(to)0 220 y(organize)37
b(who)g(do)s(es)i(what.)0 418 y Fm(Pr)-5 b(o)g(of.)48
b Fv(By)32 b(the)f Fu(n)d Ft(=)g(8)j Fv(case)h(of)e(Theorem)i(3.2)e
(there)i(is)f(an)g(8-DB)g Fu(O)s Ft(\()p Fu(n)2682 382
y Fs(1)p Fq(=)p Fs(3)2791 418 y Ft(\))p Fv(-bit)f(PIR)h(sc)m(heme.)44
b(W)-8 b(e)32 b(can)0 538 y(decrease)38 b(the)f(n)m(um)m(b)s(er)h(of)e
(databases)h(from)f(eigh)m(t)g(to)g(t)m(w)m(o)i(b)m(y)f(ha)m(ving)g(t)m
(w)m(o)g(databases)g(sim)m(ulate)f(the)0 659 y(w)m(ork)j(of)f(eigh)m(t)
f(databases.)62 b(In)38 b(particular,)g Fu(D)s(B)1877
674 y Fq(A)1972 659 y Fv(sim)m(ulates)f Fu(D)s(B)2562
674 y Fs(000)2672 659 y Fv(,)i Fu(D)s(B)2896 674 y Fs(001)3006
659 y Fv(,)h Fu(D)s(B)3231 674 y Fs(010)3340 659 y Fv(,)g
Fu(D)s(B)3565 674 y Fs(100)3675 659 y Fv(;)h(and)0 779
y Fu(D)s(B)158 794 y Fq(B)253 779 y Fv(sim)m(ulates)33
b Fu(D)s(B)839 794 y Fs(111)948 779 y Fv(,)i Fu(D)s(B)1168
794 y Fs(011)1278 779 y Fv(,)f Fu(D)s(B)1497 794 y Fs(101)1641
779 y Fv(and)g Fu(D)s(B)1990 794 y Fs(110)2100 779 y
Fv(.)48 b(The)35 b(sim)m(ulation)d(is)h(designed)i(so)f(that)g
Fu(D)s(B)3843 794 y Fq(A)0 899 y Fv(\()p Fu(D)s(B)196
914 y Fq(B)256 899 y Fv(\))c(sim)m(ulates)e(databases)j(whose)f(3-bit)e
(lab)s(els)g(are)i(of)f Fm(Hamming)i(distanc)-5 b(e)36
b Fr(\024)28 b Ft(1)i Fv(from)e(000)h(\(111\).)0 1045
y Fn(2-DB,)37 b Fu(O)s Ft(\()p Fu(n)501 1009 y Fs(1)p
Fq(=)p Fs(3)611 1045 y Ft(\))p Fn(,)g(Information-Theoretic)f(PIR)g(Sc)
m(heme)119 1276 y Fv(1.)49 b(Alice)26 b(views)j(the)f(database)g(as)g
(a)f Fu(n)1558 1240 y Fs(1)p Fq(=)p Fs(3)1681 1276 y
Fr(\002)12 b Fu(n)1828 1240 y Fs(1)p Fq(=)p Fs(3)1951
1276 y Fr(\002)g Fu(n)2098 1240 y Fs(1)p Fq(=)p Fs(3)2236
1276 y Fv(grid.)41 b(Alice)27 b(w)m(an)m(ts)i Fu(x)3042
1291 y Fq(i)3066 1300 y Fp(1)3101 1291 y Fq(;i)3145 1300
y Fp(2)3179 1291 y Fq(;i)3223 1300 y Fp(3)3261 1276 y
Fv(.)42 b(The)29 b(database)244 1396 y(is)j Fu(x)p Fv(.)119
1601 y(2.)49 b(Alice)31 b(generates)j Fu(\033)n(;)17
b(\034)6 b(;)17 b(\021)31 b Fr(2)d(f)p Ft(0)p Fu(;)17
b Ft(1)p Fr(g)1523 1565 y Fq(n)1566 1541 y Fp(1)p Fd(=)p
Fp(3)1699 1601 y Fv(and)32 b(creates)i Fu(\033)2273 1565
y Fo(0)2324 1601 y Ft(=)28 b Fu(\033)e Fr(\010)c Fu(i)2641
1616 y Fs(1)2681 1601 y Fv(,)33 b Fu(\034)2794 1565 y
Fo(0)2845 1601 y Ft(=)28 b Fu(\034)33 b Fr(\010)23 b
Fu(i)3157 1616 y Fs(2)3197 1601 y Fv(,)32 b Fu(\021)3308
1565 y Fo(0)3359 1601 y Ft(=)27 b Fu(\021)3514 1565 y
Fo(0)3560 1601 y Fr(\010)22 b Fu(i)3692 1616 y Fs(3)3732
1601 y Fv(.)119 1806 y(3.)49 b(Alice)35 b(sends)j Fu(\033)n(;)17
b(\034)6 b(;)17 b(\021)40 b Fv(to)c Fu(D)s(B)1317 1821
y Fq(A)1374 1806 y Fv(.)54 b(Clearly)36 b Fu(D)s(B)1956
1821 y Fq(A)2049 1806 y Fv(can)g(sim)m(ulate)f Fu(D)s(B)2781
1821 y Fs(000)2927 1806 y Fv(\(from)g(the)i(original)c(PIR)244
1926 y(sc)m(heme\))c(and)f(send)i(bac)m(k)f(the)f(needed)i(single)d
(bit.)41 b(Consider)28 b(what)h Fu(D)s(B)2977 1941 y
Fq(A)3062 1926 y Fv(m)m(ust)f(do)g(to)g(sim)m(ulate)244
2046 y Fu(D)s(B)402 2061 y Fs(100)512 2046 y Fv(.)76
b Fu(D)s(B)773 2061 y Fq(A)873 2046 y Fv(kno)m(ws)45
b(that)e Fu(D)s(B)1557 2061 y Fs(100)1711 2046 y Fv(w)m(ould)g(ha)m(v)m
(e)i(receiv)m(ed)g(the)f(follo)m(wing)c(strings:)65 b
Fu(\033)3662 2010 y Fo(0)3686 2046 y Fu(;)17 b(\034)6
b(;)17 b(\021)t Fv(.)244 2167 y Fu(D)s(B)402 2182 y Fq(A)493
2167 y Fv(already)34 b(has)h(t)m(w)m(o)g(of)f(the)h(three)g(strings)f
(that)g Fu(D)s(B)2423 2182 y Fs(100)2567 2167 y Fv(has)h(\(namely)-8
b(,)34 b Fu(\034)6 b(;)17 b(\021)t Fv(\))34 b(but)g(do)s(es)h(not)244
2287 y(ha)m(v)m(e)i Fu(\033)531 2251 y Fo(0)555 2287
y Fv(;)h(ho)m(w)m(ev)m(er,)i(it)35 b(kno)m(ws)j(that)e
Fu(\033)1698 2251 y Fo(0)1757 2287 y Fv(and)h Fu(\033)j
Fv(\(whic)m(h)d(it)e(do)s(es)i(ha)m(v)m(e\))g(di\033er)f(b)m(y)h(only)f
(one)h(bit.)244 2408 y Fu(D)s(B)402 2423 y Fq(A)501 2408
y Fv(can)43 b(create)h(and)f(use)g(all)e Fu(n)1570 2371
y Fs(1)p Fq(=)p Fs(3)1723 2408 y Fv(p)s(ossible)h(v)-5
b(alues)43 b(of)f Fu(\033)2581 2371 y Fo(0)2604 2408
y Fv(.)74 b(Sp)s(eci\034cally)-8 b(,)44 b Fu(D)s(B)3404
2423 y Fq(A)3504 2408 y Fv(generates)244 2528 y Fu(\033)29
b Fr(\010)c Fu(i)37 b Fv(for)f Ft(0)f Fr(\024)g Fu(i)g(<)f(n)1085
2492 y Fs(1)p Fq(=)p Fs(3)1196 2528 y Fv(.)55 b(Eac)m(h)38
b(of)e(the)h(strings)g(generated)g(is)f(a)h(candidate)f(for)g
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b(2)0 4131 y Fv(bits.)p 3829 4131 4 66 v 3833 4069 59
4 v 3833 4131 V 3891 4131 4 66 v 0 4413 a Fn(Note)52
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%%Page: 7 7
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%%Page: 8 8
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Fv(,)27 b(whic)m(h)e(means)h(that)f(it)f(sim)m(ulates)g(the)i(rest)g
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b(A)38 b(database)g(of)g(Hamming)e(distance)i Fu(h)g
Fv(transmits)f Fu(O)s Ft(\(2)3521 1083 y Fq(h)3565 1119
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Fs(1)3862 1119 y Ft(\))244 1239 y Fv(bits.)67 b(Hence)42
b Fu(D)s(B)952 1254 y Fq(B)1053 1239 y Fv(will)c(transmit)h
Fu(O)s Ft(\(2)1814 1203 y Fs(2)p Fq(k)r Fo(\000)p Fs(3)1981
1239 y Fu(n)2039 1203 y Fs(\(2)p Fq(k)r Fo(\000)p Fs(3\))p
Fq(=)p Fs(\(2)p Fq(k)r Fo(\000)p Fs(1\))2516 1239 y Ft(\))i
Fv(bits)f(bac)m(k)h(to)g(Alice.)66 b(Alice)39 b(only)244
1360 y(uses)34 b(the)f Ft(2)668 1324 y Fs(2)p Fq(k)r
Fo(\000)p Fs(3)859 1360 y Fr(\000)23 b Fu(k)i Fr(\000)e
Ft(1)32 b Fv(bits)h(corresp)s(onding)g(to)f(the)h(correct)h(guesses)h
(as)e(to)f(the)i(queries)f(that)244 1480 y(w)m(ould)f(ha)m(v)m(e)i(b)s
(een)f(ask)m(ed.)p 3829 1716 4 66 v 3833 1654 59 4 v
3833 1716 V 3891 1716 4 66 v 146 1921 a(W)-8 b(e)33 b(use)h(the)f
(lopsided)f(PIR)g(sc)m(heme)i(to)e(build)g(a)g(PIR)h(sc)m(heme)g(of)f
(the)h(desired)g(complexit)m(y)-8 b(.)0 2130 y Fn(Theorem)37
b(3.7.)42 b Fm([2)o(])35 b(F)-7 b(or)34 b(al)5 b(l)35
b Fu(k)i Fm(ther)-5 b(e)35 b(is)g(a)f Fu(k)s Fm(-DB)g
Fu(O)s Ft(\(2)2108 2094 y Fq(k)2147 2070 y Fp(2)2185
2130 y Fu(n)2243 2094 y Fs(1)p Fq(=)p Fs(2)p Fq(k)r Fo(\000)p
Fs(1)2482 2130 y Ft(\))p Fm(-bit)g(scheme.)0 2338 y Fn(KEY)52
b(IDEAS:)f(The)i Fu(k)j Fn(databases)f(sim)m(ulate)c(the)h(t)m(w)m(o)g
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b(Since)44 b(Alice)f(only)i(needs)h(one)f(bit)f(of)i(what)f(the)g
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(PIR)e(sc)m(heme)h(recursiv)m(ely)f(to)h(get)g(that)g(bit.)0
2785 y Fm(Pr)-5 b(o)g(of.)48 b Fv(W)-8 b(e)36 b(build)d(the)i(PIR)g(sc)
m(heme)i(b)m(y)e(induction.)50 b(The)35 b(base)h(case)g(is)e(the)h
(2-DB)g Fu(O)s Ft(\()p Fu(n)3393 2749 y Fs(1)p Fq(=)p
Fs(3)3502 2785 y Ft(\))p Fv(-bit)f(PIR)0 2906 y(sc)m(heme)d(from)d
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(a)g Fu(k)19 b Fr(\000)d Ft(1)p Fv(-DB,)30 b Fu(O)s Ft(\(2)3256
2869 y Fs(\()p Fq(k)r Fo(\000)p Fs(1\))3439 2846 y Fp(2)3478
2906 y Fu(n)3536 2869 y Fs(1)p Fq(=)p Fs(\(2)p Fq(k)r
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3173 y Fu(k)s Fn(-DB,)37 b Fu(O)s Ft(\(2)490 3137 y Fq(k)529
3114 y Fp(2)567 3173 y Fu(n)625 3137 y Fs(1)p Fq(=)p
Fs(2)p Fq(k)r Fo(\000)p Fs(1)864 3173 y Ft(\))g Fn
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b(Alice)31 b(has)i Fu(i)g Fv(and)g(w)m(an)m(ts)h Fu(x)1252
3424 y Fq(i)1280 3409 y Fv(.)119 3618 y(2.)49 b(Alice)31
b(b)s(egins)i(to)f(sim)m(ulate)f(the)i(lopsided)f(proto)s(col)f(b)m(y)i
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b(\033)3035 3633 y Fs(2)3074 3618 y Fu(;)g(:)g(:)g(:)f(;)h(\033)3348
3633 y Fs(2)p Fq(k)r Fo(\000)p Fs(1)3549 3618 y Fv(in)244
3738 y Fr(f)p Ft(0)p Fu(;)g Ft(1)p Fr(g)486 3702 y Fq(n)529
3679 y Fp(1)p Fd(=)p Fp(2)p Fd(k)q Fe(\000)p Fp(1)773
3738 y Fv(and)33 b(forming)d(for)i Ft(1)c Fr(\024)g Fu(j)34
b Fr(\024)28 b Ft(2)p Fu(k)d Fr(\000)d Ft(1)p Fv(,)33
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3962 y Fq(A)2701 3947 y Fv(\))h(and)h Fu(\033)3020 3911
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3911 y Fo(0)3329 3973 y Fs(2)p Fq(k)r Fo(\000)p Fs(1)3530
3947 y Fv(to)32 b(all)f(of)244 4112 y Fu(D)s(B)402 4127
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4127 y Fq(k)899 4112 y Fv(\(who)40 b(will)d(collectiv)m(ely)h(sim)m
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2921 4127 y Fs(2)p Fq(k)r Fo(\000)p Fs(1)3129 4112 y
Fr(2)39 b Fv(to)g Fu(D)s(B)3518 4127 y Fs(1)3557 4112
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4196 y Fs(1)p Fq(=)p Fs(2)p Fq(k)r Fo(\000)p Fs(1)1436
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Fs(\(2)p Fq(k)r Fo(\000)p Fs(1\))3635 4441 y Ft(\))g
Fv(bits.)119 4650 y(5.)49 b(Eac)m(h)32 b(of)f(these)i(databases)f
Fu(D)s(B)1446 4665 y Fs(2)1486 4650 y Fu(;)17 b(:)g(:)g(:)e(;)i(D)s(B)
1862 4665 y Fq(k)1936 4650 y Fv(runs)32 b(the)g(lopsided)f(PIR)h(sc)m
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4785 y Fq(B)571 4770 y Fv(,)h(and)g(computes)g Fu(O)s
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b(These)31 b(bits)f(are)g(not)f(sen)m(t)j(bac)m(k)e(to)g(Alice,)244
4890 y(but)j(are)f(left)g(at)g(the)h(database.)119 5099
y(6.)49 b(Alice)36 b(and)i Fu(D)s(B)848 5114 y Fs(2)888
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b(Alice)244 5220 y(priv)-5 b(ately)35 b(retriev)m(es)i(the)g
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5340 y(sc)m(heme)e(inductiv)m(ely)-8 b(.)43 b(This)32
b(tak)m(es)p eop end
%%Page: 9 9
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m(t)g Fu(k)s Ft(!)p Fv(.)63 b(Ishai)38 b(and)h(Kushilevitz)e(use)j(an)0
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b(are)f(imp)s(ortan)m(t)f(since)i(the)g(new)g(tec)m(hniques)i(they)e
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y(sc)m(heme)f(using)e Fu(<<)27 b(n)826 1792 y Fs(1)p
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2121 y Fk(3.4)130 b(A)45 b Fj(k)t Fk(-DB)e Fj(n)859 2078
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Fh(\))1425 2121 y Fk(-bit)44 b(PIR)g(Sc)l(heme)0 2307
y Fv(The)33 b(PIR)g(sc)m(heme)h(in)e(this)g(c)m(hapter)h(is)g(from)e
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(database)i(as)f(a)g(p)s(olynomial.)0 2661 y(De\034nition)e(3.9.)42
b Fv(Let)33 b Fu(x)28 b Fr(2)g(f)p Ft(0)p Fu(;)17 b Ft(1)p
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Fu(d;)17 b(m)32 b Fv(b)s(e)h(suc)m(h)h(that)2400 2580
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Fq(m)2512 2867 y Fv(that)32 b(has)h(exactly)g Fu(d)f
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3224 y Fq(E)t Fs(\()p Fq(i)p Fs(\))1952 3234 y Fd(j)s
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(heme)p eop end
%%Page: 10 10
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%%Page: 12 12
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%%Page: 13 13
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%%Page: 22 22
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m(hemes.)p eop end
%%Page: 25 25
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%%Page: 26 26
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5069 y(of)32 b(Comp.)g(Sci.)p FD(,)e(pages)g(364\025373,)i(1997.)0
5227 y([48])49 b(E.)29 b(Kushilevitz)h(and)f(R.)f(Ostro)m(vsky)-8
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%%Page: 31 31
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FD(,)e(1999.)0 1416 y([54])49 b(N.)41 b(Nisan)g(and)h(A.)f(Wigderson.)
73 b(Hardness)41 b(vs)g(randomness.)74 b FB(Journal)43
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2205 y(\(LNCS)e(1514\)\))p FD(,)g(pages)f(357\025371,)i(1998.)0
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2468 y(The)-5 b(ory)p FD(,)31 b(IT-34:237\025245,)h(1988.)0
2619 y([59])49 b(A.)43 b(Y)-8 b(amam)m(ura)45 b(and)e(T.)f(Saito.)78
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b(based)g(on)g(subgroup)g(mem)m(b)s(ership)189 2731 y(problem.)f(In)30
b FB(Pr)-5 b(o)g(c.)34 b(of)e(the)g(6th)h(A)n(ustr)-5
b(alasian)32 b(Conf.,)f(A)n(CISP)g(2001)p FD(,)g(2001.)0
2882 y([60])49 b(A.)26 b(Y)-8 b(ao.)33 b(An)25 b(application)i(of)e
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b(,)29 b(1990.)k(Lecture)27 b(DIMA)m(CS)189 2995 y(W)-8
b(orkshop)31 b(on)g(Structural)h(Complexit)m(y)f(and)g(Cryptograph)m(y)
-8 b(.)p eop end
%%Trailer

userdict /end-hook known{end-hook}if
%%EOF