Classical Encryption
Techniques
There are two basic building blocks of all encryption
techniques:
Substitution
Transposition
1 SUBSTITUTION TECHNIQUES
A substitution technique is one in which the words (or text)
of plaintext are replaced by other letters or by numbers or symbols. If the plaintext
is viewed as a sequence of bits, then substitution method comes into picture
which involves replacing plaintext bit patterns with cipher text bit patterns.
Caesar cipher (or) shift cipher
The earliest known use of a
substitution cipher and the simplest was by Julius Caesar. The Caesar cipher
involves replacing each letter of the alphabet with the letter standing 3
places further down the alphabet.
e.g., Plain text : pay more mone
Cipher text: SDB PRUH PRQHB
Note that the alphabet is wrapped
around, so that letter following „z‟ is „a‟. For each plaintext letter p, substitute the cipher text
letter c such that C =
E(p) = (p+3) mod 26
A shift may be any amount, so that
general Caesar algorithm is C = E (p) = (p+k) mod 26
Where k takes on a value in
the range 1 to 25. The decryption algorithm is simply P = D(C) = (C-k) mod 26
Playfair cipher
The best known multiple letter
encryption cipher is the playfair, which treats digrams in the plaintext as
single units and translates these units into cipher text digrams. The playfair
algorithm is based on the use of 5x5 matrix of letters constructed using a
keyword. Let the keyword be „monarchy‟. The matrix is constructed by filling in the letters of the
keyword (minus duplicates) from left to right and from top to bottom, and then
filling in the remainder of the matrix with the remaining letters in
alphabetical order.
The letter „i‟ and „j‟ count as one letter. Plaintext
is encrypted two letters at a time according to the following rules:
Repeating plaintext letters
that would fall in the same pair are separated with a filler letter such as „x‟.
Plaintext letters that fall in
the same row of the matrix are each replaced by the letter to the right, with
the first element of the row following the last.
Plaintext letters that fall in
the same column are replaced by the letter beneath, with the top element of the
column following the last.
Otherwise, each plaintext letter is
replaced by the letter that lies in its own row and the column occupied by the
other plaintext letter.
Plaintext = meet me at the school
house
Splitting two letters as a unit
=> me et me at th es ch ox ol ho us ex Corresponding cipher text => CL KL
CL RS PD IL HY AV MP HF XL IU
Strength of playfair cipher
Playfair cipher is a great
advance over simple mono alphabetic ciphers. Since there are 26 letters, 26x26
= 676 diagrams are possible, so identification of individual digram is more
difficult.
Frequency analysis is much more
difficult.
Polyalphabetic ciphers
Another way to improve on the simple
monoalphabetic technique is to use different monoalphabetic substitutions as
one proceeds through the plaintext message. The general name for this approach
is polyalphabetic cipher. All the techniques have the following features in
common.
A set of related
monoalphabetic substitution rules are used. A key determines which particular
rule is chosen for a given transformation.
Vigenere cipher
In this scheme, the set of
related monoalphabetic substitution rules consisting of 26 caesar ciphers with
shifts of 0 through 25. Each cipher is denoted by a key letter.
e.g., Caesar cipher with a shift of
3 is denoted by the key value 'd‟ (since a=0, b=1, c=2 and so on). To aid in
understanding the scheme, a matrix known as vigenere tableau is constructed.
Each of the 26 ciphers is laid
out horizontally, with the key letter for each cipher to its left. A normal
alphabet for the plaintext runs across the top. The process of encryption is
simple: Given a key letter X and a plaintext letter y, the cipher text is at
the intersection of the row labeled x and the column labeled y; in this case,
the ciphertext is V.
To encrypt a message, a key is
needed that is as long as the message. Usually, the key is a repeating keyword.
e.g.,
key = d e c e p t i v e d e c e p t i v e d e c e p t i
v e
PT = w e a r
e d i s c o v e r e d s a v e y o u r s e l f
CT =
ZICVTWQNGRZGVTWAVZHCQYGLMGJ
Decryption is equally simple. The
key letter again identifies the row. The position of the cipher text letter in
that row determines the column, and the plaintext letter is at the top of that
column.
Strength of Vigenere cipher
There are multiple ciphertext
letters for each plaintext letter
Letter frequency inforamiton is
obscured.
One Time Pad Cipher
It is an unbreakable cryptosystem.
It represents the message as a sequence of 0s and 1s. this can be accomplished
by writing all numbers in binary, for example, or by using ASCII. The key is a
random sequence of 0‟s
and 1‟s
of same length as the message.
Once a key is used, it is discarded
and never used again. The system can be expressed as follows:
Thus the cipher text is generated by performing the bitwise
XOR of the plaintext and the key. Decryption uses the same key. Because of the
properties of XOR, decryption simply involves the same bitwise operation:
Advantage:
Encryption method is completely
unbreakable for a ciphertext only attack.
Disadvantages:
It requires a very long key which is
expensive to produce and expensive to transmit.
Once a key is used, it is dangerous
to reuse it for a second message; any knowledge on the first message would give
knowledge of the second.
2 TRANSPOSITION TECHNIQUES
All the techniques examined so far
involve the substitution of a cipher text symbol for a plaintext symbol. A very
different kind of mapping is achieved by performing some sort of permutation on
the plaintext letters. This technique is referred to as a transposition cipher.
Rail fence is simplest of such cipher, in which the plaintext is
written down as a sequence of diagonals and then read off as a
sequence of rows.
Plaintext =
meet at the school house
To encipher this message with a rail
fence of depth 2, we write the message as
follows:
m e
a
t
e c o
l o
s
e t
t h s
H
o
h u e
The encrypted message is
MEATECOLOSETTHSHOHUE
Row Transposition Ciphers-A more complex scheme is to write the message in a
rectangle, row by row, and read the message off, column by column,
but permute the order of the columns. The order of columns then becomes the key
of the algorithm.
e.g., plaintext = meet at the school
house
CT = ESOTCUEEHMHLAHSTOETO
A pure transposition cipher is
easily recognized because it has the same letter frequencies as the original
plaintext. The transposition cipher can be made significantly more secure by
performing more than one stage of transposition. The result is more complex
permutation that is not easily reconstructed.
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