6857 Computer and Network Security Lecture 3
Project Ideas ldquoaudio and securityrdquo possibilities
1 Cryptoanalysis by sound a httpwwwcstauacil~tromeracoustic
2 Cross-platform malware communicates with sound a Slashdot 103113
3 Company Illiri (see Slashdot 72313)
Today Encryption Perfect secrecy One-time Pad (OTP)
Readings (highly recommended) KatzLindell chapters 123
1
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itt One-Trne PA
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MIT OpenCourseWarehttpocwmitedu
1HWZRUNDQGampRPSXWHU6HFXULWSpring 2014
For information about citing these materials or our Terms of Use visit httpocwmiteduterms
- ---- ----------- -----
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___ _ _
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AIice Bob
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0
IDlsquo0
M = t(qVSiW ~es5q~e __ --------
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In bq~ic e~-h~ b1te) ~cre il
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3
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riZ 1-( ~ Bob M=1)ec(K~)
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bull
5
itt One-Trne PA
i M= lsquoci IOU- (x-st srnrsquo) K to 10deg (soc A-bftrdquopdrdquo(keY)
lsquoLI- = i i i bull bull
lie K reDi IC iV Pec)J
LL tI_ iDIIOO
= re(kekrsquo) Meordquo= 11
OTP r4nr44vbn_veoahtc)y 4ecre Es
Can not break scirsquoenie1ersquoStn t trn rcck cckspAc1yotC
(Conpca to csnpu-tkraoI4 sccsee_ t npices assinng+rbn
4t amplsquoa kas Jk4 Ccrsquoptn ptrsquotr camp+ fJcr
j43t flwbrsquo42t3 lsquo)
lsquoveuml5 Ufl2rrZn Yc
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6
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lsquo3 C 3 bull iibull ~eeoe je s-ccreb
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bull
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MIT OpenCourseWarehttpocwmitedu
1HWZRUNDQGampRPSXWHU6HFXULWSpring 2014
For information about citing these materials or our Terms of Use visit httpocwmiteduterms
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riZ 1-( ~ Bob M=1)ec(K~)
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--
3
__--
-----------
_ ____
----
bull 1
- I _shy Lgt Yr(A1
SeCVI~ 1)OI~ cli~
Zrrsquos
H
UCAIt- oI~1n~~h ~Ia~~ ~(~Ilt Mi1
Ca
IS
lE]( se ~)OWgt (orchoolte~t(l ctfle MOl (MiMiiLL __c
Ri
- -- -
~p-iccn~ Joe1 t)1gtt- hide ~essq~ l-e~~ )-s
U
bull-JJ -
bi
I C
Afu~ KYIO-I c ip-her~J_
C14rsquo
lsquolsquo-k OVYl crPTp-ltil J
I lsquoIrsquo
C
mdash
I
C (lsquomdash
I ccedil
ccedil
0
)
I -iI)4)lsquoA
bullr _ -~--
1__ M~) -4 - Eve efeV
Slti~e ellj_t-)
mdash
Ri
l ot ~
Ttncrtet-oV p
-
coseV
c O~-eYl cr_ _ ____ L__ ___5 lsquo
shy-- -------- --
-C
4
- --
-
- -
-
d ~ amp ltigtS0 s-re=a-egt ~ s--e-P T
4
- -----
__
____ _
------
--
--
_____ _ ______ _ ___ __
-S
mdash
mdashamp o
7-
lsquoa
lsquoH
15
V
c13
0-
1
I---------
cr
amdashrsquo
qrsquocccedil
t
gt-
bull0bull
mdash
bullt
)
41S
ccc
OH
mdashmdash
mdash0
mdash---
II
-G1
(7 C
CI
Li bull
Doe -=Tie PqJ (0 TP)
____11____-K q~o IkL j2qd_ ii-ll n~1V ~ AIilL t~c)b
-2~esl_ca~_~~~~_~~p-J ) ----t------------------ -
8c~ - 10 lIDOmiddotmiddot It----~ 61 K= 000
7 b-~~(rIod- I ecc~ coi-)
110110middot ---------- shy
-----tt-~~====~---=~----
bull bull
-
ccedil
C-I
-
I lsquoSI
=IltNl---____ ___---_____
__Mes _Sltl~) kcmiddot_-)9J Clgb~ext- hqvt Sinc 1l~~CA-~)--1 (ej ~ ~ =C-k____-tt-__ _
___-tt-_----o c-= ~ _ I(tJcgte~ In-ec h )
- bull M
mdash C_
C= middot -----H
-----11---------
j -- ---- -------- -------- --- shy
e --J-----------IIgt k tl)~- ---
S-t
-Iia4-lsquo4
7 ~ -
bull
U= (Y) ~ A )ote-
111
(~dt- ~P-~ ( M~Se~yOIPgt weclL ~+- 01) eVtph _10l
Q 1 1--
-
lsquoI)
-xlsquoS~1s n~ct~_--J e _ __________
_~ ~ 1-o CJ Ql~ ~W)=___~=~__~~ ___-tl--____
ii JV
j $1
S -=vr~ec -ellVl 1itJ
1ieoreM OTP i (A VlCbV)ditl9 l _______ ----( e uv( ~~4~T C-Ie-S c~___-t~--- w~~
Co~ power J___-----________ CI~Q 1ftnttior)-~-eOIe~c-17 S-eCuv______
bull
5
itt One-Trne PA
i M= lsquoci IOU- (x-st srnrsquo) K to 10deg (soc A-bftrdquopdrdquo(keY)
lsquoLI- = i i i bull bull
lie K reDi IC iV Pec)J
LL tI_ iDIIOO
= re(kekrsquo) Meordquo= 11
OTP r4nr44vbn_veoahtc)y 4ecre Es
Can not break scirsquoenie1ersquoStn t trn rcck cckspAc1yotC
(Conpca to csnpu-tkraoI4 sccsee_ t npices assinng+rbn
4t amplsquoa kas Jk4 Ccrsquoptn ptrsquotr camp+ fJcr
j43t flwbrsquo42t3 lsquo)
lsquoveuml5 Ufl2rrZn Yc
lsquop (crdquoigraversquo) GJCbS lsquo0r rnesYaye 1
P (Mi1= vamps -nrsquo tL4 mt sM
ac- lwiirsquoj seen ccr-kik Crsquo
eot rOTP1 (np(jc)
bi 6 seek Crdquo
6
- - ------
51
1
root-~
I r
lsquomdashlsquo
lb
H
u
mdash
mdash
1 3 lsquomdash
F
lsquo1
A rr
1_
a-d
r
6rsquo
_mdash
lb -o
2 ii
J u
11 mdash
p
j i
lsquo2
p ii
3 3
rmdash
mdash
3
J
t
C
II f
l
rrk
gtlsquo
gtmdash
lsquot
) b
ardquo
p
~---- --I [fufj(fij - shy L~ 3-- ___--J
---~---
7
-
bull
(N3
0
Crsquo 3
z -D divide
c1__-
0C
(~ ~ il c~~ji cif~~Vt bi~ CCMe5
co((1~dJ bit J- krypkl M~~ hgt ~je ) -I-
J-
(tbull
OTP Jo~ f pViJ~ C1 Q~ertt4tb of-7
cs it
Me~$CIcye Grgtie~ Dr fttdn q~l~+ Ihodctb
( Qli)
I
lsquo3 C 3 bull iibull ~eeoe je s-ccreb
sit ~ s eco-e1 -I 5
_ C -j I 3
3
bull
bull ~eef 1hM 5epoundret
bull avoId re-Il~4 ~ (jc Veno)t I- L tpound)C~ - (M1(pound)ltj(f) (Ma tf) K)
C
n r Crsquo 0
middot I
bull
CA Sa 6) k )7I T I
rbull
- +shy tshy
8
I
l
bull
Jr I L1 5
RIIJ1ot1le $04Vte) (o MOit ci~ we(e ~l~Ccjgtb- 1-0 ClIp ~r~k~)mdash
V 0
r
mdash
lsquoP
_s Crsquo r -e V
r -c a
0 ( I
bull
St
2rc
f-JF
3
Ocy
bull fI itrtgtphol-e J
_-
mdash
-
mdashr
5_
c
lsquoo
r e Lh er ty fl in or-LCIVIf_cl AlpunR Scho~ickrlsquoIrsquo
Coin) q~tJe
I lsquoED
It
CA e (
5Olg0~ cp set
4
fl
bull 1acllt~~ 5p~ Iq middotibS
bull 0 S~ MOIleMts (I Iqp -=Sgt Clt ~ )
i
A --ey---- B l gte
t
bull3 3
T 1
3
bull
1= A ~
t ell J +r~~i~ B ~qJt -t-~i t beeps
c hrW $ W StUeTJr
~
~y
I S d5
~~q- Ket D~ir~h
I F~5 (a) ~+ ~+ (Q(f~()~)4
bull
9- a I r lsquoa r It
t ~ ~ t ~ t
fl Irsquo V
amp 0 H- 2 3r
0 3 lsquoC
S 3
A sJs ~ 1 Y+o~gt po~i 1ltd IgtI~JIt B rmiddotlgtkll1 11gt- chOI(O 11- t4 kl)o Iv 6middot~ slJ Ivc I~ c
O IS ~
C
-
0 lsquop Irsquo Dr
bulltr
a-
-v
1
9
MIT OpenCourseWarehttpocwmitedu
1HWZRUNDQGampRPSXWHU6HFXULWSpring 2014
For information about citing these materials or our Terms of Use visit httpocwmiteduterms
__--
-----------
_ ____
----
bull 1
- I _shy Lgt Yr(A1
SeCVI~ 1)OI~ cli~
Zrrsquos
H
UCAIt- oI~1n~~h ~Ia~~ ~(~Ilt Mi1
Ca
IS
lE]( se ~)OWgt (orchoolte~t(l ctfle MOl (MiMiiLL __c
Ri
- -- -
~p-iccn~ Joe1 t)1gtt- hide ~essq~ l-e~~ )-s
U
bull-JJ -
bi
I C
Afu~ KYIO-I c ip-her~J_
C14rsquo
lsquolsquo-k OVYl crPTp-ltil J
I lsquoIrsquo
C
mdash
I
C (lsquomdash
I ccedil
ccedil
0
)
I -iI)4)lsquoA
bullr _ -~--
1__ M~) -4 - Eve efeV
Slti~e ellj_t-)
mdash
Ri
l ot ~
Ttncrtet-oV p
-
coseV
c O~-eYl cr_ _ ____ L__ ___5 lsquo
shy-- -------- --
-C
4
- --
-
- -
-
d ~ amp ltigtS0 s-re=a-egt ~ s--e-P T
4
- -----
__
____ _
------
--
--
_____ _ ______ _ ___ __
-S
mdash
mdashamp o
7-
lsquoa
lsquoH
15
V
c13
0-
1
I---------
cr
amdashrsquo
qrsquocccedil
t
gt-
bull0bull
mdash
bullt
)
41S
ccc
OH
mdashmdash
mdash0
mdash---
II
-G1
(7 C
CI
Li bull
Doe -=Tie PqJ (0 TP)
____11____-K q~o IkL j2qd_ ii-ll n~1V ~ AIilL t~c)b
-2~esl_ca~_~~~~_~~p-J ) ----t------------------ -
8c~ - 10 lIDOmiddotmiddot It----~ 61 K= 000
7 b-~~(rIod- I ecc~ coi-)
110110middot ---------- shy
-----tt-~~====~---=~----
bull bull
-
ccedil
C-I
-
I lsquoSI
=IltNl---____ ___---_____
__Mes _Sltl~) kcmiddot_-)9J Clgb~ext- hqvt Sinc 1l~~CA-~)--1 (ej ~ ~ =C-k____-tt-__ _
___-tt-_----o c-= ~ _ I(tJcgte~ In-ec h )
- bull M
mdash C_
C= middot -----H
-----11---------
j -- ---- -------- -------- --- shy
e --J-----------IIgt k tl)~- ---
S-t
-Iia4-lsquo4
7 ~ -
bull
U= (Y) ~ A )ote-
111
(~dt- ~P-~ ( M~Se~yOIPgt weclL ~+- 01) eVtph _10l
Q 1 1--
-
lsquoI)
-xlsquoS~1s n~ct~_--J e _ __________
_~ ~ 1-o CJ Ql~ ~W)=___~=~__~~ ___-tl--____
ii JV
j $1
S -=vr~ec -ellVl 1itJ
1ieoreM OTP i (A VlCbV)ditl9 l _______ ----( e uv( ~~4~T C-Ie-S c~___-t~--- w~~
Co~ power J___-----________ CI~Q 1ftnttior)-~-eOIe~c-17 S-eCuv______
bull
5
itt One-Trne PA
i M= lsquoci IOU- (x-st srnrsquo) K to 10deg (soc A-bftrdquopdrdquo(keY)
lsquoLI- = i i i bull bull
lie K reDi IC iV Pec)J
LL tI_ iDIIOO
= re(kekrsquo) Meordquo= 11
OTP r4nr44vbn_veoahtc)y 4ecre Es
Can not break scirsquoenie1ersquoStn t trn rcck cckspAc1yotC
(Conpca to csnpu-tkraoI4 sccsee_ t npices assinng+rbn
4t amplsquoa kas Jk4 Ccrsquoptn ptrsquotr camp+ fJcr
j43t flwbrsquo42t3 lsquo)
lsquoveuml5 Ufl2rrZn Yc
lsquop (crdquoigraversquo) GJCbS lsquo0r rnesYaye 1
P (Mi1= vamps -nrsquo tL4 mt sM
ac- lwiirsquoj seen ccr-kik Crsquo
eot rOTP1 (np(jc)
bi 6 seek Crdquo
6
- - ------
51
1
root-~
I r
lsquomdashlsquo
lb
H
u
mdash
mdash
1 3 lsquomdash
F
lsquo1
A rr
1_
a-d
r
6rsquo
_mdash
lb -o
2 ii
J u
11 mdash
p
j i
lsquo2
p ii
3 3
rmdash
mdash
3
J
t
C
II f
l
rrk
gtlsquo
gtmdash
lsquot
) b
ardquo
p
~---- --I [fufj(fij - shy L~ 3-- ___--J
---~---
7
-
bull
(N3
0
Crsquo 3
z -D divide
c1__-
0C
(~ ~ il c~~ji cif~~Vt bi~ CCMe5
co((1~dJ bit J- krypkl M~~ hgt ~je ) -I-
J-
(tbull
OTP Jo~ f pViJ~ C1 Q~ertt4tb of-7
cs it
Me~$CIcye Grgtie~ Dr fttdn q~l~+ Ihodctb
( Qli)
I
lsquo3 C 3 bull iibull ~eeoe je s-ccreb
sit ~ s eco-e1 -I 5
_ C -j I 3
3
bull
bull ~eef 1hM 5epoundret
bull avoId re-Il~4 ~ (jc Veno)t I- L tpound)C~ - (M1(pound)ltj(f) (Ma tf) K)
C
n r Crsquo 0
middot I
bull
CA Sa 6) k )7I T I
rbull
- +shy tshy
8
I
l
bull
Jr I L1 5
RIIJ1ot1le $04Vte) (o MOit ci~ we(e ~l~Ccjgtb- 1-0 ClIp ~r~k~)mdash
V 0
r
mdash
lsquoP
_s Crsquo r -e V
r -c a
0 ( I
bull
St
2rc
f-JF
3
Ocy
bull fI itrtgtphol-e J
_-
mdash
-
mdashr
5_
c
lsquoo
r e Lh er ty fl in or-LCIVIf_cl AlpunR Scho~ickrlsquoIrsquo
Coin) q~tJe
I lsquoED
It
CA e (
5Olg0~ cp set
4
fl
bull 1acllt~~ 5p~ Iq middotibS
bull 0 S~ MOIleMts (I Iqp -=Sgt Clt ~ )
i
A --ey---- B l gte
t
bull3 3
T 1
3
bull
1= A ~
t ell J +r~~i~ B ~qJt -t-~i t beeps
c hrW $ W StUeTJr
~
~y
I S d5
~~q- Ket D~ir~h
I F~5 (a) ~+ ~+ (Q(f~()~)4
bull
9- a I r lsquoa r It
t ~ ~ t ~ t
fl Irsquo V
amp 0 H- 2 3r
0 3 lsquoC
S 3
A sJs ~ 1 Y+o~gt po~i 1ltd IgtI~JIt B rmiddotlgtkll1 11gt- chOI(O 11- t4 kl)o Iv 6middot~ slJ Ivc I~ c
O IS ~
C
-
0 lsquop Irsquo Dr
bulltr
a-
-v
1
9
MIT OpenCourseWarehttpocwmitedu
1HWZRUNDQGampRPSXWHU6HFXULWSpring 2014
For information about citing these materials or our Terms of Use visit httpocwmiteduterms
- -----
__
____ _
------
--
--
_____ _ ______ _ ___ __
-S
mdash
mdashamp o
7-
lsquoa
lsquoH
15
V
c13
0-
1
I---------
cr
amdashrsquo
qrsquocccedil
t
gt-
bull0bull
mdash
bullt
)
41S
ccc
OH
mdashmdash
mdash0
mdash---
II
-G1
(7 C
CI
Li bull
Doe -=Tie PqJ (0 TP)
____11____-K q~o IkL j2qd_ ii-ll n~1V ~ AIilL t~c)b
-2~esl_ca~_~~~~_~~p-J ) ----t------------------ -
8c~ - 10 lIDOmiddotmiddot It----~ 61 K= 000
7 b-~~(rIod- I ecc~ coi-)
110110middot ---------- shy
-----tt-~~====~---=~----
bull bull
-
ccedil
C-I
-
I lsquoSI
=IltNl---____ ___---_____
__Mes _Sltl~) kcmiddot_-)9J Clgb~ext- hqvt Sinc 1l~~CA-~)--1 (ej ~ ~ =C-k____-tt-__ _
___-tt-_----o c-= ~ _ I(tJcgte~ In-ec h )
- bull M
mdash C_
C= middot -----H
-----11---------
j -- ---- -------- -------- --- shy
e --J-----------IIgt k tl)~- ---
S-t
-Iia4-lsquo4
7 ~ -
bull
U= (Y) ~ A )ote-
111
(~dt- ~P-~ ( M~Se~yOIPgt weclL ~+- 01) eVtph _10l
Q 1 1--
-
lsquoI)
-xlsquoS~1s n~ct~_--J e _ __________
_~ ~ 1-o CJ Ql~ ~W)=___~=~__~~ ___-tl--____
ii JV
j $1
S -=vr~ec -ellVl 1itJ
1ieoreM OTP i (A VlCbV)ditl9 l _______ ----( e uv( ~~4~T C-Ie-S c~___-t~--- w~~
Co~ power J___-----________ CI~Q 1ftnttior)-~-eOIe~c-17 S-eCuv______
bull
5
itt One-Trne PA
i M= lsquoci IOU- (x-st srnrsquo) K to 10deg (soc A-bftrdquopdrdquo(keY)
lsquoLI- = i i i bull bull
lie K reDi IC iV Pec)J
LL tI_ iDIIOO
= re(kekrsquo) Meordquo= 11
OTP r4nr44vbn_veoahtc)y 4ecre Es
Can not break scirsquoenie1ersquoStn t trn rcck cckspAc1yotC
(Conpca to csnpu-tkraoI4 sccsee_ t npices assinng+rbn
4t amplsquoa kas Jk4 Ccrsquoptn ptrsquotr camp+ fJcr
j43t flwbrsquo42t3 lsquo)
lsquoveuml5 Ufl2rrZn Yc
lsquop (crdquoigraversquo) GJCbS lsquo0r rnesYaye 1
P (Mi1= vamps -nrsquo tL4 mt sM
ac- lwiirsquoj seen ccr-kik Crsquo
eot rOTP1 (np(jc)
bi 6 seek Crdquo
6
- - ------
51
1
root-~
I r
lsquomdashlsquo
lb
H
u
mdash
mdash
1 3 lsquomdash
F
lsquo1
A rr
1_
a-d
r
6rsquo
_mdash
lb -o
2 ii
J u
11 mdash
p
j i
lsquo2
p ii
3 3
rmdash
mdash
3
J
t
C
II f
l
rrk
gtlsquo
gtmdash
lsquot
) b
ardquo
p
~---- --I [fufj(fij - shy L~ 3-- ___--J
---~---
7
-
bull
(N3
0
Crsquo 3
z -D divide
c1__-
0C
(~ ~ il c~~ji cif~~Vt bi~ CCMe5
co((1~dJ bit J- krypkl M~~ hgt ~je ) -I-
J-
(tbull
OTP Jo~ f pViJ~ C1 Q~ertt4tb of-7
cs it
Me~$CIcye Grgtie~ Dr fttdn q~l~+ Ihodctb
( Qli)
I
lsquo3 C 3 bull iibull ~eeoe je s-ccreb
sit ~ s eco-e1 -I 5
_ C -j I 3
3
bull
bull ~eef 1hM 5epoundret
bull avoId re-Il~4 ~ (jc Veno)t I- L tpound)C~ - (M1(pound)ltj(f) (Ma tf) K)
C
n r Crsquo 0
middot I
bull
CA Sa 6) k )7I T I
rbull
- +shy tshy
8
I
l
bull
Jr I L1 5
RIIJ1ot1le $04Vte) (o MOit ci~ we(e ~l~Ccjgtb- 1-0 ClIp ~r~k~)mdash
V 0
r
mdash
lsquoP
_s Crsquo r -e V
r -c a
0 ( I
bull
St
2rc
f-JF
3
Ocy
bull fI itrtgtphol-e J
_-
mdash
-
mdashr
5_
c
lsquoo
r e Lh er ty fl in or-LCIVIf_cl AlpunR Scho~ickrlsquoIrsquo
Coin) q~tJe
I lsquoED
It
CA e (
5Olg0~ cp set
4
fl
bull 1acllt~~ 5p~ Iq middotibS
bull 0 S~ MOIleMts (I Iqp -=Sgt Clt ~ )
i
A --ey---- B l gte
t
bull3 3
T 1
3
bull
1= A ~
t ell J +r~~i~ B ~qJt -t-~i t beeps
c hrW $ W StUeTJr
~
~y
I S d5
~~q- Ket D~ir~h
I F~5 (a) ~+ ~+ (Q(f~()~)4
bull
9- a I r lsquoa r It
t ~ ~ t ~ t
fl Irsquo V
amp 0 H- 2 3r
0 3 lsquoC
S 3
A sJs ~ 1 Y+o~gt po~i 1ltd IgtI~JIt B rmiddotlgtkll1 11gt- chOI(O 11- t4 kl)o Iv 6middot~ slJ Ivc I~ c
O IS ~
C
-
0 lsquop Irsquo Dr
bulltr
a-
-v
1
9
MIT OpenCourseWarehttpocwmitedu
1HWZRUNDQGampRPSXWHU6HFXULWSpring 2014
For information about citing these materials or our Terms of Use visit httpocwmiteduterms
itt One-Trne PA
i M= lsquoci IOU- (x-st srnrsquo) K to 10deg (soc A-bftrdquopdrdquo(keY)
lsquoLI- = i i i bull bull
lie K reDi IC iV Pec)J
LL tI_ iDIIOO
= re(kekrsquo) Meordquo= 11
OTP r4nr44vbn_veoahtc)y 4ecre Es
Can not break scirsquoenie1ersquoStn t trn rcck cckspAc1yotC
(Conpca to csnpu-tkraoI4 sccsee_ t npices assinng+rbn
4t amplsquoa kas Jk4 Ccrsquoptn ptrsquotr camp+ fJcr
j43t flwbrsquo42t3 lsquo)
lsquoveuml5 Ufl2rrZn Yc
lsquop (crdquoigraversquo) GJCbS lsquo0r rnesYaye 1
P (Mi1= vamps -nrsquo tL4 mt sM
ac- lwiirsquoj seen ccr-kik Crsquo
eot rOTP1 (np(jc)
bi 6 seek Crdquo
6
- - ------
51
1
root-~
I r
lsquomdashlsquo
lb
H
u
mdash
mdash
1 3 lsquomdash
F
lsquo1
A rr
1_
a-d
r
6rsquo
_mdash
lb -o
2 ii
J u
11 mdash
p
j i
lsquo2
p ii
3 3
rmdash
mdash
3
J
t
C
II f
l
rrk
gtlsquo
gtmdash
lsquot
) b
ardquo
p
~---- --I [fufj(fij - shy L~ 3-- ___--J
---~---
7
-
bull
(N3
0
Crsquo 3
z -D divide
c1__-
0C
(~ ~ il c~~ji cif~~Vt bi~ CCMe5
co((1~dJ bit J- krypkl M~~ hgt ~je ) -I-
J-
(tbull
OTP Jo~ f pViJ~ C1 Q~ertt4tb of-7
cs it
Me~$CIcye Grgtie~ Dr fttdn q~l~+ Ihodctb
( Qli)
I
lsquo3 C 3 bull iibull ~eeoe je s-ccreb
sit ~ s eco-e1 -I 5
_ C -j I 3
3
bull
bull ~eef 1hM 5epoundret
bull avoId re-Il~4 ~ (jc Veno)t I- L tpound)C~ - (M1(pound)ltj(f) (Ma tf) K)
C
n r Crsquo 0
middot I
bull
CA Sa 6) k )7I T I
rbull
- +shy tshy
8
I
l
bull
Jr I L1 5
RIIJ1ot1le $04Vte) (o MOit ci~ we(e ~l~Ccjgtb- 1-0 ClIp ~r~k~)mdash
V 0
r
mdash
lsquoP
_s Crsquo r -e V
r -c a
0 ( I
bull
St
2rc
f-JF
3
Ocy
bull fI itrtgtphol-e J
_-
mdash
-
mdashr
5_
c
lsquoo
r e Lh er ty fl in or-LCIVIf_cl AlpunR Scho~ickrlsquoIrsquo
Coin) q~tJe
I lsquoED
It
CA e (
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1HWZRUNDQGampRPSXWHU6HFXULWSpring 2014
For information about citing these materials or our Terms of Use visit httpocwmiteduterms
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bulltr
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1
9
MIT OpenCourseWarehttpocwmitedu
1HWZRUNDQGampRPSXWHU6HFXULWSpring 2014
For information about citing these materials or our Terms of Use visit httpocwmiteduterms
-
bull
(N3
0
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z -D divide
c1__-
0C
(~ ~ il c~~ji cif~~Vt bi~ CCMe5
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(tbull
OTP Jo~ f pViJ~ C1 Q~ertt4tb of-7
cs it
Me~$CIcye Grgtie~ Dr fttdn q~l~+ Ihodctb
( Qli)
I
lsquo3 C 3 bull iibull ~eeoe je s-ccreb
sit ~ s eco-e1 -I 5
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3
bull
bull ~eef 1hM 5epoundret
bull avoId re-Il~4 ~ (jc Veno)t I- L tpound)C~ - (M1(pound)ltj(f) (Ma tf) K)
C
n r Crsquo 0
middot I
bull
CA Sa 6) k )7I T I
rbull
- +shy tshy
8
I
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bull
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RIIJ1ot1le $04Vte) (o MOit ci~ we(e ~l~Ccjgtb- 1-0 ClIp ~r~k~)mdash
V 0
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mdash
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_-
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5_
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lsquoo
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Coin) q~tJe
I lsquoED
It
CA e (
5Olg0~ cp set
4
fl
bull 1acllt~~ 5p~ Iq middotibS
bull 0 S~ MOIleMts (I Iqp -=Sgt Clt ~ )
i
A --ey---- B l gte
t
bull3 3
T 1
3
bull
1= A ~
t ell J +r~~i~ B ~qJt -t-~i t beeps
c hrW $ W StUeTJr
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~y
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I F~5 (a) ~+ ~+ (Q(f~()~)4
bull
9- a I r lsquoa r It
t ~ ~ t ~ t
fl Irsquo V
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0 3 lsquoC
S 3
A sJs ~ 1 Y+o~gt po~i 1ltd IgtI~JIt B rmiddotlgtkll1 11gt- chOI(O 11- t4 kl)o Iv 6middot~ slJ Ivc I~ c
O IS ~
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-
0 lsquop Irsquo Dr
bulltr
a-
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1
9
MIT OpenCourseWarehttpocwmitedu
1HWZRUNDQGampRPSXWHU6HFXULWSpring 2014
For information about citing these materials or our Terms of Use visit httpocwmiteduterms
bull
Jr I L1 5
RIIJ1ot1le $04Vte) (o MOit ci~ we(e ~l~Ccjgtb- 1-0 ClIp ~r~k~)mdash
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bull
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5_
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lsquoo
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Coin) q~tJe
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It
CA e (
5Olg0~ cp set
4
fl
bull 1acllt~~ 5p~ Iq middotibS
bull 0 S~ MOIleMts (I Iqp -=Sgt Clt ~ )
i
A --ey---- B l gte
t
bull3 3
T 1
3
bull
1= A ~
t ell J +r~~i~ B ~qJt -t-~i t beeps
c hrW $ W StUeTJr
~
~y
I S d5
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I F~5 (a) ~+ ~+ (Q(f~()~)4
bull
9- a I r lsquoa r It
t ~ ~ t ~ t
fl Irsquo V
amp 0 H- 2 3r
0 3 lsquoC
S 3
A sJs ~ 1 Y+o~gt po~i 1ltd IgtI~JIt B rmiddotlgtkll1 11gt- chOI(O 11- t4 kl)o Iv 6middot~ slJ Ivc I~ c
O IS ~
C
-
0 lsquop Irsquo Dr
bulltr
a-
-v
1
9
MIT OpenCourseWarehttpocwmitedu
1HWZRUNDQGampRPSXWHU6HFXULWSpring 2014
For information about citing these materials or our Terms of Use visit httpocwmiteduterms