Classical Encryption Techniques
Gowtham Reddy Uppunuri
Department of Electronics and Communication
National Institure of Technology, Raipur
Raipur, India
gowthamreddyuppunuri137@gmail.com
Abstract—This document details some of the classical
encryption techniques and these techniques are explained with
examples.
Keywords—encryption, decryption, plain text, key, cipher text.
I. INTRODUCTION
Now-a-days information is being received and sent in an open
networked systems. It is being misused by means of attacking
at various levels in communication. Encryption of data is the
best solution to counteract the attacks. There are two types of
encryption which are in use and are called as i) Symmetric-key
encryption using private keys and ii) Asymmetric-key
encryption using both public and private keys.
Symmetric-key algorithms are usually 1000 times faster than
public-key algorithms. Symmetric-Key is still extensively used
to solve the problem of secret communication over an insecure
channel. In an open network like internet, data encryption has
been widely used to ensure information security. Each type of
data has its own features. Thus, different encryption techniques
should be used to encrypt data from unauthorized use. In this
paper, we essentially achieve these two goals i) To introduce the
fundamentals of encryption and terms related to it and ii) To
discuss some classical encryption techniques in history.

Data origin authentication: It allows the recipient to
verify the origin of a received message.
 Entity authentication: It allows the entities of an endend connected communication to authenticate each
other.
3) Non-repudiation: It prevents the sender from later denying
that he/she sent the message.
C. Plain Text
It is the original message which is to be sent to receiver.
D. Cipher Text
It is the coded message which is the encoded version of original
message.
E. Characters of Cryptography
Alice, Bob and Eve are the main roles taken as examples. Alice
is basically Sender/Receiver, Bob is Receiver/sender and Eve
is eavesdropper or third party tries to access message.
II. BASIC TERMINOLIGIES
A. Cryptography
It is the study of encryption techniques that allow only the
sender and intended recipient of a message to view its contents.
The term is derived from the Greek word kryptos, which is
known as hidden. It is closely associated to encryption, which
is the disguising the ordinary plain text into what's called as
cipher text and then back again to normal plain text on arrival.
In addition, cryptography also deals with the embodiment of
information in images using techniques like microdots and
merging.
B. Objectives of Cryptography
The main objectives are as follows:
1) Protecting data privacy (secret writing)
2) Authentication:
 Message authentication: It allows the recipient to
check whether a received message has been modified.
Figure 1: Role of Characters in Communication
F. Encryption
Encryption protects secrecy of transmitted messages
.
B. Problem with Private-key Encryption
In this method, both the encoded message and private (secret)
key are sent to receiver. When somehow message is intercepted
by third party, they have everything they need to decrypt the
message. So, it is not secure.
To address this issue, public-key encryption system is
introduced.
Figure 2: Process of Encryption
Encryption Enck : plaintext m → ciphertext c
Decryption Deck’ : ciphertext c → plaintext m
Encryption key: k
Decryption key: k’
k and k’ can be same or different.
C. Public-key encryption
It is also known as asymmetric encryption. Here, sender and
receiver will have pair of keys like public key and private key
(secret key). pk is public, known to everyone (who wishes to
know). sk is secret and only known to the key’s owner. In this
method, senders requests public key of intended receivers,
encodes it and both encoded message and public key are sent to
receiver.
G. Brute Force Attack
In this method, we try every possible key to decipher the cipher
text. On an average, we need to try half of all possible keys.
Time needed proportional to size of key space. It is mainly
based on computational power of machines. Below table
depicts the time taken for various key sizes to decrypt the
ciphered text based on brute force method.
Figure 4: Public-key encryption
By this, only intended receiver will be able to decrypt it with
private key. From public key pk, it is hard and almost impossible
to derive private key sk. So this method is secure.
Decsk(Encpk(m)) = m.
Table 1: Time taken to crack cipher for various key sizes
III. TYPES OF ENCRYPTION
A. Private-key Encryption
It is also called as symmetric-key encryption. It is a classical
encryption method. Here both sender and receiver share a
common private key and it is used for encryption and
decryption
Encryption key k = decryption key k
Dec(k, Enc(k,m)) = m Or Deck(Enck (m)) = m.
IV. CLASSICAL ENCRYPTION TECHNIQUES
Classical encryption techniques are foundation to modern
encryption techniques. Some of the types of Classical encryption
techniques are as follows.
V. SUBSTITUTION CIPHER
It is a classical encryption technique in which characters in the
original plain text are replaced by other characters or symbols
or numbers. For instance, if the plain text (original message) is
considered as string of alphabet characters, then this technique
would replace the pattern of alphabets with other characters
which is cipher text. Types of substitution techniques are
explained as follows.
A. Caesar Cipher
It is one of the earliest and simplest classical encryption
technique. In this method, each letter in the given plain text is
replaced by a letter which comes by shifting fixed number of
positions.
For example with shift of 3 positions, A would be replaced
by D, B would be replaced by E and so on.
Figure 3: Symmetric Encryption Model
Figure 7: Example of Mono-alphabetic cipher
D. Polyalphabetic Cipher
A strong and well-formed cipher disguises and misleads the
original fingerprint. By the mid of 15Th century, cryptography
has advanced to encipher using Polyalphabetic Cipher
For Example:
Message to be sent: Hide the money
Secret word as key: RICH
Letter positions of RICH are 17-8-2-7
Adding positions of message with positions of key word, we
get
Figure 5: Depiction of Caesar Cipher
The method is named after Roman Statesman Julius Caesar,
who used this technique to communicate with his officials.
The encryption is done using modular arithmetic essentially
addition and subtraction by first converting the letters into
numbers.
For instance, A = 0, B = 1, C = 2 …., Z = 25. Encryption of a
letter by shifting n positions can be described mathematically
as shown in figure above.
B. Loophole of Caesar Cipher
The loophole of this model was proposed 800 years later by an
Arab mathematician Al-Kindi. Al-Kindi was able to break the
Caesar Cipher by using a clue based on a shared property which
is frequency of alphabets of the language used in the message.
Figure 6: Frequency analysis of English alphabets
C. Mono-alphabetic
It is a substitution technique in which for a given key, the cipher
alphabet for each plain text alphabet is shifted by random
positions and it is same for all occurrences of that plain text
alphabet.
For example, if ‘B’ is encrypted as ‘E’ then for all occurrences
in that plaintext, ‘B’ will always get encrypted to ‘E’. • The
number of possible shifts is 26!, which makes it much more
complicated than Caesar Cipher to break.
Figure 8: Example of Polyalphabetic cipher
E. Playfair cipher
The play fair cipher was the first substitution cipher based on
digraph. This technique was invented by Charles Wheatstone in
the year 1854, but was named after Lord playfair who
popularized this and promoted to use this cipher. Unlike,
Traditional ciphers till now, we encrypt a pair of alphabets
(characters) which are called digraphs instead of single
alphabet.
It was used by British forces during World War-1 and also by
Australians during World War-2. This was fast enough to use
and do not require a special equipment.
• We can follow 2 important steps with 3 main rules to encrypt
a plaintext using the Play fair Cipher.
• Firstly, we need to set a key. Example: monarchy
• Lets the word “instruments” be our plain text to encrypt.
Generate the key Square (5×5):
The key square is a 5×5 grid of alphabets that acts as key for
enciphering the plaintext. Each of the 25 alphabets should be
unique and one letter of the alphabet (usually J) is not present
in the table (since the table can hold only up to 25 alphabets).
If the plaintext message is having J, then it should be replaced
with I. The first few alphabets in the key square are the unique
and distinct alphabets of the key in the order in which they
appear followed by the remaining letters which comes in order.
This is shown in figure.
Figure 9: Key in playfair cipher
Algorithm for encrypting the plain text:
The plaintext is split into pairs of two letters which are called
digraphs. If there are odd number of letters, then Z is appended
to the last letter.
For example
Plaintext: "instruments" After Split: ‘in’,’st’, ‘ru’, ‘me’, ‘nt’,
‘sz’.
Rules for Encryption:
1) If both the letters considered are in the same column:
Take the letter below each one (go back to the top if letter is at
the bottom).
For example
Diagraph: "me" Encrypted Text: cl Encryption: m -> c, e -> l
Figure 10: Cipher text of digraph
2) If both the letters are in the same row: Take the letter to
the right of each one (go back to the leftmost if letter is at the
rightmost position)
For example
Diagraph chosen: st
Encrypted Text: tl
Encryption: s -> t and t -> l
3) If neither of the above two rules is satisfied then form a
rectangle with the two letters and take the letters on the
horizontal opposite corner of the rectangle which means that
encipher text would be the vertices of opposite diagonal.
For example
Diagraph chosen: nt
Encrypted Text: rq
Encryption: n -> r and t -> q
Application of Playfair cipher
Plaintext: “instrumentsz”
Encrypted Text: gatlmzclrqtx
Figure 11: Enciphering using playfair cipher
Encrypted as follows:
i -> g, n-> a, s -> t, t -> l, r -> m, u-> z, m->c, e-> l, n-> r, t ->
q, s -> t, z -> x
F. One time pad Cipher
It is one of classical encryption technique in which private key
is generated at random and is used only once to encipher the
message which is to be deciphered by the receiver using a
matching one-time pad key.
Messages encrypted using random keys have a huge advantage
that there is no way to “break the code” theoretically.
Each encryption is unique and do not have a common relation
to next encryption so that some common pattern can be
detected.
How it Works?
 First step involves converting plaintext to binary.
 Generate a random key in binary and is at least as long
as plaintext.
 Generate the cipher text by applying bitwise XOR on
binary plaintext and the binary key.
Example:
Fig 12: Example of One-time pad cipher
G. Hill Cipher
It is one of the classical encryption techniques. Example of Hill
Cipher is as follows:
Plaintext; ACT
Key used: GYBNQKURP
Cipher text: POH
The size of plaintext = n = 3.
We have to form a nxn matrix with the key as follows
[[G,Y,B],[N,Q,K],[U,R,P]].
VI. TRANSPOSITION CIPHER
The message ‘ACT’ is written as vector as follows:
[[A],[C],[T]]
It is a cryptographic technique in which letter of the plain text
are rearranged/permutated to get the cipher text. In this method,
original plain text letters are not included.
It is also called Permutation Cipher.
A simple example of this cipher is columnar transposition
cipher in which each character in the plain text is written in the
form a table with specific width. The cipher is formed by
writing the characters vertically to get the different cipher text.
Plain Text: helloworld
Apply columnar transposition
Cipher Text: holewdlolr
The enciphered (nx1) vector is given as
Figure 13: Key Generation in permutation cipher
Which is formed by writing vertically from the table.
Which corresponds to cipher text POH
Deciphering hill cipher
To decrypt the message, we multiply the inverse of key matrix
with cipher text vector.
It is done as follows
From the previous Cipher text ‘POH’
Which gives us plain text ‘ACT’ again.
A. Book Cipher or running key cipher
This cipher works on the basic principle of one-time pad cipher
in which key at least as long as plain text and excess is discarded
later. Every time a new key is taken for encryption.
The small improvement to the onetime pad cipher is that the
key of the one-time pad cipher is taken from the book.
It is detailed as follows:
Step 1: Convert plain text alphabets to their equivalent numeric
values
A = 0, B = 1, C = 2 …, Z = 25.
Step 2: Choose a onetime pad key from the book and convert
this into numeric form. Ensure key is as long as plain text.
Step 3: Now add numeric forms of both plain text and onetime
pad key. If addition values exceeds 26, do modular division by
26.
Figure 14: Encrypting using Book Cipher
For example:
Plain text: Meet Tomorrow
Key: ANENCRYPTION (taken from the book)
Now convert both the plain text and key into their numeric
forms and add them to get the desired cipher text as shown in
figure.
Cipher text: MRIGVFKDKZDJ
VII. PRODUCT CIPHER
It is a technique in which plain text is encrypted by two or more
times. It means after one encryption, the encrypted text further
encrypted to get the more secure encrypted text.
It is a combination of two or more simple ciphers like
substitution ciphers and transposition ciphers.
One of the most famous ciphers is fractionation system, the
ADFGVX cipher employed by the German during World War1. This system utilized a 6x6 matrix to substitution-encrypt the
26 letters and 10 digits into pairs of symbols A, D, F, G, V and
X. The resulting cipher which is bilateral was written into a
rectangular matrix and is encrypted by extracting text from the
columns in the order depicted in the key word.
This technique was deciphered by French cryptanalyst J.
Painvin in 1918 which shown a devastating effect for German
army in battle for Paris.
For Example
Figure 15: Enciphering using product cipher
ACKNOWLEDGMENT
This paper is solely written by me by carefully understanding
the topics for various resources mentioned in references.
CONCLUSION
Some Classical Encryption techniques were reviewed and
discussed how they work. Mostly are classical as they were
mainly used during the wars.
A thoughtful frequency analysis is able to break the cipher of
most classical techniques. However, these are main foundation
pillars to modern cryptography.
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