Spartan: Efficient and general-purpose zkSNARKs without trusted setup

Spartan Review in Japanese , Spartanの解説(暗号通貨輪読会 #31) @ the University of Tokyo

Title: Spartan: Efficient and general-purpose zkSNARKs without trusted setup
Author: Srinath Setty (Microsoft Research)
Published: May 22, 2019
Link: https://eprint.iacr.org/2019/550

P.S. (追記) Aug 3, 2019
added 52nd page, 52ページ目追加しました。

Transcript

1. 4QBSUBO ʲ҉߸௨՟ྠಡձʳ4QBSUBO
   !
   ϑϨηοπɺ౦ژେֶೆݚڀ౩
   
   ϑϩϯςΟΞύʔτφʔζ߹ಉձࣾ
   ૑ۀऀ୅ද$&0
   6OJUFE
   #JUDPJOFST
   *OD
   ڞಉ૑ۀऀ$50
   ϑϨηοπגࣜձࣾɹٕज़ސ໰
   ࠓҪਸ໵
2. ࣗݾ঺հ ϑϩϯςΟΞύʔτφʔζ߹ಉձࣾ ୅දCEO United Bitcoiners Inc. ڞಉ૑ۀऀˍऔక໾CTO ϑϨηοπגࣜձࣾɹٕज़ސ໰ ϚελϦϯάϏοτίΠϯɺ຋༁ऀ୅ද ੈքͰॳΊͯͷɺ೔ຊޠʹΑΔϏοτίΠϯɾϒϩοΫνΣʔ ϯͷৄࡉٕज़ॻ(NTTग़൛ࣾ) શମͷׂ̕Λ຋༁ ୈ̍̎࡮ 2016/7/14ग़൛ ిࢠॻ੶൛(kindle)΋ ΦʔϓϯΤσΟγϣϯ൛ https://www.bitcoinbook.info ίϯαΠε൛ͱ߹Θͤͯ13,300෦ൃߦ
3. ࣗݾ঺հ όοΫάϥ΢ϯυ ৽ׁେֶେֶӃɹૉཻࢠཧ࿦෺ཧɹത࢜(ཧ) ΦϑνΣʔϯΞΧσϛʔ୅ද ೔ຊͰ࠷ॳͷϥΠτχϯάωοτϫʔΫϋοΧιϯ(off-chain academy hackday)Λओ ࠵ ΧΧΫίϜ ݕࡧΤϯδϯ։ൃɹݕࡧαʔόΫϥελߏஙӡ༻ɹେن໛σʔλॲཧɹػցֶ शɹը૾ೝࣝ σʔλλϫʔגࣜձࣾɹ୅දऔక໾
4. ໨࣍ w ࿦จͷ֓ཁ
   w ࿦จͷத਎
    *OUSPEVDUJPO
    3FMBUFE
   XPSL
    1SFMJNJOBSJFT
    0WFSWJFX
   PG
   4QBSUBO
    "
   OFX
   QVCMJD
   DPJO
   TVDDJODU
   JOUFSBDUJWF
   BSHVNFOU
   GPS
   /1
    $PNQVUBUJPO
   DPNNJUNFOUT
   "
   UFDIOJRVF
   UP
   BDIJFWF
   TVCMJOFBS
   WFSJpDBUJPO
   UJNF
5. ࿦จͷ֓ཁ w 5JUMF
   w 4QBSUBO
   &⒏DJFOU
   BOE
   HFOFSBMQVSQPTF
   [L4/"3,T
   XJUIPVU
   USVTUFE
   TFUVQ
   w "VUIPS
   w 4SJOBUI
   4FUUZ
   .JDSPTPGU
   3FTFBSDI
   w 1VCMJTIFE
   w .BZ
   
   
   w -JOL
   w IUUQTFQSJOUJBDSPSH
6. IUUQTXXXNJDSPTPGUDPNFOVTSFTFBSDIQFPQMFTSJOBUI
7. IUUQTFQSJOUJBDSPSH
8. https://twitter.com/VitalikButerin/status/1131636529481359364
9. ࿦จͷ֓ཁ ݕূऀͷෛ୲ΛͲ͏΍ͬͯܰݮ͢Δ͔ʁ
   
   #VMMFUQSPPG͸0 O ɺ4QBSUBO͸0 O? 
10. ࿦จͷ֓ཁ ݕূऀͷෛ୲ΛͲ͏΍ͬͯܰݮ͢Δ͔ʁ
    
    #VMMFUQSPPG͸0 O ɺ4QBSUBO͸0 O? 
11. ࿦จͷ֓ཁ ݕূऀͷෛ୲ΛͲ͏΍ͬͯܰݮ͢Δ͔ʁ
    
    લ͸ઢܗ࣌ؒͰղ͚ΔΑ͏ʹ͢Δ͜ͱʹҙຯ͕͋ͬͨ ͕ɺ࠷ۙ͸TVCMJOFBS ྼઢܗ ࣌ؒͱ͍͏ઢܗ࣌ؒΑΓ΋ ୹͍ෛ୲Ͱղ͚ΔΑ͏ʹɻ
12. ࿦จͷ֓ཁ ͡Ό͋[L45"3,TͰΑ͍ͷͰ͸ʁ
    
    ࢖༻Ͱ͖Δ৔߹͕ݶΒΕͯ͠·͏ɻ
    ·ͨɺ݈શੑͷূ໌ʹ·ͩάϨʔͳ఺͕͋Δɻ
13. ࿦จͷ֓ཁ ໨త͸ɺར༻৔໘ΛݶΒΕΔ͜ͱͳ͘ɺ
    ηΩϡϦςΟతʹڧݻ͔ͭ࢖͍΍͍͢҉߸ֶతલఏͰɺ
    ূ໌ऀͱݕূऀͷ
    ܭࢉ͓ΑͼίϛϡχέʔγϣϯίετΛԼ͛Δ͜ͱ
    
    4QBSUBO
14. ࿦จͷ֓ཁ ิ଍
    
    QSJWBUF
    DPJO
    QVCMJD
    DPJOͱ͍͏ͷ͕ग़͖ͯ·͕͢ɺ
    ͜ͷzDPJOzͱ͍͏ͷ͸
    ϥϯμϜ஋ΛܾΊΔίΠϯτε͔Βདྷ͍ͯ·͢ɻ
15. 
    *OUSPEVDUJPO
18. [L4/"3,T w[FSP
    LOPXMFEHF
    wূ໌ऀ 1SPWFS ͸ݕূऀ 7FSJpFS ʹൿີΛ౉͢͜ͱͳ͘
    w4VDDJODU
    w؆ܿͰ
    w/POJOUFSBDUJWF
    wඇର࿩ͳܗͰ
    w"3HVNFOU
    PG
    ,OPXMFEHF
    w஌ࣝͷࠜڌΛ౉͢ํ๏
    wl1SPPGz
    PG
    ,OPXMFEHFͰ͸ͳ͍ɻ
19. ;FSP
    ,OPXMFEHF
    1SPPG
    θϩ஌ࣝূ໌ w[FSP
    LOPXMFEHF
    wূ໌ऀ 1SPWFS ͸ݕূऀ 7FSJpFS ʹൿີΛ౉ ͢͜ͱͳ͘
    wྫ
    5VNCMF#JU
    w4VDDJODU ؆ܿ ͔͸ஔ͍͓͍ͯͯ
20. IUUQXXXVOJUFECJUDPJOFSTDPNCMPHUVNCMFCJU
21. IUUQXXXVOJUFECJUDPJOFSTDPNCMPHUVNCMFCJU
22. IUUQXXXVOJUFECJUDPJOFSTDPNCMPHUVNCMFCJU
23. /POJOUFSBDUJWF
    ඇର࿩ܕ "MJDF ূ໌ऀ #PC ݕূऀ ίϛοτϝϯτ νϟϨϯδ ϓϧʔϑ ਖ਼͍͔͠ΛνΣοΫ ͜Ε͸4JHNB
    1SPUPDPMͱݺ͹ΕΔର࿩ܕ
24. /POJOUFSBDUJWF
    ඇର࿩ܕ "MJDF ূ໌ऀ #PC ݕূऀ ίϛοτϝϯτ ϓϧʔϑ ਖ਼͍͔͠ΛνΣοΫ ͜Ε͸ඇର࿩ܕɻ
    'JBU4IBNJSώϡʔϦεςΟοΫͱ͔ɺ
    $PNNPO
    3FGFSFODF
    4USJOH $34 ͱ͔͕ؔ࿈ɻ
25. ༻ޠઆ໌ w5SBOTQBSFOU ಁ໌ͳ
    [L4/"3,
    w
    [L4/"35
    XJUIPVU
    USVTUFE
    TFUVQ ࣄલʹ৴ ༻͞ΕͨηοτΞοϓ͕͍Βͳ͍
    wd
    [L45"3,
28. 
    3FMBUFE
    XPSL
31. 1$1 1SPCBCJMJTUJDBMMZ
    $IFDLBCMF
    1SPPGT
    ֬཰తʹ֬ೝՄೳͳূ໌ wূ໌ऀ͕౴͑Λ஌͓ͬͯΓɺ·ͨਖ਼͍͠ϓϩτίϧΛ༻ ͍Ε͹ɺߴ͍֬཰Ͱݕূऀʹೲಘͤ͞Δ͜ͱ͕Ͱ͖Δ
    w͜ͷ֬཰͕ߴ͍͜ͱΛ׬શੑ $PNQMFUFOFTT ͕͋Δ ͱ͍͏ɻ
    wূ໌ऀ͕ӕ ౴͑Λ஌Βͳ͍ͷʹ஌͍ͬͯΔͱݴ͏ Λͭ ͍ͯ͠·ͬͯ΋௨ͬͯ͠·͏͔΋ɻ
    wূ໌ऀ͕ӕΛ͍ͭͨ৔߹ʹݕূऀ͕ӕͩͱ൑அ͢Δ֬ ཰͕ߴ͍͜ͱΛ݈શੑ 4PVOEOFTT ͕͋Δͱ͍͏ɻ
32. 1$1ʹ·ͭΘΔྺ࢙ w೥Ҏલ͸੩తূ໌ TUBUJD
    QSPPG
    w೥୅ɺ೥୅͸*OUFSBDUJWF
    1SPPG ର࿩ܕূ໌
    w*OUFSBDUJWF
    l1SPPGz͸׬શੑɺ݈શੑ "SHVNFOUͰ͸ͳ͘
    w࣮༻ੑ͸ஔ͍͓͍ͯͯɺର࿩ܕʹ͢Δ͜ͱͰ׬ᘳΛٻΊͯ Έͨ
    w࣍ୈʹ1$1ʹҠ͍ͬͯ͘
    w*OUFSBDUJWF
    1SPPGΛߦ͏ͨΊʹTVNDIFDL
    QSPUPDPM͕ ग़͖ͯͨͷ͕೥ IUUQTQFPQMFFFDTCFSLFMFZFEVdBMFYDIEPDT$44MFDUVSFQEG
33. 1$1ʹ·ͭΘΔྺ࢙ w1$1͸೥͔Β
    wTIPSU
    1$1
    ೥
    wMJOFBS
    1$1
    ೥
    w((13 ॳΊͯͷ2"1
    1JOPDDIJP
    ೥
    w(SPUI
    ೥
34. 1$1ʹ·ͭΘΔྺ࢙ 4UBUJD
    1SPPG *OUFSBDUJWF
    1SPPG .*1 .VMUJ
    1SPWFST (,3
    EPVCMZ
    F⒏DJFOU
    *1
    ೥ %BUB
    QBSBMMFMJTN
    DJSDVJU
    TUSVDUVSF 1$1 TIPSU
    1$1 MJOFBS
    1$1 2"1 *01 *OUFSBDUJWF
    0SBDMF
    1SPPG 
    [L45"3, ೥ Ұ෦ಡΈҧ͑ͯΔ͔΋͠Ε·ͤΜ *OOFS
    1SPEVDU #VMMFUQSPPG ೥ 4QBSUBO 4VN$IFDL
    1SPUPDPM 1PMZOPNJBM
    $PNNJUNFOU
    4DIFNF
    
    $PNQVUBUJPO
    $PNNJUNFOU
    )ZSBY
    ೥ 1JOPDDIJP
    (SPUI
35. 1$1ʹ·ͭΘΔྺ࢙ 2"1 *OUFSBDUJWF
    1$1 EPVCMZ
    F⒏DJFOU
    *1 *OOFS
    1SPEVDU *01
36. [L4/"3,zTz w[L4/"3,͸ݻ༗໊ࢺͰ͸ͳ͍ͬ͘ͺ͍͋Δ
    w4VDDJODU ؆ܿ Ͱ͋Δ͔Ͳ͏͔
37. 
    1SFMJNJOBSJFT
40. "SJUINFUJD
    $JSDVJU
    4BUJTpBCJMJUZ
    ࢉज़ճ࿏ॆ଍Մೳੑ wॆ଍ՄೳੑΛௐ΂Δ͜ͱΛɺ4BUJTpBCJMJUZ
    1SPCMFN ॆ଍Մೳੑ໰୊ ͱ͍͍ɺ4"5ͱུه͢Δɻ
    wͨͩී௨4"5ͱ͍͏࣌͸
    Y㱹Y㱹ʜ 㱸 Y㱹™Y㱹ʜ 㱸ʜ
    ͷΑ͏ͳܗΛͨ͠ ࿦ཧࣜͷ૊Έ߹Θ͕ͤଘࡏ͢Δ͔Ͳ͏͔ͷ໰୊Λࢦ ͢Α͏ɻ
    w͜Ε͸۩ମతͳ΋ͷ͕ͳ͍ͱΠϝʔδ͕͚ͭͮΒ͍ɻ ޙ΄Ͳɻ
41. 4VN$IFDL
    1SPUPDPM wॆ଍ՄೳੑΛௐ΂Δͱ͖ʹ࢖͏ϓϩτίϧͷ̍ͭ
    wͳΜͱͳ͘ͷΠϝʔδ ຊ౰͸ͪΐͬͱҧ͍·͕͢
    w"MJDF͸ɺٱอాͱീւࢁ ڞʹ৽ׁͷ೔ຊञ ͷར͖ ञ͕Ͱ͖Δͱࣗຫ͍ͯ͠Δɻ
    w#PC͸ɺຊ౰ʹ"MJDFʹར͖ञ͕Ͱ͖Δ͔Ͳ͏͔Λࢼ ͍ͨ͠ɻ
    wͲ͏΍Δ͔ʁ
42. 4VN$IFDL
    1SPUPDPM  #PC͸ɺ
    ͱϥϕϧ͕షΒΕͨίοϓʹٱอాͱീւࢁΛೖΕɺͲͪΒͷϥ ϕϧͷίοϓʹٱอాΛೖΕ͔ͨΛϝϞ͓֮ͯ͑ͯ͘͠ɻ
     #PC͸ɺ"MJDFʹϥϕϧͷ৘ใΛӅͨ͠ঢ়ଶͰ̎ͭͷίοϓΛ"MJDFʹ౉͠ɺͲ ͪΒ͕ٱอా͔Λڭ͑ΔΑ͏ʹݴ͏ɻ
     "MJDF͸ɺ೔ຊञΛವΈɺϥϕϧΛ#PCʹ౴͑Δɻ
     #PC͸"MJDF͕౰͔ͨͬͨͲ͏͔ΛνΣοΫ͠ɺ౰͔ͨͬͨͲ͏͔ΛϝϞ͢ Δɻ౰ͨͬͨ৔߹͸5SVFɺؒҧͬͨ৔߹͸'BMTFΛΞ΢τϓοτͱͯ͢͠Δɻ
     #PC͸खॱʹ໭Γɺ͜ΕΛ̍̌ճ܁Γฦ͢ɻ
     #PC͸̍̌ճ܁Γฦͨ͠ͷͪɺΞ΢τϓοτશͯͷ࿦ཧੵΛऔΔɻ݁Ռ͕ 5SVFͰ͋Ε͹"MJDFʹར͖ञͷೳྗ͕͋Δͱ൑அ͢Δɻ
43. 4VN$IFDL
    1SPUPDPM
44. "SJUINFUJD
    $JSDVJU
    4BUJTpBCJMJUZ
    ࢉज़ճ࿏ॆ଍Մೳੑ wॆ଍ՄೳੑΛௐ΂Δ͜ͱΛɺ4BUJTpBCJMJUZ
    1SPCMFN ॆ଍Մೳੑ໰୊ ͱ͍͍ɺ4"5ͱུه͢Δɻ
    wͨͩී௨4"5ͱ͍͏࣌͸
    Y㱹Y㱹ʜ 㱸 Y㱹™Y㱹ʜ 㱸ʜ
    ͷΑ͏ͳܗΛͨ͠ ࿦ཧࣜͷ૊Έ߹Θ͕ͤଘࡏ͢Δ͔Ͳ͏͔ͷ໰୊Λࢦ ͢Α͏ɻ
    w͜Ε͸۩ମతͳ΋ͷ͕ͳ͍ͱΠϝʔδ͕͚ͭͮΒ͍ɻ ޙ΄Ͳɻ
45. 1$1ʹ·ͭΘΔྺ࢙ 4UBUJD
    1SPPG *OUFSBDUJWF
    1SPPG .*1 .VMUJ
    1SPWFST (,3
    EPVCMZ
    F⒏DJFOU
    *1
    ೥ %BUB
    QBSBMMFMJTN
    DJSDVJU
    TUSVDUVSF 1$1 TIPSU
    1$1 MJOFBS
    1$1 2"1 *01 *OUFSBDUJWF
    0SBDMF
    1SPPG 
    [L45"3, ೥ Ұ෦ಡΈҧ͑ͯΔ͔΋͠Ε·ͤΜ *OOFS
    1SPEVDU #VMMFUQSPPG ೥ 4QBSUBO 4VN$IFDL
    1SPUPDPM 1PMZOPNJBM
    $PNNJUNFOU
    4DIFNF
    
    $PNQVUBUJPO
    $PNNJUNFOU
    )ZSBY
    ೥ 1JOPDDIJP
    (SPUI 4QBSUBOͱ
    ௚઀͸ඥ෇͔ͳ͍͕ྫͱͯ͠࢖͏
46. 2"1
    2VBESBUJD
    "SJUINFUJD
    1SPHSBN
    ̎࣍ࢉज़ϓϩάϥϜ w "SJUINFUJD
    1SPHSBNͱ͸ʁ
    w ࿦ཧճ࿏ʹࢉज़Λ౰ͯ͸Ί͍ͯͬͯɺਅِҎ֎ͷ਺Λ ࢖͑ΔΑ͏ʹม׵ͨ͠΋ͷɻࢉज़Λ౰ͯ͸Ί͍ͯ͘͜ ͱΛ"SJUINFUJ[BUJPOͱ͍͏ɻ
47. 2"1
    2VBESBUJD
    "SJUINFUJD
    1SPHSBN
    ̎࣍ࢉज़ϓϩάϥϜ w ྫ͑͹
    w Y
    㱹
    Z
    㱹
    ™[
    w 㱹
    l࿦ཧ࿨zɺ㱸
    l࿦ཧੵzɺ™
    z൱ఆz
    w ஔ͖׵͑
    w Y
    㱹
    Z
    ︎ˠ
    Y
    
    ZɺY
    㱸
    Z
    ︎ˠ
    Y
    º
    Zɺ™Y
    ︎ˠ
    
    —
    Y
    w Y
    
    Z
    
    
    —
    [ Y5
    Z5
    ['ͷͱ͖ɺ5SVF Y
    Z
    [ͷͱ͖ɺɻ
    Ҏ֎Ͱ͋Ε͹5SVFͱ൑அɻ
48. 2"1
    2VBESBUJD
    "SJUINFUJD
    1SPHSBN
    ̎࣍ࢉज़ϓϩάϥϜ w 2"1ͱ͸
    w ূ໌͍ͨ͠࿦ཧΛɺ"SJUINFUJ[BUJPOΛ௨ͯ͠ɺ
    w " Y # Y
    
    $ Y
    
    5 Y ; Y
    w ͷܗʹม׵͠ɺ౴͑Λ஌͍ͬͯΔ͜ͱΛ; Y Λ஌͍ͬͯ Δ͜ͱʹؼண͠ίετΛݮΒ͢ํ๏
49. "SJUINFUJD
    $JSDVJU
    4BUJTpBCJMJUZ
    ࢉज़ճ࿏ॆ଍Մೳੑ wॆ଍ՄೳੑΛௐ΂Δ͜ͱΛɺ4BUJTpBCJMJUZ
    1SPCMFN ॆ଍Մೳੑ໰୊ ͱ͍͍ɺ4"5ͱུه͢Δɻ
    wͨͩී௨4"5ͱ͍͏࣌͸
    Y㱹Y㱹ʜ 㱸 Y㱹™Y㱹ʜ 㱸ʜ
    ͷΑ͏ͳܗΛͨ͠ ࿦ཧࣜͷ૊Έ߹Θ͕ͤଘࡏ͢Δ͔Ͳ͏͔ͷ໰୊Λࢦ ͢Α͏ɻ
    w͜Ε͸۩ମతͳ΋ͷ͕ͳ͍ͱΠϝʔδ͕͚ͭͮΒ͍ɻ ޙ΄Ͳɻ
50. 7JUBMJLͷ[L4/"3,આ໌ͱ
    "SJUINFUJD
    $JSDVJUͷ۩ମܭࢉ IUUQTNFEJVNDPN!7JUBMJL#VUFSJORVBESBUJDBSJUINFUJDQSPHSBNTGSPN[FSPUPIFSPGEDFB
51. 7JUBMJLͷ[L4/"3,આ໌ͱ
    "SJUINFUJD
    $JSDVJUͷ۩ମܭࢉ w -BZFS9
    3FTFBSDIͷ೔ຊޠ຋༁υΩϡϝϯτ͕͋ͬͨͷ Ͱഈआ͠આ໌͢Δɻ
    w IUUQTTDSBQCPYJPMBZFSY[L 4/"3,T@$@MPHJD@HBUFT@ˠ@3$4@ˠ@2"1
    
52. 7JUBMJLͷ[L4/"3,આ໌ͱ
    "SJUINFUJD
    $JSDVJUͷ۩ମܭࢉ w ۩ମతͳܭࢉաఔ͸ϗϫΠτϘʔυͰ΍ͬͨͷͰɺҎԼͷ ʮηϛφʔ$$4UVEZ
    ʯಈըࢀরɻ
    w IUUQTXXXZPVUVCFDPNDIBOOFM 6$ZFX;.DZ-R2;J&#WO;RX
53. 7JUBMJLͷ[L4/"3,આ໌ͱ
    "SJUINFUJD
    $JSDVJUͷ۩ମܭࢉ w"SJUINFUJD
    $JSDVJUͷྫ
    w7JUBMJL͕ྫͱͯ͠ग़͍ͯ͠Δࢉज़ճ࿏ɻϧʔϓ͸͋ͬͯ͸͍͚ ͳ͍ɻ
    w
    9 4ZN 4ZN : d0VU d0OF
54. 3BOHF
    1SPPGͷ࣮૷ํ๏ w 3JOH
    4JHOBUVSF
    XJUI
    1FEFSTFO
    $PNNJUNFOU
    w "04
    3JOH
    4JHOBUVSF
    w ࠓҪͷαϯϓϧίʔυ
    w IUUQTHJUIVCDPNUBLBZBJNBJTDSJQUMFTT@TDSJQUCMPCNBTUFS BPT@SJOH@TJHOBUVSFKT
    w #PSSPNFBO
    3JOH
    4JHOBUVSF
    w $JDMJD
    (SPVQ
    XJUI
    4JHNB
    1SPUPDPM
    w ʜ
    w ຊ౰͸ಡॻձͰ͜ΕΛ࣮ࡍʹ4QBSUBOͰ΍ͬͯΈ͔͕ͨͬͨɺ࿩͕࣌ؒ͢ͳ͔ͬͨ
55. 3FGFSFODFT w IUUQTWJUBMJLDBHFOFSBMTUBSLT@QBSU@IUNM
    
    w IUUQTNFEJVNDPN!7JUBMJL#VUFSJO[LTOBSLTVOEFSUIFIPPECBG
    w IUUQTDSZQUPTUBDLFYDIBOHFDPNRVFTUJPOTQSPWFJOUFHFSJTXJUIJO UIFJOUFSWBMBC
    w IUUQXXXDTVDMBDVLTUB⒎+(SPUI
    w IUUQT[LQTDJFODF
    w IUUQTNFEJVNDPNRFEJUEJWJOHJOUPUIFTOBSLTTFUVQQIBTFCBE
    w IUUQTNFEJVNDPN!TPVJUJFYQMBJOJOHTOBSLTͷղઆCCDFCDG
    w IUUQTTDSBQCPYJPMBZFSY[L4/"3,T@$@TFUVQQSPPWJOHWFSJGZJOH
56. 3FGFSFODFT w IUUQTTDSBQCPYJPMBZFSY#VMMFUQSPPGT
    w IUUQTTDSBQCPYJPMBZFSY[L4/"3,T@$@TFUVQQSPPWJOH WFSJGZJOH
    w IUUQTTDSBQCPYJP4UBLFE5FDIOPMPHJFT4UBLFE@;,4/"3,T
    w IUUQTTDSBQCPYJP&UI1FEJB#MJOE@&WBMVBUJPO@PG@1PMZOPNJBMT
    w IUUQTUBTVTVIBUFOBCMPHDPNFOUSZ
    w IUUQTFDDDXFJ[NBOOBDJMSFQPSU
    w IUUQXXXDTQSJODFUPOFEVDPVSTFTBSDIJWFTQSDPTJQQEG
57. 3FGFSFODFT w IUUQTXXXKBJTUBDKQdVFIBSBDPVSTFJFQEGOQQEG
    w IUUQTUXJUUFSDPN1FSGFDU@*OTJEFSTUBUVT
    w IUUQTXXXXFCMJPKQXLQKBDPOUFOU1$1 ܭࢉෳࡶੑཧ࿦@1$1 ܭࢉෳࡶੑ ཧ࿦ͷ֓ཁ
    w %PVCMFF⒏DJFOU
    [L4/"3,T
    8JUIPVU
    5SVTUFE
    4FUVQ
    IUUQTXXXZPVUVCFDPNXBUDI WZR"G-M.XX
    w IUUQTBLBEFNFJBJOGPJOEFYQIQ $JSDVJU4"5
    w IUUQT[DBTIKBUFDIOPMPHZ[LTOBSLT
    w IUUQTDSZQUPTUBDLFYDIBOHFDPNRVFTUJPOTXIBUEPFTJUNFBOGPSBO BEWFSTBSZUPSVOJOQQU
    w IUUQMBCJJTFDBDKQdBSJUBQEGTJHNBQEG
58. pO