KA@ACAH –@_NZTLM_AEN ACML_NTKA FCMAKAC‛ Zfraigaimai Aiacnsns Acmlrntka Caibut
Dn susui lcfh2
Dnkas Kaidacni Zutra (?:1616::61) Euad Ahkad Fidaryaitl Fidaryaitl (?:1616::65) Gatra Aidn`a Aidn`a _akadhain (?:1616::=1)
EA@VCTAW TF@IN@ DAI NCKV @LKZVTF_ VINUF_WNTAW WANIW AC - QV_„AI BA]A TFIMAH TAHVI ?:1=
DAETA_ NWN
DAETA_ NWN............................................................... ..................................................................................... ........................................ ..................? @ATA ZFIMAITA_ ............................................. ................................................................... ........................................... ..................... 7 OAO N 2 ZFIDAHVCVAI A. CATA_ OFCA@AIM ............................................ ................................................................... ................................ ......... 4 O. _VKVWAI KAWACAH................................ KAWACAH.......................................................... ........................................4 ..............4 OAO NN 2 ZFKOAHAWAI A. ZFIMFIACAI A CML_NTKA FCMAKAC ........................................ ........................................ 6 O. @FAKAIAI ACML_NTKA FCMAKAC .......................... .......................................... ................ 17 G. Z_LM_AK AZCN@AWN FCMAKAC .............................................. ................................................... ..... 17 OAO NNN 2 ZFIVTVZ A. @FWNKZVCAI ............................................ .................................................................. ......................................... ................... 16 DAETA_ ZVWTA@A .......................................... ................................................................ ............................................ ........................ 15
?
@ATA ZFIMAITA_
Zubn syu`ur `akn paibat`ai `fpada Accah W]T atas sfcfsaniya pfiucnsai ka`acah nin dfimai buduc ‘@_NZTLM_AEN ‘ @_NZTLM_AEN ACML_NTKA FCMAKAC„ FCMAKAC „. Ka`acah nin dnsusui muia kfkfiuhn tumas kata `ucnah Zfraigaimai dai Aiacnsns Acmlrntka Caibut, dai buma sfoaman rfefrfisn oamn pfkoaga uitu` kfiakoah pfimftahuai tfitaim Ncku @rnptlmraen. Dacak pfiyusuiai ka`acah nin tnda` sfdn`nt hakoatai yaim `akn hadapn. @akn kfiyadarn oahwa dacak pfiyusuiai ka`acah nin bauh darn sfkpuria,
oan`
darn
sfmn
pfiyusuiai,
oahasa,
pfkoahasaai,
ataupui
pfiucnsaiiya. Lcfh `arfia ntu `akn kfimharap `rntn` yaim sneatiya kfkoaimui, `hususiya darn dlsfi kata `ucnah Zfraigaimai Aiacnsns Acmlrntka Caibut Nou Fria Dwn Astutn K.@lk, muia kfibadn aguai of`ac oamn `akn uitu` cfonh oan` dn kasa yaim a`ai dataim.
]lilslol, :6 L`tlofr ?:1=
Zfiyusui
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OAO N ZFIDAHVCVAI A. Catar Ofca`aim
Zfr`fkoaimai tf`ilclmn kfkaim ofr`fkoaim sfka`ni gfpat, yaim kfkuim`ni`ai kaiusna dapat ofrnitfra`sn sacnim ofrtu`ar data dai nielrkasn. Wfnrnim dfimai ntu tuitutai a`ai sf`urntas (`fakaiai) tfrhadap `frahasnaai nielrkasn yaim sacnim dnpfrtu`ar`ai tfrsfout sfka`ni kfinim`at. Oaiya` pfimmuia tnda` nimni nielrkasn yaim dnsakpan`aiiya dn`ftahun lcfh lraim cani. Lcfh `arfia ntu dn`fkoaim`aicah gaoaim ncku yaim kfkpfcabarn tfitaim garagara pfimakaiai data atau dn`fiac dfimai nstncah @rnptlmraen. @rnptlmraen kfrupa`ai ncku sf`acnmus sfin uitu` kfibama `frahasnaai pfsai dfimai gara kfiyakar`aiiya kfibadn ofitu` tfrsaidn yaim tnda` kfkpuiyan ka`ia. Wfka`ni tnimmn tnim`at `fakaiai suatu `rnptlmraen onasaiya dnsfrtan dfimai kfinim`taiya ofoai prlsfs fi`rnpsn dai dfs`rnpsniya. @rnptlmraen tfcah kfibadn suatu oamnai yaim tnda` dapat dnpnsah`ai darn snstfk `fakaiai barnimai. Ada ofroaman acmlrntka `rnptlmraen yaim sf`araim nin tfcah dai sfdaim dn`fkoaim`ai, sacah satuiya dnaitaraiya Acmlrntka FcMakac.
O. _ukusai Kasacah
a. Zfimfiacai Acmlrntka FcMakac o. @fakaiai Acmlrntka FcMakac g. Zrlmrak Apcn`asn @rnptlmraen FcMakac
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OAO NN ZFKOAHAWAI A. Zfimfiacai Acmlrntka FcMakac
Acmlrntka FcMakac Acmlrntka FcMakac kfrupa`a kfrupa`a acmlrntka dacak `rnptlmraen yaim tfrkasu` dacak `atfmlrn acmlrntka asnkftrns (`uign fi`rnpsn dai dfs`rnpsniya ofrofda). @uign Zrnvat
@uign Zuocn`
Gnphfrtf`s Zcanitf`s
Fi`rnpsn
Df`rnpsn
Zcanitf`s
Makoar 1. W`fka @rnptlmraen Asnkftrns
@fakaiai acmlrntka FcMakac tfrcfta` pada `fsucntai pfimhntuimai clmarntka dns`rft pada oncaimai klducl prnka yaim ofsar sfhnimma upaya uitu` kfiyfcfsan`ai kasacah clmarntka nin kfibadn saimat sucnt. Kasacah clmarntka dns`rft dfimai kfkpfrhatn`ai hac ofrn`ut. Bn`a dnofrn`ai suatu oncaimai a, ka`a kfimhntuim o ≡ αa (kld p) adacah kudah, tftapn bn`a dnofrn`ai suatu oncaimai o, ka`a uitu` kfifku`ai a sfhnimma o ≡ αa (kld p) p) adacah pfrkasacahai yaim sucnt. Acmlrntka nin dn`fkoaim`ai pfrtaka `acn lcfh nckuai Kfsnr Tahfr FcMakac pada tahui 1>86. Acmlrtnka FcMakac kfkpuiyan `uign puocn` ofrupa tnma pasaim oncaimai dai `uign rahasna ofrupa satu oncaimai. Acmlrntka nin kfkpuiyan `frumnai pada gnphfrtfxtiya yaim kfkpuiyan paibaim dua `acn cnpat darn pcanitfxtiya. A`ai tftapn, acmlrntka nin kfkpuiyan `fcfonhai pada fi`rnpsn. Vitu` pcanitfxt yaim saka, acmlrntka nin kfkofrn`ai gnphfrtfxt yaim ofrofda (dfimai `fpastnai yaim df`at) sftnap `acn pcanitfxt dn fi`rnpsn. Dacak acmlrtnka FcMakac kfkpuiyan tnma prlsfs, yantu prlsfs pfkofitu`ai `uign, prlsfs fi`rnpsn dai prlsfs dfs`rnpsn. Acmlrntka nin kfrupa`ai gnphfr ocl`, yantu kfca`u`ai prlsfs fi`rnpsn pada ocl`-ocl` pcanitfxt dai kfimhasnc`ai ocl`-ocl` gnphfrtfxt yaim `fkudnai dnca`u`ai prlsfs df`rnpsn dai hasnciya dnmaouim`ai.
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Zrlsfs Zfkofitu`ai @uign
Zrlsfs pfkofitu`ai `uign kfrupa`ai prlsfs pfifituai suatu oncaimai yaim `fkudnai a`ai dnmuia`ai sfoaman `uign pada prlsfs fi`rnpsn dai df`rnpsn pfsai. @uign fi`rnpsn tfrdnrn darn incan p, m, y sfdaim`ai `uign df`rnpsn tfrdnrn darn incan x, p. Kasnim-kasnim incan kfkpuiyan pfrsyaratai yaim harus dnpfiuhn. Caim`ah-caim`ah dacak pfkouatai `uign pada acmlrntka FcMakac sfoaman ofrn`ut. n.
Zncnh sfkoaraim oncaimai prnka p prnka p,, dfimai syarat p9?66. syarat p9?66. a. Gf` oncaimai prnka. o. Gf` prnka sfku (gf` oncaimai `lkplsnt)
∟1 ?
; , bn`a ₣
oncaimai prnka ka`a p ka`a p ₣ oncaimai ₣ oncaimai prnka. nn.
Zncnh oncaimai fcfkfi prnkntne m prnkntne m dfimai dfimai syarat 13 m ≤ p-1. p-1. m ?kld p ≪ 1 dai m dai m
∟1 ?
kld p ≪ 1.
nnn.
Zncnh oncaimai aga` x aga` x,, dfimai syarat 1 ≤ x x ≤ p-?. p-?.
nv.
Hntuim y Hntuim y ; mx kld p.
Darn caim`ah-caim`ah dnatas a`ai dnpfrlcfh `uign puocn` yaim dnmuia`ai uitu` fi`rnpsn adacah incan p, m, y dai `uign prnoadn yaim dnmuia`ai uitu` df`rnpsn adacah incan x, p. Incan p, m, y ofrsneat tnda` rahasna sfdaim`ai incan x ofrsneat rahasna.
5
Eclwghart pfkofitu`ai `uign Kucan
Kasu``ai incan p, m, y
Gf` Zrnka (p)
T
Gf` Zrnka (p) ; :
Z ou`ai oncaimai prnka
^ Gf` Zrnka Wfku (p)
Gf` Zrnka Wfku (p) ; :
T
Z oncaimai prnka sfku
^ Gf` Incan m 3 ? atau m 9 p - 1
T
Incan m harus 13m≤p -1
^ Gf` Zrnkntne (m)
Gf` Incan prnkntne (m) ; :
T
Incan m ou`ai oncaimai prnkntne akai
^ Gf` Incan x 3 1 atau x 9 p-?
^ Hntuim y Hntuim y ; mx kld p.
T
Incan x harus 1≤ x≤ p - ?
=
Incan y
Wfcfsan
Zrlsfs Fi`rnpsn
Zrlsfs fi`rnpsn kfrupa`ai prlsfs kfimuoah pcanitfxt `f gnphfrtfxt . Zada prlsfs nin dnmuia`ai `uign puocn` (p, m, y). Caim`ah-caim`ah y). Caim`ah-caim`ah dacak kfimfi`rnpsn pfsai pada acmlrntka FcMakac. n.
Zltlim pcanitfxt kfibadn ocl`-ocl` k 1,k?, ..., incan sftnap ocl` dn dacak sfcaim
P:, p-1[.
nn.
Voah incan ocl` pfsai `f dacak AWGNN.
nnn.
Zncnh oncaimai aga` ` , dfimai syarat 1 ≤ ` ≤ p-?.
nv.
Wftnap ocl` k dnfi`rnpsn dfimai rukus sfoaman ofrn`ut. makka (η) ; m` ; m` kld p. kld p. (1) dfcta (δ) ; y` ; y` k kld p. kld p. (?)
v.
Wusui gnphfrtfxt dfimai urutai η1,δ1, η?,δ?,...,ηi,δi.
Zasaimai η dai δ adacah gnphfrtfxt uitu` ocl` pfsai k. Hasnc yaim dndapat darn prlsfs fi`rnpsn ofrupa gnphfrtfxt.
Makoar ?. Zrlsfs Fi`rnpsn
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Glitlh prlsfs fi`rnpsn sfgara kaiuac
Dn`ftahun 2 Zcanitfxt 2 –akai`ai –akai`ai dl`ukfi ntu‛ ntu ‛ Incan p Incan p ; 787, m 787, m ; 148 dai y dai y ; ?>6. @ 1 ; 71>
@ 5 ; ?=>
@ 11 11 ; 75:
@ 15 15 ; ?:
@ ? ; ?6>
@ = ; 1>:
@ 1? 1? ; 17>
@ 1= 1= ; 78
@ 7 ; 767
@ 8 ; ?6?
@ 17 17 ; 48
@ 18 18 ; 77:
@ 4 ; 1:6
@ > ; 5:
@ 14 14 ; 7=5
@ 1> 1> ; ?11
@ 6 ; ?5=
@ 1: 1: ; 8=
@ 16 16 ; 115
Bawao2 a. Voah pfsai ascn ( pcanitfxt ) `f dacak AWGNN dacak AWGNN a ; >=
a ; >=
` ; 1:=
Wpasn ; 7?
k ; 1:>
i ; 11:
u ; 11=
n ; 1:6
a ; >=
Wpasn ; 7?
k ; 1:>
t ; 115
i ; 11:
d ; 1::
f ; 1:1
u ; 11=
` ; 1:=
l ; 111
i ; 11:
sfhnimma incan pfsai AWGNN pfsai AWGNN adacah sfoaman ofrn`ut 2 K 1 ; >=
K 5 ; >=
K 11 11 ; 1:=
K 15 15 ; 7?
K ? ; 1:>
K = ; 11:
1? ; 11= K 1?
1= ; 1:6 K 1=
K 7 ; >=
K 8 ; 7?
17 ; 1:> K 17
18 ; 115 K 18
K 4 ; 11:
K > ; 1::
14 ; 1:1 K 14
1> ; 11= K 1>
K 6 ; 1:=
1: ; 111 K 1:
16 ; 11: K 16
o. Hntuim makka Hntuim makka (η ) dfimai rukus η ; m ; m ` kld p. kld p. η 1 ; 14871> kld 787; 1>= η ? ; 148?6> kld 787; 1?? η 7 ; 148767 kld 787; 86 Dst... >
Hasnc incan η1 ; 1>=
η5 ; ?5>
η11 ; 78
η15 ; 717
η? ; 1??
η= ; 77>
η1? ; 765
η1= ; ?65
η7 ; 86
η8 ; 71
η17 ; 144
η18 ; ?=
η4 ; 7=>
η> ; 158
η14 ; 5>
η1> ; =:
η6 ; 74:
η1: ; 7=
η16 ; 6:
g. Hntuim dfcta dfimai rukus δ ; y ; y` . k kld p kld p δ1 ; ?>671> . >= kld 787 ; 14: δ? ; ?>6?6> . 1:> kld 787 ; =8 δ7 ; ?>6767. >= kld 787 ; 71? Dst... Hasnc incan δ1 ; 14:
δ5 ; 7?1
δ11 ; 154
δ15 ; 767
δ? ; =8
δ= ; ?85
δ1? ; ?=6
δ1= ; 7=4
δ7 ; 71?
δ8 ; 14?
δ17 ; =:
δ18 ; ?1=
δ4 ; 1=?
δ> ; ?>?
δ14 ; 14?
δ1> ; 1:
δ6 ; 71:
δ1: ; 75?
δ16 ; =
d. Wusui hasnc pfrhntuimai makka pfrhntuimai makka (η ) dai dfcta (δ) Gnphfrtfxt 2 1>=, 14:, 1??, =8, 86, 71?, 7=>, 1=?, 74:, 71:, ?5>, 7?1, 77>, ?85, 71, 14?, 158, ?>?, 7=, 75?, 78, 154, 765, ?=6, 144, =:, 5>, 14?, 6:, =, 717, 767, ?65, 7=4, ?=, ?1=, =:, 1: Zrlsfs Df`rnpsn
Zrlsfs df`rnpsn kfrupa`ai prlsfs kfimuoah pfsai rahasna (gnphfrtfxt ( gnphfrtfxt ) kfibadn pfsai ascn ( pcanitfxt pcanitfxt ). ). Zada prlsfs nin dnmuia`ai `uign prnoadn ( x ( x,, p). p). Caim`ah-caim`ah dacak kfidf`rnpsn pfsai adacah sfoaman ofrn`ut. n.
Zfifituai incan makka incan makka dai dfcta. dfcta. Incan makka Incan makka (η) dnpfrlcfh darn gnphfrtfxt dfimai urutai maibnc sfdaim`ai dfcta (δ) dfimai urutai mfiap.
1:
nn.
Hntuim pcanitfxt Hntuim pcanitfxt k dfimai pfrsakaai rukus ofrn`ut. k ; δ. η( p-1-x) kld p (7) p-1-x) kld p
nnn.
Voah incan k yaim dndapat `fdacak incan AWGNN.
nv.
Wusui pcanitfxt Wusui pcanitfxt dfimai urutai k1,k?,...,k ,...,ki. Hasnc yaim dndapat darn prlsfs fi`rnpsn ofrupa pfsai ascn ( pcanitfxt pcanitfxt ). ).
Makoar 7. Zrlsfs Df`rnpsn
Glitlh prlsfs df`rnpsn sfgara kaiuac
Caim`ah-caim`ah pfiyfcfsanai prlsfs df`rnpsn sfgara kaiuac Dn`ftahun 2
11
Gnphfrtfxt 2 1>=, 14:, 1??, =8, 86, 71?, 7=>, 1=?, 74:,71:, ?5>, 7?1, 77>, ?85, 71, 14?, 158, ?>?, 7=, 75?, 78,154, 765, ?=6, 144, =:, 5>, 14?, 6:, =, 717, 767, ?65, 7=4,?=, ?1=, =:, 1: Incan p Incan p ; 787, x 787, x ; 778. Bawao 2 a. Znsah`ai incan makka incan makka dai dfcta pada dfcta pada pfsai rahasna (gnphfrtfxt (gnphfrtfxt ). ). η ; Gnphfrtfxt urutai maibnc.
δ ; Gnphfrtfxt urutai mfiap.
Incan maka η1 ; 1>=
η5 ; ?5>
η11 ; 78
η15 ; 717
η? ; 1??
η= ; 77>
η1? ; 765
η1= ; ?65
η7 ; 86
η8 ; 71
η17 ; 144
η18 ; ?=
η4 ; 7=>
η> ; 158
η14 ; 5>
η1> ; =:
η6 ; 74:
η1: ; 7=
η16 ; 6:
δ1 ; 14:
δ5 ; 7?1
δ11 ; 154
δ15 ; 767
δ? ; =8
δ= ; ?85
δ1? ; ?=6
δ1= ; 7=4
δ7 ; 71?
δ8 ; 14?
δ17 ; =:
δ18 ; ?1=
δ4 ; 1=?
δ> ; ?>?
δ14 ; 14?
δ1> ; 1:
δ6 ; 71:
δ1: ; 75?
δ16 ; =
Incan dfcta
o. Hntuim k (pfsai ascn) dfimai rukus 2 k ; δ. η ( p-1-x) kld p p-1-x) kld p k1 ; 14:. 1>= (787-1-778) kld 787 ; 14:. 1>= 44 kld 787; >= k? ; =8. 1?? (787-1-778) kld 787 ; =8. 1?? 44 kld 787 ; 1:> k7 ; 71?. 86 (787-1-778) kld 787 ; 71?. 86 44 kld 787 ; >= Dst.. Wfhnimma Hasnc iya 2 K 1 ; >=
K 5 ; >=
K 11 11 ; 1:=
K 15 15 ; 7?
K ? ; 1:>
K = ; 11:
K 1? 1? ; 11=
K 1= 1= ; 1:6
1?
K 7 ; >=
K 8 ; 7?
K 17 17 ; 1:>
K 18 18 ; 115
K 4 ; 11:
K > ; 1::
K 14 14 ; 1:1
K 1> 1> ; 11=
K 6 ; 1:=
K 1: 1: ; 111
K 16 16 ; 11:
g. Voah k `fdacak AWGNN `fdacak AWGNN . >= ; a
>= ; a
1:= ; `
7? ; Wpasn
1:> ; k
11: ; i
11= ; u
1:6 ; n
>= ; a
7? ; Wpasn
1:> ; k
115 ; t
11: ; i
1:: ; d
1:1 ; f
11= ; u
1:= ; `
111 ; l
11: ; i
Hasnc darn pfiyusuiai nincah yaim kfrupa`ai pfsai ascn ( pcanitfxt ( pcanitfxt ) yaim dnhasnc`ai pada prlsfs df`rnpsn. Zcanitfxt df`rnpsn. Zcanitfxt 2 –akai`ai –akai`ai dl`ukfi ntu‛. ntu ‛. Hasnc prlsfs pfrhntuimai fi`rnpsn df`rnpsn dfimai prlmrak apcn`asn dai sfgara kaiuac adacah saka. Wfcani ntu pcanitfxt ntu pcanitfxt sftfcah df`rnpsn saka dfimai incan Zcanitfxt sfofcuk dn fi`rnpsn.
O. @fakaiai Acmlrntka FcMakac
Dfimai kfcnhat pfrgloaai fi`rnpsn pfsai dnatas. Darn hasnc ntu tfrcnhat oahwa bukcah gnphfrtfxt yaim dnhasnc`ai tnda` saka dfimai bukcah pcanitfxt . Hac nin tfrbadn dn`arfia`ai gnphfrtfxt tfrdnrn darn incan makka dai dfcta. dfcta. A`noat prlsfs tfrsfout kfibadn`ai bukcah gnphfrtfxt cfonh oaiya` darn bukcah pcanitfxt bukcah pcanitfxt . Dfimai adaiya pfrofdaai bukcah tfrsfout tfituiya a`ai kfiyucnt`ai kfifoa` pcanitfxt sfofiariya kfs`npui `rnptaiacns kfkncn`n gnphfrtfxt . G. Zrlmrak Apcn`asn Acmlrntka FcMakac
Dacak
pfimnkpcfkfitasnaiiya
pfkrlmrakai
Zythli,
Zhp
FcMakac
kaupui
dapat
BavaWgrnpt.
kfimmuia`ai Oaiya`
sf`acn
oahasa oahasa
pfkrlmrakai yaim onsa kfkouat prlmrak dfimai acmlrntka nin. Wacah satuiya adacah dfimai kfimmuia`ai prlmak pfkrlmrakai BavaWgrnpt
17
Gryptlsystfk FcMakac yaim dntakpnc`ai kfimmuia`ai oahasa pfkrlmrakai BavaWgrnpt2
Makoar 4. Zrlmrak apcn`asnFcMakac dfimai BavaWgrnpt
Makoar 6 Zrlmrak apcn`asnFcMakac dfimai BavaWgrnpt
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OAO NNN ZFIVTVZ A. @FWNKZVCAI
Acmlrntka asnkftrn FcMakac saimat oan` uitu` kfimatasn kasacah kaiabfkfi dnstrnousn `uign. Acmlrntka FcMakac tfrkasu` acmlrntka yaim oan` (akai sfgara `lkputasn). Dfimai bukcah gnphfrtfxt yaim cfonh oaiya` darn pcanitfxt kfima`noat`ai ea`tlr `frba (wlr` (wlr` eagtlr ) yaim dnoutuh`ai uitu` kfca`u`ai pfkfgahai ghnpfrtfxt kfibadn cfonh caka dnoaidnim`ai dfimai acmlrntka cani yaim haiya kfkncn`n bukcah gnphfrtfxt yaim saka dfimai bukcah pcanitfxt bukcah pcanitfxt iya. iya. Acmlrntka nin kfkpuiyan `ftahaiai yaim oan` tfrhadap kftldf sfraimai Gnphfrtfxt licy attag` dai @ilw dai @ilw pcani attag`. Wfka`ni paibaim `ara`tfr `uign yaim dnpncnh sfka`ni caka wa`tu yaim dnoutuh`ai dacak kldfc sfraimai orutf elrgf attag`.. Wfka`ni paibaim pcanitfxt a`ai kfinim`at`ai paibaim ghnpfrtfxt yaim dnhasnc`ai. Dfimai ghnpfrtfxt yaim paibaim a`ai kfkpfrcakoat saat prlsfs pfimnrnkai, sfhnimma acmlrntka FcMakac nin `uraim sfsuan uitu` bfins apcn`asn yaim ofrbacai rfac tnkf. tnkf.
16
DAETA_ ZVWTA@A
Ardhnai. A, A. Aghkad, K .R. _nyaitl., –Aigakai @fakaiai `lkuin`asn dai Wfraimai Tfrhadap @rnptlmraen‛, http2//saidn.kath.wfo.nd, ?::8
http2//rfplsntlry.pltfisn-utaka.ag.nd/bspun/haidcf/1?7465=8>/?4: :6/1:/1= 16.?1 ]NO
Wadn`ni, _ne`n. ?:1?. @rnptlmraen uitu` @fakaiai Barnimai . ^lmya`arta2 AIDN.
Kuinr, _niacdn, –@rnptlmraen‛,Nielrkatn`a,Oaiduim, –@rnptlmraen‛,Nielrkatn`a,Oaiduim, ?::5.
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