CIS 5371
C
t
h
Cryptography
7. Symmetric encryption
symmetric cryptography
1

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C
t
hi
t
Cryptographic systems
C
t
t
(
M C K K’ G E D
)
Cryptosystem: (
M,C,K,K’,G,E,D
M, plaintext message space
C, ciphertext message space
K, K’, encryption and decryption key spaces
G
N
K
K’ k
i
l
i h
G :
K’, key generation algorithm
E : M
K
C, encryption algorithm
D : C
K’
M decryption algorithm
K
M, decryption algorithm
G,E,D must be efficient
symmetric cryptography
2

E
l
Examples
C
t
t
(
M C K K’ G E D
)
Cryptosystem: (
M,C,K,K’,G,E,D
Substitution Cipher
:
M = C
=
Z
26
, with
K=K’
The encryption algorithm
is a mapping E
k
:M
C
--
E
k
(x) =
(x), where k
K
is the key.
The dencryption algorithm is a mapping D
k
:M
C
--
D
k
(y) =
-1
(y).
Shift Ciphe
M
C
K
K’
Z
ith
Shift Cipher
:
M = C = K = K’
=
26
, with
--
E
k
(x) =
x + k mod26
--
D
k
(y) = y
–
k mod26
symmetric cryptography
3
(y)
y k mod26
where x,y
Z
26

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