Lec 7 : Data Security
Stream Cipher Systems
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3.1 RUNNING-KEY CIPHER:
If we choose a key with its length as long as the plaintext message, then the
cipher is called running-key cipher. A text of a book can be used as a key sequence in
a substitution cipher based on shifted alphabets (i.e. non-periodic vigenere). Running
key might be expected to be unbreakable because it has non-periodic key;
but the key has redundancy due to non-randomness of its characters.
Example:
Giving a key K selected from a textbook and a message M:
M:
T H E T R E A S U R E I S B U R I E D....
K:
T H E S E C O N D C I P H E R I S A N....
EK (M): M O I L V G O F X T M X Z F L A A E Q....
If the key has redundancy, the cipher may be breakable using friend Nan's
method.Fried Nan's approach is based on the observation that a large proportion of
letters in the cipher text will correspond to encipherments , where both, the plaintext
and key letters fall in the high frequency category.
3.2 VERNAM CIPHER:
The implementation of one-time раd cipher is in vented by Gilbert Vernam in
1917; he designed a cryptographic device based on 32-character Baudot code for new
teletype writer developed at AT&T. Each character is represented as a combination of
five marks and spaces corresponding to 1 and 0. A Vemam idea is to run a second
synchronized non repeating random sequence of key character punched on paper tape
during transmission which would cause each Baudot (0 or 1) on the message tape to
be Xored with its corresponding value on the key tape. Each plain text is added
(mod 2) to the key stream, and generates a cipher text bit stream.
C = Ek (m) =C1 , C2 ,C3, …..
Where Ci = (mi +kj) mod 2
Vernam cipher is efficiently implemented in microelectronics by taking the
(exlusive_or) (XOR).
Lec 7 : Data Security
Stream Cipher Systems
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Ci =Mi ki
Ci ki =mi (ki ki)
Where ki ki=0
XOR Truth table:
X1
X2
XOR
0
0
0
1
0
1
0
1
1
0
0
0
Example:
M=A: 11000
K=D: 10010
E (M): 01010
If Vernam key is repeated then the cipher is equal to a running-key Cipher with a
text as a key. There were two immediate problems; first both a party has to possess
identical copies of key tape, secondly, repeated use carried the danger of working out
the period of repetition cycle.
3.3 ONE-TIME PAD CIPHER:
Army cryptologist Major Joseph Mauborgne who carried out a research into
Vemam's system, he suggested an endless tape contain sequence of random characters
which is used as a key stream, and used one time and one time only. If a peace of this
key is used to encrypt a message, then there is not enough information to break the
cipher. Such a cipher called one-time pad cipher, because the key is not repeated (i.e.
it is not periodic). If plaintext message M consist of m1 m2 m3... ..............md , then a
Lec 7 : Data Security
Stream Cipher Systems
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piece of one-time key k1 k2 k3............... ...kd will be used to encrypt this message.
C =Ek (M)
where Ci = (mi +ki) mod n
The main drawback of the cipher is that; it requires a long and random key sequence,
which should be available for both parties. Figure 3-1 illustrates One-time pad system.
Random sequence K1 K2….. Kn
Mixer
Cryptogram C1C2…CN
Message m1m2... mn
Figure (3-1) One Time Pad System.
Reusing one-time pad can lead to a catastrophe. Suppose, a two plaintext M
1
2
and M are encrypted modulo 26 with the same random key K as shown in the
following .
M1 S E L L S I L V E R
18 4 11 11 18 8 11 21 4 17
K
11 6 20 4 1 5 6 9 5 20
C 1 3 10 5 15 2 13 17 4 9 11
D K F P C N R E J L
l
Cli = M i + KI mod 26
C2i = M2i + KI mod 26
M2 B U Y C O C A I N E
1 20 24 2 14 2 0 8 13 4
K 11 6 20 4 1 5 6 9 5 20
C2 12 0 18 6 24 7 6 17 18 24
MA S G Y H G R S Y
Lec 7 : Data Security
Stream Cipher Systems
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If both cipher text C1 and C2 are intercepted, cryptanalyst may create a third cipher
text C3 from C1 and C2: C3 I = Cli - C2i mod 26
Now we can decrypt C3 by: M1 = C3 + M2 mod 26
C1
D K F P C N R E J L
3
10 5 15 2 13 17 4 9
11
C2
M A S G Y H G R S Y
12 0 18 6 24 7 6 17 18
24
C3
17 10 13 9 4 6 11 13 17
13
R K N J E G L N
R
B U Y C O C A
N
N
M2
I
E
1 20 24 2 14 2
0
8
13
4
M1
18 4 11 11 18 8 11 21 4
17
S E L L S I L V E
R
As mentioned above One-Time-Pad system (OTP) is a perfect secrecy
cryptographic system, and indeed there are some applications in today's world,
primarily for Ultra-Secure low bandwidth channels. Hot line between the United
State and the former Soviet Union was (is it still active!) rumored to be encrypted
with a One-Time-Pad (OTP). Unfortunately most practical applications can not use
OTP for many reasons, among them, key distribution and storage problems. Since
the famous paper of Shannon in 1947 till now, a tremendous work has been done to
build (or more precisely to simulate) a perfect secrecy cryptographic system.