Symmetric Cipher Model

Introduction
Symmetric encryption, also referred to as
conventional encryption or single-key encryption, was the only type of encryption in use prior to the
development of public-key encryption in
It remains by far the most widely used of types of encryption.
Beginning with a look at a general model
the
the
1970s.
two
for
the
symmetric encryption process; this will enable us to
understand the context within which the algorithms are used

Content
Symmetric cipher
Secure Use of Conventional Encryption
1.
–
–
2.
3.
–
–
Symmetric Encryption
Cryptographic systems
Cryptanalysis
Cryptanalytic Attacks
Brute-force attack
Scheme
Brute-Force Cryptanalysis
of
Caesar Cipher
●
4.
–
Monoalphabetic Ciphers
Breaking Monoalphabetic Cipher

Symmetric
cipher
A form of cryptosystem in which encryption and
decryption are performed using the same key. Also
●
known as conventional encryption.
A symmetric encryption scheme has five ingredients.
●

Secure Use of Conventional Encryption
Two requirements for secure use of conventional
encryption:
1. Strong algorithm – an opponent unable to decipher the ciphertext or figure out the key.
2. Shared secret key – sender and receiver must have obtained copies of the secret key in a secure fashion and must keep the key secure.

Symmetric Encryption Scheme
We do not need to keep the algorithm secret; we
need to keep only the key secret.
●

Cryptographic systems
Characterized
1. The type plaintext to
along three independent dimensions:
of operations used for transforming ciphertext. All encryption algorithms
are based on two general principles:
Substitution: the plaintext is mapped into
another element
Transposition: the plaintext elements are rearranged
●
●

2.
–
The number of keys used.
Symmetric: both sender and receiver use the same key (a.k.a. single-key, secret-key, or conventional encryption)
Asymmetric: the sender and receiver use different key (a.k.a. two-key, or public-key encryption)
The way in which the plaintext is processed.
A block-cipher: processes the input one block of elements at a time, producing an output block for
–
3.
–
each input block.
A stream-cipher: processes the input elements continuously, producing output one element at a time, as it goes along
–

Cryptanalysis
Two general approaches to attacking a conventional
encryption scheme:
Cryptanalysis: exploits the characteristics of the
algorithm to attempt to deduce a specific plaintext or to deduce the key being used.
Brute-force attack: tries every possible key on a piece of ciphertext until an intelligible translation into plaintext is obtained
–
–

Cryptanalytic
Attacks
Ciphertext only:
●
Encryption algorithm
Ciphertext
–
–
Known plaintext:
●
Encryption algorithm
Ciphertext
One or more plaintext-ciphertext with the secret key
–
–
–
pairs
formed

Chosen plaintext:
●
Encryption algorithm
Ciphertext
Plaintext message chosen by cryptanalyst,
–
–
–
together with its corresponding
generated with the secret key
Chosen ciphertext:
ciphertext
●
Encryption algorithm
Ciphertext
Purported ciphertext chosen by together with its corresponding
–
–
–
cryptanalyst,
decrypted
plaintext generated with the secret key

Chosen text:
●
Encryption algorithm
Ciphertext
Plaintext message chosen by cryptanalyst,
–
–
–
together with its corresponding
generated with the secret key Purported ciphertext chosen by together with its corresponding
ciphertext
cryptanalyst,
decrypted
–
plaintext generated with the secret key

A
Brute-Force
Attack
Trying every possible key until an intelligible
●
translation of the ciphertext into plaintext is
obtained.
On average, half of all possible keys must be tried achieve success.
to
●

Brute-Force Cryptanalysis of Caesar
Cipher
Three important characteristics of this problem enabled
us
to use a brute-force cryptanalysis:
1. The encryption and decryption algorithms are
known.
2. There are only 25 keys to try.
3. The language of the plaintext is known and easily recognizable.

Example: Let's encipher some text using Caesar
cipher with the secret key is
3. toga
WRJD
plain:
cipher:
meet
PHHW
me
PH
the
after
DIWHU
the
WKH
party
SDUWB
Simply try all
the results.
25 possible keys. Below shown

Monoalphabetic Ciphers
With only 25 possible keys, the Caesar cipher is far
●
from secure. A dramatic increase in the key
space
can be achieved by
substitution.
allowing an arbitrary
plain:
cipher:
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
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
If instead,
the
"cipher"
line can
be any
permutation
●
of the 26 alphabetic characters,
then there are 26! or
greater than 4 x
1026
possible keys.

Breaking
Monoalphabetic
Cipher
The ciphertext to be solved is
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXU
DBMETSXAIZVUEPHZHMDZSHZOWSFPAPPDTSV
PQUZWYMXUZUHSXEPYEPOPDZSZUFPOMBZWPF
UPZHMDJUDTMOHMQ
The relative frequency of the letters
P 13.33
H 5.83
F 3.33
B 1.67
C 0.00
Z 11.67
D 5.00
W 3.33
G 1.67
K 0.00
S 8.33
E 5.00
Q 2.50
Y 1.67
L 0.00
U 8.33
V 4.17
T 2.50
I 0.83
N 0.00
O 7.50
X 4.17
A 1.67
J 0.83
R 0.00
M 6.67

Relative Frequency of Letters in English Text

Comparing two previously shown
letters P and Z are the equivalents and t, but it is not certain which is
tables that cipher
of plain letters
which
e
The letters S, U, O, M, and H are all of relatively
high frequency and probably correspond to plain letters from the set {a, h, i, n, o, r, s}.
The letters with the lowest frequencies (namely, A,
B, G, Y, I, J) are likely included in the set {b, j, k,
v, x, z}.
A more systematic approach is to look for other regularities. For example, certain words may be known to be in the text. Or we could look for repeating sequences of cipher letters and try to deduce their plaintext equivalents.
q,

A powerful tool is to look at the frequency
of
two-letter
combinations,
known
as
digrams.
The most common digram in cipher
is ZW, which
appears three times. So we make the correspondence:
Z →
t and W →
h.

So far, then, we have
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
t
a
e
e
te
a
that
e
e
a
a
VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
e
t
ta
t
ha
e
ee
a
e
th
t
a
EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
e
e e
tat
e
the
t
Only four letters have
have quite a bit of the
been identified,
message.
but
already
we

Continued analysis of frequencies plus trial and
error should easily yield a solution from this point.
it
was
disclosed
yesterday
that
several
informal
but
direct
contacts
have
been
the
made
with
cong
political
representatives
of
viet
in
moscow
The complete plaintext, with spaces added between
words, above.