Docsity
Docsity

Prepara tus exámenes
Prepara tus exámenes

Prepara tus exámenes y mejora tus resultados gracias a la gran cantidad de recursos disponibles en Docsity


Consigue puntos base para descargar
Consigue puntos base para descargar

Gana puntos ayudando a otros estudiantes o consíguelos activando un Plan Premium


Orientación Universidad
Orientación Universidad


Notas de clase sobre criptografía y seguridad informática, Apuntes de Matemáticas

Este documento contiene notas de clase sobre criptografía y seguridad informática, incluyendo conceptos básicos de criptografía simétrica y asimétrica, ataques de criptoanálisis y protocolos de seguridad. También aborda temas como la firma digital, el intercambio de claves y la autenticación de mensajes.

Tipo: Apuntes

2019/2020

Subido el 10/12/2020

juan-david-villa-loaiza
juan-david-villa-loaiza 🇨🇴

4 documentos

1 / 43

Toggle sidebar

Esta página no es visible en la vista previa

¡No te pierdas las partes importantes!

bg1
'(3$57$0(172'(75$160,6,21&LUFXLWRV(OpFWULFRV,
9LUJLQLD6RODUWH0XxR]9LFWRU0DQXHO4XLQW HUR)ORUH]
&$3,78/2,
12&,21(6*(1(5$/(6
 ,1752'8&&,21
(Q ORV ~OWLPRV  DxRV ORV FDPSRV GH OD ,QJHQLHUtD KDQ UHSUHVHQWDGR XQ
LPSRUWDQWH SDSHO HQ OD IRUPD GH YLGD GH ODV SHUVRQDV /D FUHDFLyQ GH JUDQ
FDQWLGDGGHVLVWHPDVKDJHQHUDGRFDPELRVVLJQLILFDWLYRVHQODIRUPDGHYLGDGHODV
SHUVRQDV
+R\HQ GtD VH SXHGHKDEODUGH PXFKRV VLVWHPDV TXH GHILQHQR UHSUHVHQWDQ XQD
VRFLHGDG WHFQROyJLFD PRGHUQD FRPR SRU HMHPSOR ORV VLVWHPDV WHOHIyQLFRV ORV
HQODFHV GH FRPXQLFDFLyQ YtD VDWpOLWH ORV HTXLSRV PpGLFRV XWLOL]DGRV SDUD
GLDJQyVWLFR\FLUXJtDORVURERWV\ODVKHUUDPLHQWDVHOpFWULFDV
/D,QJHQLHUtDHVXQ iUHD DWUDFWLYD GH HVWXGLR GHELGR D OD QHFHVLGDGGHPHMRUDU\
UHILQDU FRQWLQXDPHQWH GLFKRV VLVWHPDV DVt FRPR HO GHVHR GH GHVFXEULU \
GHVDUUROODUQXHYRVVLVWHPDV
3DUD SRGHU HQWHQGHUHQ TXH OXJDUVH DSOLFDQ ORV FLUFXLWRV HOpFWULFRV HVQHFHVDULR
FRQRFHUXQSRFRVREUHOD,QJHQLHUtD(OpFWULFD
/D ,QJHQLHUtD (OpFWULFD VH RFXSD GHO HVWXGLR GH ORV VLVWHPDV TXH VRQ FDSDFHVGH
SURGXFLUWUDQVPLWLU \ PHGLUVHxDOHVGHWLSRHOpFWULFR6HGLVWLQJXHSRUTXH FHQWUD
VXV HVIXHU]RV HQ OD FUHDFLyQ GH VLVWHPDV WDQJLEOHV D SDUWLU GH PRGHORV TXH
GHVFULEHQ IHQyPHQRV QDWXUDOHV LQWHUSUHWDGRV SRU ORV ItVLFRV \ VRSRUWDGRV SRU
HOHPHQWRVPDWHPiWLFRV TXH VDWLVIDFHQ XQD GHWHUPLQDGD QHFHVLGDG SDUWLHQGR GH
ORVTXHODQDWXUDOH]DQRVEULQGD
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff
pf12
pf13
pf14
pf15
pf16
pf17
pf18
pf19
pf1a
pf1b
pf1c
pf1d
pf1e
pf1f
pf20
pf21
pf22
pf23
pf24
pf25
pf26
pf27
pf28
pf29
pf2a
pf2b

Vista previa parcial del texto

¡Descarga Notas de clase sobre criptografía y seguridad informática y más Apuntes en PDF de Matemáticas solo en Docsity!

'(3$57$0(172'(75$160,6,21 &LUFXLWRV(OpFWULFRV,

9LUJLQLD6RODUWH0XxR] 9LFWRU0DQXHO4XLQWHUR)ORUH]

(Q ORV ~OWLPRV  DxRV ORV FDPSRV GH OD ,QJHQLHUtD KDQ UHSUHVHQWDGR XQ

LPSRUWDQWH SDSHO HQ OD IRUPD GH YLGD GH ODV SHUVRQDV /D FUHDFLyQ GH JUDQ

FDQWLGDGGHVLVWHPDVKDJHQHUDGRFDPELRVVLJQLILFDWLYRVHQODIRUPDGHYLGDGHODV

SHUVRQDV

+R\ HQ GtD VH SXHGH KDEODU GH PXFKRV VLVWHPDV TXH GHILQHQ R UHSUHVHQWDQ XQD

VRFLHGDG WHFQROyJLFD PRGHUQD FRPR SRU HMHPSOR ORV VLVWHPDV WHOHIyQLFRV ORV

HQODFHV GH FRPXQLFDFLyQ YtD VDWpOLWH ORV HTXLSRV PpGLFRV XWLOL]DGRV SDUD

GLDJQyVWLFR\FLUXJtDORVURERWV\ODVKHUUDPLHQWDVHOpFWULFDV

/D,QJHQLHUtDHVXQiUHDDWUDFWLYD GHHVWXGLRGHELGRDODQHFHVLGDGGHPHMRUDU\

UHILQDU FRQWLQXDPHQWH GLFKRV VLVWHPDV DVt FRPR HO GHVHR GH GHVFXEULU \

GHVDUUROODUQXHYRVVLVWHPDV

3DUD SRGHU HQWHQGHU HQ TXH OXJDU VH DSOLFDQ ORV FLUFXLWRV HOpFWULFRV HV QHFHVDULR

FRQRFHUXQSRFRVREUHOD,QJHQLHUtD(OpFWULFD

/D ,QJHQLHUtD (OpFWULFD VH RFXSD GHO HVWXGLR GH ORV VLVWHPDV TXH VRQ FDSDFHV GH

SURGXFLUWUDQVPLWLU\PHGLUVHxDOHVGHWLSRHOpFWULFR6HGLVWLQJXHSRUTXHFHQWUD

VXV HVIXHU]RV HQ OD FUHDFLyQ GH VLVWHPDV WDQJLEOHV D SDUWLU GH PRGHORV TXH

GHVFULEHQ IHQyPHQRV QDWXUDOHV LQWHUSUHWDGRV SRU ORV ItVLFRV \ VRSRUWDGRV SRU

HOHPHQWRV PDWHPiWLFRV TXH VDWLVIDFHQ XQD GHWHUPLQDGD QHFHVLGDG SDUWLHQGR GH

ORVTXHODQDWXUDOH]DQRVEULQGD



/RVVLVWHPDVHOpFWULFRVSXHGHQFODVLILFDUVHHQORVVLJXLHQWHVJUXSRV

 6LVWHPDV GH &RPXQLFDFLyQ ORV FXDOHV JHQHUDQ WUDQVPLWHQ UHFLEHQ \

GLVWULEX\HQLQIRUPDFLyQ&RPRHMHPSORVHWLHQHQORVHTXLSRVGHWHOHYLVLyQORV

UDGLRWHOHVFRSLRV ORV VLVWHPDV GH VDWpOLWHV ORV VLVWHPDVGH UDGDU ORV VLVWHPDV

WHOHIyQLFRVORVVLVWHPDVGHUDGLRHWF

 6LVWHPDV GH &RPSXWDFLyQ ORV FXDOHV XWLOL]DQ ODV VHxDOHV HOpFWULFDV SDUD

SURFHVDU LQIRUPDFLyQ (MHPSORV 'HVGH OD FDOFXODGRUD PiV VHQFLOOD KDVWD HO

FRPSXWDGRUPiVVRILVWLFDGR

 6LVWHPDV GH &RQWURO TXH UHJXODQ SURFHVRV LQGXVWULDOHV R GHWHUPLQDQ HO

IXQFLRQDPLHQWRGHGLYHUVRVVLVWHPDVEDViQGRVHHQODVPDJQLWXGHVGHVHxDOHV

HOpFWULFDV TXH UHSUHVHQWDQ IHQyPHQRV FRPR WHPSHUDWXUD SUHVLyQ QLYHO \

FDXGDOGHXQUtRPRWRUHVHWF$OJXQRVHMHPSORVVRQHOFRQWUROGHODVOXFHVGH

XQ DVFHQVRU OD WHPSHUDWXUD \ HO WLHPSR HQ ORV KRUQRV PLFURRQGDV HO FRQWURO

GH OD DSHUWXUD \ FLHUUH GH ODV HVFOXVDV HQ HO FDQDO GH SDQDPi HO DWHUUL]DMH

DXWRPiWLFR GH ORV DYLRQHV HWF /RV 6LVWHPDV GH 3URFHVDPLHQWR GH 6HxDOHV

KDFHQ SDUWH GH ORV VLVWHPDV GH FRQWURO \ GHVFULEHQ XQD DPSOLD JDPD GH

VLVWHPDVXWLOL]DGRVSDUDSURSyVLWRVHVSHFLDOHV8QHMHPSORGHHVWRVVLVWHPDVHV

HO VLVWHPD GH EDUULGR WRPRJUiILFR DVLVWLGR SRU FRPSXWDGRU &$7 XWLOL]DGR SDUD

GLDJQyVWLFRGHHQIHUPHGDGHV

 6LVWHPDVGH3RWHQFLDTXHJHQHUDQ\GLVWULEX\HQHQHUJtDHOpFWULFD

([LVWH JUDQ LQWHUDFFLyQ HQWUH ODV GLIHUHQWHV GLVFLSOLQDV QRPEUDGDV DQWHULRUPHQWH

TXHLQWHUYLHQHQHQHOGLVHxR\RSHUDFLyQGHHVWDVFODVHVGHVLVWHPDV/D,QJHQLHUtD

(OHFWUyQLFD LQYROXFUD HO HVWXGLR GH VLVWHPDV TXH PDQHMDQ QLYHOHV GH SRWHQFLD

EDMRV

/RV FLUFXLWRV HOpFWULFRV VRQ XQ DVSHFWR FRP~Q SDUD WRGDV ODV UDPDV GH OD

,QJHQLHUtD VH DSOLFDQHQLQJHQLHUtDHOpFWULFDHOHFWUyQLFD\PHFiQLFDHQWUHRWUDV 



EDMDED GHVGH XQD FRPHWD UHPRQWDGD D JUDQ DOWXUD KDVWD XQD OODYH TXH

pOWHQtDHQODPDQR

+DFLDPHGLDGRVGHOVLJOR;9,,,VHHVWDEOHFLyODGLVWLQFLyQHQWUHPDWHULDOHVDLVODQWHV

\ FRQGXFWRUHV /RV DLVODQWHV HUDQ DTXHOORV D ORV TXH *LOEHUW KDEtD FRQVLGHUDGR

HOpFWULFRV HQ WDQWR TXH ORV FRQGXFWRUHV HUDQ ORV DQHOpFWULFRV (VWR SHUPLWLy

TXH VH FRQVWUX\HUD HO SULPHU DOPDFHQDGRU UXGLPHQWDULR HVWDED IRUPDGR SRU GRV

SODFDVFRQGXFWRUDVTXHWHQtDQXQDOiPLQDDLVODQWHHQWUHHOODV)XHFRQRFLGRFRPR

ERWHOODGH/H\GHQSRUODFLXGDGHQTXHVHLQYHQWy

$SULQFLSLRVGHOVLJOR;,;HOFRQGH$OHVVDQGUR9ROWDFRQVWUX\yXQDSLODJDOYiQLFD

&RORFyFDSDVGH]LQFSDSHO\FREUH\GHVFXEULyTXHVLVHXQtDODEDVHGH]LQFFRQ

OD~OWLPDFDSDGHFREUHHOUHVXOWDGRHUDXQDFRUULHQWHHOpFWULFDTXHIOXtDSRUHOKLOR

GH XQLyQ (VWH VHQFLOOR DSDUDWR IXH HO SURWRWLSR GH ODV SLODV HOpFWULFDV GH ORV

DFXPXODGRUHV \ GH WRGD FRUULHQWH HOpFWULFD SURGXFLGD KDVWD OD DSDULFLyQ GHO

GtQDPR

0LHQWUDVWDQWR*HRUJ6LPRQ2KPVHQWyODVEDVHVGHOHVWXGLRGHODFLUFXODFLyQGH

ODVFDUJDVHOpFWULFDVHQHOLQWHULRUGHPDWHULDVFRQGXFWRUDV

(Q+DQV2HUVWHGGHVFXEULyTXHXQDDJXMDPDJQpWLFDFROJDGDGHXQKLORVH

DSDUWDED GH VX SRVLFLyQ LQLFLDO FXDQGR SDVDED SUy[LPD D HOOD XQD FRUULHQWH

HOpFWULFD\SRVWXOyTXHODVFRUULHQWHVHOpFWULFDVSURGXFtDQXQHIHFWRPDJQpWLFR'H

HVWDVLPSOHREVHUYDFLyQVDOLyODWHFQRORJtDGHOWHOpJUDIRHOpFWULFR6REUHHVWDEDVH

$QGUp$PSpUHGHGXMRTXHODVFRUULHQWHVHOpFWULFDVGHEtDQFRPSRUWDUVHGHOPLVPR

PRGRTXHORVLPDQHV

(VWROOHYyD0LFKDHO)DUDGD\DVXSRQHUTXHXQDFRUULHQWHTXHFLUFXODUDFHUFDGHXQ

FLUFXLWRLQGXFLUtDRWUDFRUULHQWHHQpO(OUHVXOWDGRGHVXH[SHULPHQWRIXHTXHHVWR



VyOR VXFHGtD DO FRPHQ]DU \ FHVDU GH IOXLU OD FRUULHQWH HQ HO SULPHU FLUFXLWR

6XVWLWX\yODFRUULHQWHSRUXQLPiQ\HQFRQWUyTXHVXPRYLPLHQWRHQODSUR[LPLGDG

GHO FLUFXLWR LQGXFtD HQ pVWH XQD FRUULHQWH 'H HVWH PRGR SXGR FRPSUREDU TXH HO

WUDEDMR PHFiQLFR HPSOHDGR HQ PRYHU XQ LPiQ SRGtD WUDQVIRUPDUVH HQ FRUULHQWH

HOpFWULFD

/RV H[SHULPHQWRV GH )DUDGD\ IXHURQ H[SUHVDGRV PDWHPiWLFDPHQWH SRU -DPHV

0D[ZHOOTXLHQ HQSUHVHQWyVXVHFXDFLRQHVTXHXQLILFDEDQODGHVFULSFLyQGH

ORV FRPSRUWDPLHQWRV HOpFWULFRV \ PDJQpWLFRV \ VX GHVSOD]DPLHQWR D WUDYpV GHO

HVSDFLRHQIRUPDGHRQGDV

(Q7KRPDV$OYD(GLVRQFRPHQ]yORVH[SHULPHQWRVTXHWHUPLQDUtDQXQDxR

PiVWDUGHFRQODLQYHQFLyQGHODOiPSDUDHOpFWULFDTXHXQLYHUVDOL]DUtDHOXVRGHOD

HOHFWULFLGDG

'HVGH TXH HQ  HQWUy HQ IXQFLRQDPLHQWR HQ /RQGUHV OD SULPHUD FHQWUDO

HOpFWULFDGHVWLQDGDDLOXPLQDUODFLXGDGODVDSOLFDFLRQHVGHHVWDIRUPDGHHQHUJtD

VHKDQH[WHQGLGRSURJUHVLYDPHQWH/DHOHFWULFLGDGVHKDFRQYHUWLGRHQXQDIXHQWH

GH HQHUJtD LQGLVSHQVDEOH SUHVHQWDQGR ODV YHQWDMDV GH VX OLPSLH]D VX IiFLO

WUDQVSRUWH\FRQYHUVLyQHQRWURVWLSRVGHHQHUJtD

7RGR HOHPHQWR HQ HO FXDO H[LVWD XQD GLIHUHQFLD GH SRWHQFLDO \ SRU HO FXDO FLUFXOH

XQDFRUULHQWHHVXQJHQHUDGRUGHFDPSRVHOpFWULFRV\PDJQpWLFRV(VWRVFDPSRV

VRQSHUSHQGLFXODUHVHQWUHVt\SHUSHQGLFXODUHVDODGLUHFFLyQHQTXHYLDMDODRQGD

HOHFWURPDJQpWLFD 'HVGH RWUR SXQWR GH YLVWD FLHQWtILFR ORV FDPSRV

HOHFWURPDJQpWLFRV H[SOLFDQ FLHUWDV IXHU]DV QDWXUDOHV +DVWD KDFH PX\ SRFR OD

JHQWH VyOR SRGtD HQWHQGHU IXHU]DV SURGXFLGDV SRU FRQWDFWR ItVLFR GLUHFWR 8QD

FXFKDUDHQODWLHUUDSRGUtDPRYHUVHVLDOJXLHQODPRYtDGLUHFWDPHQWHFRQVXPDQR



HVWiQHQPRYLPLHQWR&DUJDVHOpFWULFDVHQPRYLPLHQWRDEDUFDODOODPDGDFRUULHQWH

HOpFWULFD

6H SXHGH REVHUYDU TXH PDJQHWLVPR  \ HOHFWULFLGDG HVWiQ tQWLPDPHQWH DVRFLDGRV

FRQORVFDPSRV\TXHHVWRVVHHQFXHQWUDQLQWHUUHODFLRQDGDVHQWUHVt8QDIXHU]D

HOpFWULFDRPDJQpWLFDVHGHELOLWDFRQHOLQFUHPHQWRGHODGLVWDQFLDDVXIXHQWH8Q

LPiQWLHQHGRVSRORVQRUWH\VXU8QDEDWHUtDWLHQHGRVWHUPLQDOHVXQRSRVLWLYR\

RWURQHJDWLYR8QJHQHUDGRU'&WDPELpQWLHQHGRVWHUPLQDOHVXQRSRVLWLYR\RWUR

QHJDWLYR3HURHQXQJHQHUDGRU$&ORVGRVWHUPLQDOHVFDPELDQGHSRODULGDGVHJ~Q

OD IUHFXHQFLD /RV FXHUSRV TXH VH HQFXHQWUDQ FDUJDGRV HOpFWULFDPHQWH WDO FRPR

XQDSHLQHWD SXHGHQVHUGHXQDVRODSRODULGDG SRVLWLYRRQHJDWLYR SHURHOLPiQ

VLHPSUHWLHQHGRVSRORV

'RVLPDQHVVHDWUDHQVLORVGRVSRORVTXHLQWHUDFWXDQVRQGHSRODULGDGFRQWUDULD

VL VRQ GH OD PLVPD SRODULGDG HOORV VH UHSHOHQ 8Q FDPSR HOpFWULFR WLHQH XQD

SRODULGDGGHILQLGDSXHGHDWUDHUXQDSDUWtFXODFDUJDGDHOpFWULFDPHQWHGHSRODULGDG

RSXHVWD OOHYiQGROD KDFLD OD IXHQWH HO FDPSR UHSHOH SDUWtFXODV VL HVWDV VRQ GH OD

PLVPD SRODULGDG TXH HO FDPSR HOpFWULFR /RV FDPSRV PDJQpWLFRV SXHGHQ HMHUFHU

IXHU]DVRPRYLPLHQWRGHFDUJDVHOpFWULFDVODVFXDOHVVRQOOHYDGDVSRUXQFDPLQR

TXHHVSDUDOHORDODVOtQHDVGHIXHU]DPDJQpWLFD

8Q HQUROODPLHQWR GH DODPEUH ERELQD  DFW~D FRPR XQ HOHFWURLPiQ FXDQGR FLUFXOD

XQD FRUULHQWH HOpFWULFD SRU HO DODPEUH /D PDJQLWXG GHO FDPSR HOHFWURPDJQpWLFR

UHVXOWDQWHGHSHQGHGHODLQWHQVLGDGGHODFRUULHQWH\GHOQ~PHURGHYXHOWDVGHOD

ERELQD6LODFRUULHQWHGLUHFWDIOX\HHQODERELQDODSRODULGDGGHOFDPSRPDJQpWLFR

HVILMD6LODFRUULHQWHDOWHUQDIOX\HHQODERELQDODSRODULGDGGHOFDPSRPDJQpWLFR

HV FRQPXWDGD FRQ HO SDVR GH OD FRUULHQWH HM (O WLPEUH  (O FDPSR PDJQpWLFR

GHVDSDUHFH VL ODFRUULHQWH$&R'&GHVDSDUHFH $Vt PLVPRFXDQGRVHJHQHUDXQ

FDPSR PDJQpWLFR DOWHUQDQWH HVWH HV FDSD] GH LQGXFLU FRUULHQWH HQ RWURV



HQUROODPLHQWRV R ERELQDV FHUFDQDV HV DVt FRPR WUDEDMD XQ JHQHUDGRU HOpFWULFR

7tSLFDPHQWHXQDPDTXLQDGLHVHOXQDPDTXLQDGHYDSRUXQDPDTXLQDGHDJXDR

GH YLHQWR SURGXFH OD URWDFLyQ GH XQ LPiQ FHUFD D XQ JUDQ HQUROODPLHQWR GH

DODPEUH (O FDPSR PDJQpWLFR URWDQWH LQGXFH XQD FRUULHQWH HOpFWULFD TXH IOX\H D

WUDYpV GHO HQUROODPLHQWR GH DODPEUH \ DVt VH JHQHUD OD HQHUJtD HOpFWULFD /RV

PRWRUHV HOpFWULFRV VRQ HVHQFLDOPHQWH JHQHUDGRUHV HOpFWULFRV RSHUDQGR HQ IRUPD

FRQWUDULD (OORV XWLOL]DQ IXHU]DV PDJQpWLFDV DWUDFWLYDV \ UHSXOVLYDV JHQHUDGDV SRU

HOHFWURLPDQHVTXHFRQYLHUWHQHOHFWULFLGDGHQSRWHQFLDPHFiQLFD

3DUD GLVWULEXLU HFRQyPLFDPHQWH OD HOHFWULFLGDG VREUH JUDQGHV GLVWDQFLDV VH KDFH

XVR GH DOWRV YROWDMHV (QWUH OD SODQWD GH HQHUJtD \ XQD FDVD XQD VHULH GH

WUDQVIRUPDGRUHVUHGXFHHOYROWDMHSDUDTXHHVWHSXHGDVHUXWLOL]DGRSRUFXDOTXLHU

KRJDUHOYROWDMHHVUHGXFLGRGHQLYHOHVDOWRVGHORUGHQGHNLORYROWLRVDQLYHOHVGH

YROWLRVGHXVR UHVLGHQFLDO

/DV XQLGDGHV GHO 6LVWHPD ,QWHUQDFLRQDO VH EDVDQ HQ VHLV FDQWLGDGHV GHILQLGDV

 /RQJLWXG  0DVD  7LHPSR  &RUULHQWH (OpFWULFD  7HPSHUDWXUD

7HUPRGLQiPLFD  ,QWHQVLGDG /XPLQRVD (Q OD 7DEOD  VH SUHVHQWDQ HVWDV

FDQWLGDGHVMXQWRFRQODXQLGDGEiVLFD\ORVVtPERORVFRUUHVSRQGLHQWHV



7DEOD35(),-263$5$327(1&,$6'(

\RFWR \ 



]HSWR ] 



DWWR D 



IHPWR I 



SLFR S 



QDQR Q 

 

PLFUR P 

 

PLOL P 

 

FHQWL F 

 

GHFL G 

 

'HFD ' 

+HFWR + 



.LOR. 



0HJD 0 



*LJD * 



7HUD 7 



3HWD 3 



([D ( 



=HWWD = 



<RWWD < 



3DUDIDFLOLWDUODVRSHUDFLRQHV PDWHPiWLFDVFRQQ~PHURVH[WUHPDGDPHQWHJUDQGHV

R SHTXHxRV VH GHEHQ UHFRUGDU ODV SURSLHGDGHV GH QRWDFLyQ FLHQWtILFD PDWHPiWLFD

DSOLFDEOHDODVSRWHQFLDVGHGLH]



















(MHPSORV 

 RKPV [



RKPV .LORRKP .:

 FHQWtPHWURV [



FHQWtPHWURV PHWURV P

 VHJXQGR [



VHJXQGRV PLOLVHJXQGR PV

 )DUDGLRV [



)DUDGLRV PLOLIDUDGLRV P)

$ FRQWLQXDFLyQ VH LQGLFDQ ODV SURSLHGDGHV PDWHPiWLFDV SDUD ODV RSHUDFLRQHV FRQ

SRWHQFLDVGHGLH]

3URGXFWR  

Q

P

QP

'LYLVLyQ  

Q

P

QP

3RWHQFLD  

Q P

QP

(MHPSORV 





























 





 

  





 

 



&XDQGR VH WUDEDMD FRQ Q~PHURV DUELWUDULRV VH SXHGHQ UHSUHVHQWDU FRQ SRWHQFLDV

GHEDVHGLH]



/DVPDVDVGHOSURWyQ\HOQHXWUyQVRQDSUR[LPDGDPHQWHLJXDOHV\DVXYH]XQDV

 YHFHV PD\RU TXH OD GHO HOHFWUyQ SRU OR WDQWR OD PDVD GH XQ iWRPR HVWi

FRQFHQWUDGDHQHOQ~FOHR

/RV iWRPRV GH GLYHUVRV HOHPHQWRV GLILHUHQ HQWUH Vt SRU HO WDPDxR GHO Q~FOHR

DWyPLFR\SRUHOQ~PHURGHHOHFWURQHVTXHJLUDQDOUHGHGRUGHOQ~FOHR

 0RGHORV$WyPLFRV

 0RGHORGH--7KRPSVRQ

/DVEDVHVHQTXHVHDSR\y7KRPSVRQSDUDHODERUDUVXPRGHORIXHURQ

x /DPDWHULDVHSUHVHQWDQRUPDOPHQWHQHXWUDORTXHVXSRQHTXHMXQWRDORV

HOHFWURQHV ORV iWRPRV KDQ GH FRQWHQHU HOHPHQWRV R SDUWtFXODV FDUJDGDV

SRVLWLYDPHQWH

x /RV HOHFWURQHV SXHGHQ VHU H[WUDtGRV GH ORV iWRPRV GH FXDOTXLHU VXVWDQFLD

SHURQRRFXUUHLJXDOFRQODFDUJDSRVLWLYD

 0RGHORGH5XWKHUIRUG

5XWKHUIRUG LQWURGXFH HO PRGHOR QXFOHDU GHO iWRPR FRQ ODV VLJXLHQWHV

FDUDFWHUtVWLFDV

x ([LVWHXQQ~FOHRFDUJDGRSRVLWLYDPHQWHHQHOTXHVHHQFXHQWUDFRQFHQWUDGD

WRGDODPDVD

x /RV HOHFWURQHV JLUDQ DOUHGHGRU GHO Q~FOHR HQ Q~PHUR LJXDO D OD FDUJD

QXFOHDU



x /DFDUJDSRVLWLYDGHOQ~FOHRFRLQFLGHFRQHOQ~PHURDWyPLFR

x /RViWRPRVHQVXPD\RUSDUWHVRQHVSDFLRYDFtR

 0RGHOR&XiQWLFRGH%RKU

%RKUVHEDVyHQORVVLJXLHQWHVSRVWXODGRV

x /RVHOHFWURQHVHQHOiWRPRHVWiQORFDOL]DGRVHQyUELWDVR QLYHOHVGHHQHUJtD

DOUHGHGRU GHO Q~FOHR %RKU HVWDEOHFLy OD FRPSDUDFLyQ HQWUH HO iWRPR \ HO

VLVWHPD VRODU HO VRO HQ HO FHQWUR FRUUHVSRQGH DO Q~FOHR PLHQWUDV TXH ORV

SODQHWDV D GLVWDQFLDV UHODWLYDPHQWH JUDQGHV GHO VRO FRUUHVSRQGHQ D ORV

HOHFWURQHV

x /RV iWRPRV FRQWLHQHQ XQ Q~PHUR LJXDO GH SURWRQHV \ HOHFWURQHV HV GHFLU

TXHODPDWHULDHVHOpFWULFDPHQWHQHXWUDRTXHHVWiGHVFDUJDGD

x 6XSXVR TXH OD HQHUJtD GH ORV HOHFWURQHV WLHQH YDORUHV GHILQLGRV TXH

FRUUHVSRQGHQ DORVQLYHOHVGHHQHUJtDHOYDORUHQHUJpWLFRGHHVWRVQLYHOHV

GLVPLQX\H D PHGLGD TXH VH DOHMDQ GHO Q~FOHR 9HU ILJXUD   (O SULPHU

QLYHOTXHHVHOPiVFHUFDQRDOQ~FOHRSXHGHFRQWHQHUVRORGRVHOHFWURQHV

VLXQiWRPRGHEHWHQHUWUHVHOHFWURQHVHQWRQFHVHOWHUFHURGHEHUiSDVDUDO

VLJXLHQWH QLYHO (O VHJXQGR QLYHO SXHGH FRQWHQHU XQ Pi[LPR GH 

HOHFWURQHV HO WHUFHU QLYHO GH  \ HO FXDUWR GH  FRPR VH GHWHUPLQD SRU

PHGLR GH OD IyUPXOD Q GRQGH Q HV HO Q~PHUR GHO QLYHO $ FDGD QLYHO R

FDSD VH OH DVLJQD XQ Q~PHUR OODPDGR 1~PHUR &XiQWLFR 3ULQFLSDO \ VH

UHSUHVHQWDFRQODOHWUDQTXHWRPDORVYDORUHVGHHWFSDUWLHQGRGHO

QLYHOPiVFHUFDQRDOQ~FOHRKDFLDDIXHUD7DPELpQVHXVDQODVOHWUDVNOP

Q &DGD QLYHO VH VXEGLYLGH HQ VXEQLYHOHV HO SULPHUR SXHGH FRQWHQHU 

HOHFWURQHVHOVHJXQGRHOHFWURQHVHOWHUFHURHOHFWURQHV\HOFXDUWR



(QWUHSDUWtFXODVHOpFWULFDPHQWHFDUJDGDVVHSXHGHQSUHVHQWDUIXHU]DVTXHSXHGHQ

VHUDWUDFWLYDVRUHSXOVLYDV$VtORVSURWRQHVHMHUFHQIXHU]DVGHUHSXOVLyQVREUHORV

SURWRQHVORVHOHFWURQHVHMHUFHQIXHU]DVGHUHSXOVLyQVREUHORVHOHFWURQHVPLHQWUDV

TXHORVHOHFWURQHV\ORVSURWRQHVVHDWUDHQPXWXDPHQWHFRQGXFLHQGRDOVLJXLHQWH

HQXQFLDGR

≥&DUJDVGHODPLVPDFODVHVHUHSHOHQFDUJDVGHFODVHRSXHVWDVHDWUDHQ¥

8QiWRPRQRUPDOFRQWLHQHLJXDOQ~PHURGHSURWRQHV\HOHFWURQHVHVGHFLUTXHQR

SUHVHQWD FDUJD GH H[FHVR &XDQGR XQ HOHFWUyQ VDOH GH VX yUELWD HQ HO iWRPR

FRPLHQ]DDSURYRFDUIHQyPHQRVHQHOPDWHULDOSRUGRQGHGHDPEXODRFRUUH(VWH

IHQyPHQRVHOODPDHOHFWULFLGDGQRPEUHTXHVHGHULYDGHVXDJHQWHSURGXFWRU

+D\ PXFKRV PHGLRV SRU ORV FXDOHV SXHGH DOWHUDUVH HO HTXLOLEULR HQWUH ODV FDUJDV

SRVLWLYDV \ QHJDWLYDV 8QR GH HOORV HV HO IHQyPHQR GH OD HOHFWUL]DFLyQ SRU

IURWDPLHQWR R FRQWDFWR SDUD OR FXDO VH UHTXLHUH XQ FRQWDFWR PtQLPR HQWUH ODV

VXSHUILFLHV

6H SXHGH FRQFOXLU TXH ORV HOHFWURQHV GHO ~OWLPR QLYHO GH HQHUJtD R HOHFWURQHV GH

YDOHQFLDWLHQHQOLEHUWDGSOHQDSDUDPRYHUVHGHXQiWRPRDRWUR(VWDFDUDFWHUtVWLFD

GH ORV HOHFWURQHV GH YDOHQFLD HV OD UHVSRQVDEOH GHO SURFHVR GH FRQGXFFLyQ GH OD

HOHFWULFLGDG 'HVGH HO SXQWR GH YLVWD HOpFWULFR ORV VyOLGRV VH FODVLILFDQ GH OD

VLJXLHQWHIRUPD

x $LVODGRUHVR1R&RQGXFWRUHVQRSHUPLWHQHOSDVRGHFDUJDVDWUDYpVGHHOORV

&RPRSRUHMHPSORHODOJRGyQHOFDXFKRHWF

x 6HPLFRQGXFWRUHV7LHQHQH[DFWDPHQWHFXDWUR  HOHFWURQHVHQVX~OWLPRQLYHO

GH HQHUJtD \ DHVWHJUXSRSHUWHQHFHQ ORVHOHPHQWRVGHO *UXSR,9 (MHPSORV

6LOLFLR\*HUPDQLR



x &RQGXFWRUHV SHUPLWHQ HO SDVR GH FDUJDV D WUDYpV GH HOORV (MHPSORV 2UR

3ODWDHWF

 /H\GH&RXORPE

&KDUOHV$JXVWtQ&RXORPE  UHDOL]yODSULPHUDLQYHVWLJDFLyQFXDQWLWDWLYD

GHODOH\TXHULJHODVIXHU]DVTXHVHHMHUFHQHQWUHORVFXHUSRVFDUJDGRV(ODQiOLVLV

OR UHDOL]y PHGLDQWH HO XVR GH XQD EDODQ]D GH WRUVLyQ GHPRVWUDQGR TXH OD IXHU]D

GH DWUDFFLyQ R UHSXOVLyQ HQWUH GRV FXHUSRV HV LQYHUVDPHQWH SURSRUFLRQDO DO

FXDGUDGRGHODGLVWDQFLD

3RVWHULRUPHQWH VH GHPRVWUy TXH D XQD VHSDUDFLyQ GDGD OD IXHU]D HQWUH GRV

FXHUSRVFDUJDGRVHVSURSRUFLRQDODOSURGXFWRGHVXVFDUJDV LQGLYLGXDOHVT



\T



GH

ORFXDOREWHQHPRV

'RQGH

) 1HZWRQV HVODIXHU]DHQWUHODVGRVSDUWtFXODV

T



&RXORPEV (VODFDUJDQHWDGHODSDUWtFXOD$

T



&RXORPEV (VODFDUJDQHWDGHODSDUWtFXOD%

G PHWURV HVODGLVWDQFLDHQWUHODVSDUWtFXODV

NHVXQDFRQVWDQWHGHSURSRUFLRQDOLGDGODFXDOHVLJXDOD 



1P





/DGLUHFFLyQGHODIXHU]DHVVREUHODOtQHDTXHXQHXQDSDUWtFXODDODRWUD

/RDQWHULRUPHQWHGLFKRVHGHQRPLQD/H\GH&RXORPE\VHSXHGHHQXQFLDUDVt



 

U

T T





H



GHUHFKDGH$(OREMHWR& 



&VHHQFXHQWUDDPSRUGHEDMR

GH$&XDOHVODIXHU]DQHWD\HOiQJXORVREUH$" 6 



1*UDGRV

(QODWHRUtDGHFLUFXLWRVODVHSDUDFLyQGHFDUJDVFUHDXQDIXHU]DHOpFWULFD OODPDGD

YROWDMH \HOPRYLPLHQWRGHFDUJDVFUHDXQIOXLGRHOpFWULFR OODPDGRFRUULHQWH 

$FRQWLQXDFLyQVHDQDOL]DQHVWRVGRVFRQFHSWRV

 &RUULHQWH

6H FRQVLGHUD XQ WUR]R FRUWR GH DODPEUH GH FREUH FRQ XQ SODQR SHUSHQGLFXODU

LPDJLQDULRJHQHUDQGRDVtXQFRUWHWUDQVYHUVDOFRPRVHLQGLFDHQODILJXUDDVt

)LJXUD$/$0%5('(&2%5(

&XDQGRHODODPEUHVHHQFXHQWUDDWHPSHUDWXUDDPELHQWH\VLQSUHVHQFLDGHDOJXQD

IXHU]D H[WHUQD VH SUHVHQWD XQ PRYLPLHQWR DOHDWRULR GH HOHFWURQHV OLEUHV VRQ

HOHFWURQHV TXH REWLHQHQ VXILFLHQWH HQHUJtD GHO PHGLR SDUD DEDQGRQDU HO iWRPR 

RULJLQDGRSRUHQHUJtDWpUPLFDTXHREWLHQHQORVHOHFWURQHVGHOPHGLRDPELHQWH

H



$ODPEUH

3ODQR,PDJLQDULR



(QHOHYHQWRGHTXH XQiWRPR SLHUGDXQHOHFWUyQOLEUH HVWHDGTXLHUHFDUJDQHWD

SRVLWLYD \ VH GHQRPLQD LRQ SRVLWLYR HQWRQFHV HO HOHFWUyQ OLEUH VH GHVSOD]D HQWUH

HVRVLRQHVSRVLWLYRV\GHMDOD]RQDGHOiWRPRRULJLQDOPLHQWUDVORVLRQHVSRVLWLYRV

RVFLODQ HQ XQD SRVLFLyQ ILMD VLHQGR HO HOHFWUyQ OLEUHHOSRUWDGRUGHODFDUJDHQHO

PHWDOVLWXDFLyQPRVWUDGDHQODILJXUD'HQWURGHHVWHFRQMXQWRORVHOHFWURQHV

OLEUHV JDQDQ R SLHUGHQ HQHUJtD HQ YLUWXG GH ODV FDPELRV GH GLUHFFLyQ \ YHORFLGDG

FRPR SRU HMHPSOR FROLVLRQHV FRQ LRQHV SRVLWLYRV \ RWURV HOHFWURQHV IXHU]DV GH

DWUDFFLyQ KDFLD LRQHV SRVLWLYRV \ IXHU]DV GH UHSXOVLyQ HQWUH HOHFWURQHV (VWH

PRYLPLHQWR HV WDO TXH GXUDQWH FLHUWR SHUtRGR HO Q~PHUR GH HOHFWURQHV TXH VH

GHVSOD]DQKDFLDODGHUHFKDGHOFRUWHHVLJXDODOGHODL]TXLHUGDVLHPSUH\FXDQGR

QR VH DSOLTXHQ IXHU]DV H[WHUQDV HO IOXMR QHWR GH FDUJD HQ FXDOTXLHU GLUHFFLyQ HV

FHUR

)LJXUD,21(6326,7,926<(/(&7521(6/,%5(

$KRUDVHFRQHFWDXQDODPEUHHQWUHORVWHUPLQDOHVGHXQDSLODFRPRVHLQGLFDHQ

ODILJXUD

)LJXUD&21(;,21'(/$/$0%5('(&2%5($/267(50,1$/(6'(













H

H

,H

,FRQYHQFLRQDO

,RQHV

SRVLWLYRV

3ODQR

H



H



H



H



H



H



H