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Introduction
Statistical and
Computational Security
Cryptography and Protocols
Andrei Bulatov
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View Full Document Cryptography and Protocols – Statistical Security
52
Symmetric Encryption Scheme
A symmetric encryption scheme is a triple of algorithms
(K,E,D)
 K
keys generation
 E
encryption algorithm
 D
decryption
algorithm
For simplicity assume that
k
←
K
uniformly at random,
or
plaintext
In general,
E
(and possibly
D)
are randomized
l
k
}
1
,
0
{
∈
l
U
k
∈
m
P
}
1
,
0
{
∈
C
P
E
E
k
m
l
=
→
×
)
(

}
1
,
0
{
}
1
,
0
{
}
1
,
0
{
:
*
P
C
D
D
k
m
l
=
→
×
)
(

}
1
,
0
{
}
1
,
0
{
}
1
,
0
{
:
*
Cryptography and Protocols – Statistical Security
53
Perfect Security
Let
(K,E,D)
be a symmetric encryption scheme. It is said to be
perfectly secure
if for any two plaintexts
and
a
ciphertext
C
where the probability is over the random choice
k
←
K,
and also
over the coins flipped by
E
],
)
(
Pr[
]
)
(
Pr[
2
1
C
P
E
C
P
E
k
k
=
=
=
2
1
,
P
P
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View Full Document X
Y
000
001
010
011
100
101
110
111
Let
X
and
Y
be two distributions over
The statistical
distance
between
X
and
Y
,
denoted
∆
(
X
,
Y
)
is
Cryptography and Protocols – Statistical Security
54
Statistical Distance

]
Pr[
]
Pr[

max
}
1
,
0
{
T
T
m
T
∈

∈
⊆
Y
X
m
}
1
,
0
{
T
If
∆
(
X
,
Y
) ≤
ε
we write
Y
X
ε
≡
Cryptography and Protocols – Statistical Security
55
Statistical Security
A symmetric encryption scheme is said to be
ε
statistically secure,
if for any two plaintexts
distributions
are
ε
equivalent
Theorem
.
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This note was uploaded on 03/05/2012 for the course CMPT 404 taught by Professor Andreia.bulatov during the Spring '12 term at Simon Fraser.
 Spring '12
 AndreiA.Bulatov

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