INF3510 Information Security University of Oslo Spring 2014 Lecture 5 Cryptography University of Oslo, spring 2014 Leif Nilsen Outline • What is cryptography? • Brief crypto history • Security issues • Symmetric cryptography – Stream ciphers – Block ciphers – Hash functions • Asymmetric cryptography – Factoring based mechanisms – Discrete Logarithms – Digital signatures L05 Cryptography INF3510 - UiO 2014 2 Want to learn more? Look up UNIK 4220 What is cryptology? L05 Cryptography INF3510 - UiO 2014 3 Secure communication over unsecure channels - Confidentiality - Integrity - Authenticity - Non-repudiation Alice Bob Symmetric crypto Asymmetric crypto Oscar Terminology • Cryptography is the science of secret writing with the goal of hiding the meaning of a message. • Cryptanalysis is the science and sometimes art of breaking cryptosystems. L05 Cryptography INF3510 - UiO 2014 4 Cryptology Cryptography Cryptanalysis
Transcript
INF3
510
Info
rmat
ion
Sec
urity
Uni
vers
ity o
f Osl
oS
prin
g 20
14
Lect
ure
5C
rypt
ogra
phy
Uni
vers
ity o
f Osl
o, s
prin
g 20
14Le
if N
ilsen
Out
line
•W
hat i
s cr
ypto
grap
hy?
•B
rief c
rypt
o hi
stor
y•
Sec
urity
issu
es•
Sym
met
ric c
rypt
ogra
phy
–S
tream
cip
hers
–B
lock
cip
hers
–H
ash
func
tions
•A
sym
met
ric c
rypt
ogra
phy
–Fa
ctor
ing
base
d m
echa
nism
s–
Dis
cret
e Lo
garit
hms
–D
igita
l sig
natu
res
L05
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ptog
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2
Wan
t to
lear
n m
ore?
Look
up
UN
IK 4
220
Wha
t is
cryp
tolo
gy?
L05
Cry
ptog
raph
yIN
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143
Se
cu
re c
om
mu
nic
atio
no
ver
un
sec
ure
ch
an
ne
ls
-C
on
fid
en
tia
lity
-In
teg
rity
-A
uth
en
tic
ity
-N
on
-re
pu
dia
tio
n
Alic
eB
ob
Sym
me
tric
cry
pto
Asy
mm
etr
ic c
ryp
to
Osc
ar
Term
inol
ogy
•C
rypt
ogra
phy
is th
e sc
ienc
e of
sec
ret w
ritin
g w
ith th
e go
al o
f hid
ing
the
mea
ning
of a
m
essa
ge.
•C
rypt
anal
ysis
is th
e sc
ienc
e an
d so
met
imes
ar
t of b
reak
ing
cryp
tosy
stem
s.
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ptog
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4
Cry
ptol
ogy
Cry
ptog
raph
yC
rypt
anal
ysis
Taxo
nom
y of
cry
ptog
raph
ic p
rimiti
ves
L05
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ptog
raph
yIN
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5L0
5 C
rypt
ogra
phy
Whe
n is
cry
ptog
raph
y us
ed?
•S
ome
exam
ple
situ
atio
ns:
–H
isto
rical
ly, t
he m
ilitar
y an
d sp
y ag
enci
es w
ere
the
mai
n us
ers
of c
rypt
olog
y•
Situ
atio
n: tr
ansm
ittin
g m
essa
ges
over
inse
cure
cha
nnel
s–
Now
, it i
s us
ed in
man
y ot
her a
reas
, esp
ecia
lly in
el
ectro
nic
info
rmat
ion
proc
essi
ng a
nd
com
mun
icat
ions
tech
nolo
gies
: •
Ban
king
:you
r fin
anci
al tr
ansa
ctio
ns, s
uch
as E
FTP
OS
•C
omm
unic
atio
ns:y
our m
obile
pho
ne c
onve
rsat
ions
•In
fo s
tore
d in
dat
abas
es:h
ospi
tals
, uni
vers
ities
, etc
.•
Cry
ptog
raph
y ca
n be
use
d to
pro
tect
info
rmat
ion
in
stor
age
or d
urin
g tra
nsm
issi
onIN
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6
Mod
el o
f sym
met
ric c
rypt
osys
tem
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ptog
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Term
inol
ogy
•E
ncry
ptio
n: p
lain
text
(cle
ar te
xt) M
is c
onve
rted
into
a c
iphe
rtext
C u
nder
the
cont
rol o
f a k
ey k
.–
We
writ
e C
= E
(M, k
).•
Dec
rypt
ion
with
key
kre
cove
rs th
e pl
aint
ext M
fro
m th
e ci
pher
text
C.
–W
e w
rite
M =
D(C
, k).
•S
ymm
etric
cip
hers
: the
sec
ret k
ey is
use
d fo
r bot
h en
cryp
tion
and
decr
yptio
n.•
Asy
mm
etric
cip
hers
: Pai
r of p
rivat
e an
d pu
blic
ke
ys w
here
it is
com
puta
tiona
lly in
feas
ible
to
deriv
e th
e pr
ivat
e de
cryp
tion
key
from
the
corr
espo
ndin
g pu
blic
enc
rypt
ion
key.
8L0
5 C
rypt
ogra
phy
INF3
510
-UiO
201
4
L05
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ptog
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Cae
sar c
iphe
r
Exam
ple:
Cae
sar c
iphe
rP
={abcdefghijklmnopqrstuvwxyz}
C=
{DEFGHIJKLMNOPQRSTUVWXYZABC}
Plai
ntex
t:kryptologi er et spennende fag
Chi
pher
text
:NUBSWRORJL HU HT VSHQQHQGH IDJ
Not
e: C
aesa
r chi
pher
in th
is fo
rm d
oes
not i
nclu
de a
va
riabl
e ke
y, b
ut is
an
inst
ance
of a
“shi
ft-ci
pher
” us
ing
key
K=
3.
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ptog
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Num
eric
al e
ncod
ing
of th
e al
phab
et
Usi
ng th
is e
ncod
ing
man
y cl
assi
cal c
rypt
o sy
stem
s ca
n be
exp
ress
ed a
s al
gebr
aic
func
tions
ove
r Z26
(E
nglis
h al
phab
et) o
r Z29
(Nor
weg
ian
alph
abet
)
ab
cd
ef
gh
ij
kl
mn
o
01
23
45
67
89
1011
1213
14
pq
rs
tu
vw
xy
zæ
øå
1416
1718
1920
2122
2324
2526
2728
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ptog
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Shi
ft ci
pher
Let P
=C
=Z
29.
For 0
�K�
28, w
e de
fine
E(x
, K) =
x+
K(m
od 2
9)an
d D(y
, K) =
y-K
(mod
29)
(x, y
�Z
29)
Que
stio
n:W
hat i
s th
e si
ze o
f the
key
spa
ce?
Puz
zle:
ct =
LA
HY
CX
PA
JYQ
HR
BW
NN
MN
MO
XA
BN
LDA
NLX
VV
DW
RLJ
CR
XW
BFi
nd th
e pl
aint
ext!
Exh
aust
ive
sear
ch
For[i
=0, i
<26,
i++,
Prin
t["K
ey =
", i,
" P
lain
= ",
dec
rypt
[ct,1
,i]]]
Key
= 0
Pla
in =
LA
HY
CX
PA
JYQ
HR
BW
NN
MN
MO
XA
BN
LDA
NLX
VV
DW
RLJ
CR
XW
BK
ey =
1 P
lain
= K
ZGX
BW
OZI
XP
GQ
AVM
MLM
LNW
ZAM
KC
ZMK
WU
UC
VQ
KIB
QW
VA
Key
= 2
Pla
in =
JY
FWA
VN
YH
WO
FPZU
LLK
LKM
VY
ZLJB
YLJ
VTT
BU
PJH
AP
VU
ZK
ey =
3 P
lain
= IX
EV
ZUM
XG
VN
EO
YTK
KJK
JLU
XY
KIA
XK
IUS
SA
TOIG
ZOU
TYK
ey =
4 P
lain
= H
WD
UY
TLW
FUM
DN
XSJ
JIJI
KTW
XJH
ZWJH
TRR
ZSN
HFY
NTS
XK
ey =
5 P
lain
= G
VC
TXS
KV
ETL
CM
WR
IIHIH
JSV
WIG
YV
IGS
QQ
YR
MG
EX
MS
RW
Key
= 6
Pla
in =
FU
BS
WR
JUD
SK
BLV
QH
HG
HG
IRU
VH
FXU
HFR
PP
XQ
LFD
WLR
QV
Key
= 7
Pla
in =
ETA
RV
QIT
CR
JAK
UP
GG
FGFH
QTU
GE
WTG
EQ
OO
WP
KE
CV
KQ
PU
Key
= 8
Pla
in =
DS
ZQU
PH
SB
QIZ
JTO
FFE
FEG
PS
TFD
VS
FDP
NN
VO
JDB
UJP
OT
Key
= 9
Pla
in =
CR
YP
TOG
RA
PH
YIS
NE
ED
ED
FOR
SE
CU
RE
CO
MM
UN
ICA
TIO
NS
Key
= 1
0 P
lain
= B
QX
OS
NFQ
ZOG
XH
RM
DD
CD
CE
NQ
RD
BTQ
DB
NLL
TMH
BZS
HN
MR
Key
= 1
1 P
lain
= A
PW
NR
ME
PY
NFW
GQ
LCC
BC
BD
MP
QC
AS
PC
AM
KK
SLG
AY
RG
MLQ
Key
= 1
2 P
lain
= Z
OV
MQ
LDO
XM
EV
FPK
BB
AB
AC
LOP
BZR
OB
ZLJJ
RK
FZX
QFL
KP
•.
• L05
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Sub
stitu
tion
ciph
er-e
xam
ple
8841
7619
9373
9701
9545
4361
6000
000 �
2103
ab
cd
ef
gh
ij
kl
mn
o
UD
MI
PY
ÆK
OX
SN
ÅF
A
pq
rs
tu
vw
xy
zæ
øå
ER
TZ
BØ
CQ
GW
HL
VJ
Pla
inte
xt:f
erm
atss
iste
teor
emC
iphe
rtext
:YP
TÅU
BZZ
OZB
PB
PATP
Å
Wha
t is
the
size
of t
he k
ey s
pace
?
Lette
r Fre
quen
cies
� s
tatis
tical
atta
cks
•E
ncry
ptio
n m
ust h
ide
stat
istic
al p
atte
rns
in d
ata
•A
chie
ved
with
a s
erie
s of
prim
itive
func
tions
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Lette
r fre
quen
cies
in
Eng
lish
Less
ons
lear
ned
•A
cip
her w
ith a
sm
all k
eysp
ace
can
easi
ly b
e at
tack
ed b
y ex
haus
tive
sear
ch•
A la
rge
keys
pace
is n
eces
sary
for a
sec
ure
ciph
er, b
ut it
is b
y its
elf n
ot s
uffc
ient
•M
onoa
lpha
betic
al s
ubst
itutio
n ci
pher
s ca
n ea
sily
be
bro
ken
L05
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15
Vig
enér
e (1
523-
1596
)A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
B C D E F G H I J K L M N O P Q R S T U V W X Y Z A
C D E F G H I J K L M N O P Q R S T U V W X Y Z A B
D E F G H I J K L M N O P Q R S T U V W X Y Z A B C
E F G H I J K L M N O P Q R S T U V W X Y Z A B C D
F G H I J K L M N O P Q R S T U V W X Y Z A B C D E
G H I J K L M N O P Q R S T U V W X Y Z A B C D E F
H I J K L M N O P Q R S T U V W X Y Z A B C D E F G
I J K L M N O P Q R S T U V W X Y Z A B C D E F G H
J K L M N O P Q R S T U V W X Y Z A B C D E F G H I
KL M N O P Q R S T U V W X YZ A B C D E F G H I J
L M N O P Q R S T U V W X Y Z A B C D E F G H I J K
M N O P Q R S T U V W X Y Z A B C D E F G H I J K L
N O P Q R S T U V W X Y Z A B C D E F G H I J K L M
O P Q R S T U V W X YZ A B C D E F G H I J K L M N
P Q R S T U V W X Y Z A B C DE F G H I J K L M N O
Q R S T U V W X Y Z A B C D E F G H I J K L M N O P
R S T U V W X Y Z A B CD E F G H IJ K L M N O P S
S T U V W X Y Z A B C D E F G H I J K L M N O P Q R
T U V W X Y ZA B C D E F G H I J K L M N O P Q R S
U V W X Y Z A B C D E F G H I J K L M N O P Q R S T
V W X Y Z A B C D E F G H I J K L M N O P Q R S T U
W X Y Z A B C D E F G H I J K L M N O P Q R S T U V
X Y Z A B C D E F G H I J K L M N O P Q R S T U V W
YZ A B C D E F GH I J K L M N O P Q R S T U V W X
Z A B C D E F G H I J K L M N O P Q R S T U V W X Y
