%PDF-1.4 % 5 0 obj << /S /GoTo /D (section.1) >> endobj 8 0 obj (1. Introduction) endobj 9 0 obj << /S /GoTo /D (section.2) >> endobj 12 0 obj (2. Number-theoretic problems) endobj 13 0 obj << /S /GoTo /D (subsection.2.1) >> endobj 16 0 obj (2.1. The discrete logarithm problem) endobj 17 0 obj << /S /GoTo /D (subsection.2.2) >> endobj 20 0 obj (2.2. Factoring large integers) endobj 21 0 obj << /S /GoTo /D (section.3) >> endobj 24 0 obj (3. Public key cryptosystems) endobj 25 0 obj << /S /GoTo /D (subsection.3.1) >> endobj 28 0 obj (3.1. RSA Cryptosystem) endobj 29 0 obj << /S /GoTo /D (subsection.3.2) >> endobj 32 0 obj (3.2. ElGamal cryptosystem) endobj 33 0 obj << /S /GoTo /D (section.4) >> endobj 36 0 obj (4. Digital signature) endobj 37 0 obj << /S /GoTo /D (subsection.4.1) >> endobj 40 0 obj (4.1. RSA digital signature scheme) endobj 41 0 obj << /S /GoTo /D (subsection.4.2) >> endobj 44 0 obj (4.2. Schnorr's digital signature scheme) endobj 45 0 obj << /S /GoTo /D (section.5) >> endobj 48 0 obj (5. Zero knowledge proof) endobj 49 0 obj << /S /GoTo /D (subsection.5.1) >> endobj 52 0 obj (5.1. Fiat-Shamir identification protocol) endobj 53 0 obj << /S /GoTo /D (subsection.5.2) >> endobj 56 0 obj (5.2. Schnorr's zero-knowledge protocol) endobj 57 0 obj << /S /GoTo /D (section.6) >> endobj 60 0 obj (6. A group signature scheme based on the discrete logarithm problem) endobj 61 0 obj << /S /GoTo /D (subsection.6.1) >> endobj 64 0 obj (6.1. Premises) endobj 65 0 obj << /S /GoTo /D (subsection.6.2) >> endobj 68 0 obj (6.2. Group signature algorithm) endobj 69 0 obj << /S /GoTo /D (section.7) >> endobj 72 0 obj (7. Group signature scheme based on elliptic curves) endobj 73 0 obj << /S /GoTo /D (subsection.7.1) >> endobj 76 0 obj (7.1. Premises) endobj 77 0 obj << /S /GoTo /D (subsection.7.2) >> endobj 80 0 obj (7.2. Algebraic settings) endobj 81 0 obj << /S /GoTo /D (subsection.7.3) >> endobj 84 0 obj (7.3. Elliptic curve group signature algorithm) endobj 85 0 obj << /S /GoTo /D (section.8) >> endobj 88 0 obj (8. Conclusions and comparison) endobj 89 0 obj << /S /GoTo /D (section*.2) >> endobj 92 0 obj (Acknowledgments) endobj 93 0 obj << /S /GoTo /D (section*.3) >> endobj 96 0 obj (References) endobj 97 0 obj << /S /GoTo /D [98 0 R /Fit ] >> endobj 103 0 obj << /Length 2730 /Filter /FlateDecode >> stream xڍv8Э" ILN$8Xr`HQOm)[7P( z<{&ГDֆDll&F*Mr=]42ުQUe{."W1uWW9]UL-êxت {32MWtFg|#x|~z&D.:̴Vidyb~lڛYj}s}%۩Iݿx}_;UdV6kr뎕pw$^KlpE+XY-HA寮柗%M_.HH7o./?.z|Y?9d4c^~o>|f ۏ,9.?\t4U03q T%_A =Xf9:3,͇Wo3MGòE /ux+Fʄ3\tCpnY$nS^+^Ӥusͪ??3* "X0VdM[gSNX,8z_Yf "w[nk\I<ʕ۷<~Cf]\3s1;o g^);'^\-p[7&o&ߔ?"w ds|o ZuFI@[g|MBalFG8@ LdQ+&֮ZVo1 BkPH6CcX 7LGjo9WDİ"IKIFjy]s֭J:v8B3/nx4rta}ԃIb Y@S*(6$U }ͤϪ*;kPiNǮr.^i݀? o&U%quЏB{0Ɲ0$ghboR˪0Z54xq|7Rq"{R"0(iV'@%\skW@\:?4k[#W1jȇw_1qFkauę# E@&ی$#x+טg,ʊN_˚"BkQ 5OS$q8 n[eSt >j}Y!/WV5u rGP=N_%H6#HiKFeB %%Q?94*j༄6eVOCӂ݅~HKBQ":JD)z&\ftJeEB*+"}eEkMO93\N4 e,"avIj&*'2b2zBDJ$LS]BJ6Vh"0M81I A1!E< AfNYJ/fcQxt<UYԃyj/CZ{@[L"」~ԫX) 3pE*SfC!>wxp5ލx@- Ra c->T"܍Ldu;G/Z|s̋={Dݲ/Lg7lՂC4-_;f2v4MJ7*@\Oc&Xl-cnvM .a `8 6gP!ؑBaN($+FgŁ>TTK[n3)p0AXq'}u ?RF}P]Vodd^)ǪChnwt[ +ܛb 1sM@:GtфDY> k ͇*뉝-G͢\uSKV2``(J _y{~âo6c- djv;ܹuIYhp(>ph#|w@\3 K$ !_ ԉWH$^;*95+ӈcw&(>]㳍b?ڍoptf"qrt2; 3C;B""劅N.CY+Gn=ϐG娡 GELl2TQ!숕ĵS4rLwIH7Vdk"h-gdW2gK LK|%$IESU94qn*>O,uVBK!'BUꪐeHa4r{I'z!㴏憺Ocڵ czir&}Pij\{c$3tm*ê8͟aRALDc|Mg>{/Gw:kIvH N!mƪEw"3](1EC%u<}<ԁU&'_^Ph#yk֏ g:aI@Iɫ=Tt|+bmo LHQ7q~,AKK^16tƋG)<`?N5*
> endobj
99 0 obj <<
/Type /Annot
/Border[0 0 1]/H/I/C[0 1 0]
/Rect [476.583 355.939 483.556 364.352]
/Subtype /Link
/A << /S /GoTo /D (cite.ch91) >>
>> endobj
100 0 obj <<
/Type /Annot
/Border[0 0 1]/H/I/C[0 1 0]
/Rect [389.717 248.343 396.69 256.756]
/Subtype /Link
/A << /S /GoTo /D (cite.cs97) >>
>> endobj
101 0 obj <<
/Type /Annot
/Border[0 0 1]/H/I/C[0 1 0]
/Rect [203.389 217.829 210.363 226.242]
/Subtype /Link
/A << /S /GoTo /D (cite.cam97) >>
>> endobj
104 0 obj <<
/D [98 0 R /XYZ 126.672 689.898 null]
>> endobj
105 0 obj <<
/D [98 0 R /XYZ 126.672 675.95 null]
>> endobj
6 0 obj <<
/D [98 0 R /XYZ 126.672 386.823 null]
>> endobj
113 0 obj <<
/D [98 0 R /XYZ 126.672 235.447 null]
>> endobj
102 0 obj <<
/Font << /F31 106 0 R /F30 107 0 R /F34 108 0 R /F15 109 0 R /F33 110 0 R /F32 111 0 R /F8 112 0 R /F14 114 0 R /F36 115 0 R /F19 116 0 R /F7 117 0 R >>
/ProcSet [ /PDF /Text ]
>> endobj
135 0 obj <<
/Length 2627
/Filter /FlateDecode
>>
stream
xڭr6>_PU߹9N*Sٝx0,"8|HƩ4F݇͒ y*vDiv7^ΝiB_2,a< Ə"6L0LO*O> <>|dnQVn3/6cF7|jFJR7TmNWG9Ǎtn*u'a/842=yXFL't 9پ9 p]ffQ9A8M> C"Q4j<Ԉ"zw]EDoWpE ~̕d))!2Ǯ}OeUC3HW+PhZh6B9dMȉjpX<({ߏG