Classical crypto techniques

Classical Crypto Techniques
Name: Parves kamal
Abstract
Cryptography is the art of processing data into unintelligible form without losing any original data.
[1] one of the keys to cryptography is the encrypted text must be retrievable to its original text
after it’s been decrypted. In the short paper below we will try to understand some of the
substitutions and Permutations technique used in Classical Cryptography.
Introduction
If we look at the figure below we can better understand the cryptography.
Fig-1: Cryptography Process
The Cryptography technique is been used from ancient time and in the past the encryption was
as simple as just writing message as most of the people could not read. [2] In ancient time people
were more concerned about hiding messagein somesort unreadable format so that the message
can be transported from one place to other place safely. Since human started to living out of cave
and form civilization different race and groups started to evolve along with hatred and the power,
violence and secrecy started to sprout. So in this paper we will try to have an idea about what are
those different forms of ancient classical encryption techniques that they used to carry their
message secretly around.
Caesar Shift

One of the earliest form of encryption techniques used by the Romans named Caesar Shift
Cipher. The idea of Caesar shift Cipher was basically simple where the each character of the
plain text is replaced with fixed predefined number of the character from the alphabet. Usually it
is called shifting of the letter as each letter is replaced by a letter further along in the alphabet.
The decryption process was completely reverse. The encrypted text then needs to be replaced
with same sifting of the letter.
Encryption: If we consider the following English Alphabet with their corresponding positions
below:
0 1 2 3 4 5 6 7 8 9 10 11 12
A B C D E F G H I J K L M
13 14 15 16 17 18 19 20 21 22 23 24 25
N O P Q R S T U V W X Y Z
Now let’s consider my name as plain text which is PARVES. So if we look at the position of the
letter of each alphabet we get 15, 0, 17, 21, 4, 18 . Now if we have sift key of 3 then we get the
number as 18, 3, 20, 24, 7, 21. So we get the name now as SDUYHV.
If by shifting key goes beyond the maximum numericalalphabet letters 26 we have to wrap around
and start from 0. The mathematical explanation for suchshifting can be illustrated by the following
formula:
a ≡ b (mod m) means m is a divisor of a − b.
In our case m is the size of the key which is in our case the number of character set which is 26.
Now we have to take each numeric number of the character of our plain text and add 3 with it. If
that number is between 0 to 15 do nothing if not after doing modules whatever is the reminder will
be the new numeric number of the character set.
So in our case the encryption is done by following steps
P −→ 15 −→ 15 + 3 ≡ 18 (mod 26) −→ S
A −→ 0 −→ 0 + 3 ≡ 3 (mod 26) −→ D
R −→ 17 −→ 17 + 3 ≡ 20 (mod 26) −→ U
V −→ 21 −→ 21 + 3 ≡ 24 (mod 26) −→ Y
E −→ 4 −→ 4 + 3 ≡ 7 (mod 26) −→ H
S −→ 8 −→ 8 + 3 ≡ 11 (mod 26) −→ V
Decryption: If the take the decrypted text and sift it to the right 3 character we will get the original
message. So in these encryption techniques the memorization of the key was not required as
there was no pattern to it. Also since the key space of 26 English character even if the attacker
did not know the key sift he/she can try all the combination and make sense out of the encrypted

message by trying out all the 26 shifting possible. In the figure below we can understand how the
Caesar Cipher works better:
Fig-2: Caesar Cipher
Route Cipher
It’s one type of transposition cipher. It’s much more like Vigenère Cipher except it has periodic
pattern to its key. This cipher was first used back in American Civil war.
Encryption: At first the plaintext is written around grid. The size of the grid is predetermined also
the number of the columns or number of rows of the grid we need to decide beforehand. Then we
write down our plaintext message around the grid. After the plaintext has been written we need
to determine the route it will follow to encrypt it.
For example if we want to encrypt "abort the mission, you have been spotted" plaintext with grid
size of column 5 we would do so as shown on the following figure

Fig-3: Route Cipher [3]
Now if we decide to read down the columnwe get encrypted text "ATSYV NTBHSOESEO EIUBP
DRMOH EOXTI NAETX". And by spiraling inwards counter-clockwise from the bottom right we
get: "XTEAN ITROB ATSYV NTEDX OEHOM EHSOE SPBUI". [3]
Decryption: Decrypting the Route cipher all it takes is to find out the route it takes and the width
or height of the grid. After that by placing the cipher text in the grid and following the route one
can decrypt the encrypted text.
The route cipher is relatively easy way to encrypt message. Sometimes when the plaintext is big
the route it took can be hard to follow while encrypting the message but that does not limits one’s
ability to take any route. The route can be taken in any imaginary possible way but the ease of
usage and understanding needs to be taken to consideration.
ADFGVX Cipher
ADFGVX was first used in World War I by the German. The original encryption was ADFGX and
it was further extended to ADFGVX. The name ADFGVX came from the six letters from the name
which is the only key used in the cipher text. It uses the transposition and substitution.
Encryption: It has two steps in encrypting plain text.
In first step ADFGVX is arranged in 6*6 Grid table. Then the grid is filled with Alphabet 26
characters and 10 numbers randomly. Then the each character of the plaintext is substituted with
pair of Column and Row matching characters from the Grid as shown from the figure below.[4]

Fig-4: ADFGVX Cipher (Stage -1)
For example for Name: Parves Kamal
The first character ‘P’ will be substituted by ‘AD’ and a character will be substituted by ‘VD’ AND
so on.
In The stage 2 the cipher text generated from the previous stage is arranged in a grid of which
the column and row size is predetermined. The column is that rearranged by predefined
permutations. The final cipher text is made by writing the column in order.
Decryption: It is done by determining the number of columns used. Usually the number of column
is factor of number of characters used in plain text. Whenthe number of columnis know the cipher
text is written backwards on the column and finding the possible pairings. Then frequency analysis
is performed on all possible pairing. Once the original order of the column is found out then
decrypting is done the way it is done on monoalphabetic substitution cipher. [5]
Myszkowski transposition
It’s a form of transposition cipher which use substitution techniques in columnar way. It was
proposed by Émile Victor Théodore Myszkowski in 1902.[6]
Encryption: The way it works is first we choose a keyword and make column on the basis of the
number of the letters on the keyword. Then we alphabetically give number underneath the
keywords while giving the same number position same number and we write down our plaintext
in the grid. Then we read down the column if that has the only unique column number like for
example if there is only one column name with ‘1’ we read down the text on that column. If any
other column has two same number say two ‘2’ column we read down each letter from left to right
column. Then we read the cipher text out the block size depending on the size of the keyword.
For example if we consider the key ‘Parves’ and the Plain text is ‘I Love cryptography’

We get grid like below:
P A R V E S
3 1 4 6 2 5
I L O V E C
R Y P T O G
R A P H Y
Fig-5: Myszkowski Grid table
Now if we take the Column 1 then 2, and so on we get encrypted text as LYAEO YIRRO
PPCGVTH
Decryption: If we want to decipher we put the keyword and put the alphabetic order. Then we
divide the cipher text with the keyword to find out the rows we need for the grid. Then we put the
cipher text back to the grid accordingly. Then we start from the column number on and move to
the next column. If more than one column has same alphabetic order we start from left to right
and we end up getting our plaintext.
Playfair Cipher
Playfair Cipher encrypts not a single letter instead pairs of letters so it’s harder to break with
frequency analysis like some other mono alphabetic cipher.
Encryption: The way encryption works is by at first creating 5 by 5 matrix which fill in by the
chosenkeyword and restof the keyword filled by the other letters in the alphabet. If any duplication
is there in the keyword substitute it with the other alphabet and complete the Grid.
If we make keyword MONARCHY we get 5 by 5 grid like this below
M O N A R CHYBD EFGIK PQST UVWXZ
Plaintext is then encrypted two letters a pair. If the both letters are same it get replaced by the
letter ‘X’. If both letter falls in the same row replace each letter with the letter in the right and if
both letter falls in the same column replace it with the letter below. But if the letter are in different
row and the columns then replace it with the others pair in the row which is on the same row.
Decryption: Decryption is much like same as like encryption. We don’t replace the same letter
with ‘X’ while for next two phase we do the shift up and left instead of down and right. We also
leave the rectangle letter swapping. We then drop any extra meaning less Xs which does not
make any sense while replacing any missing Qs and any Is WITH Js. [7]
The security of Playfair cipher is harder as it has 26 by 26 in total 676 diagram for frequency
table to look at. But still it can be broken easily since the the encrypted text keeps much of the
plaintext structure.

Affine Cipher
Affine cipher is another form of monoalphabetic Substitution cipher but different in a way as it
works on modular m which depends on the length of the alphabet used.
Encryption: The encryption is done by the function below:
e(x) = ax+b mod 26
For encryption at first each letter in the plaintext is transformed to the corresponding integer from
the alphabetic letter order where the integer range is from 0 to m-1. With this done, the encryption
process for each letter is done by the above function. On the above function the ‘a’ and the ‘b’ is
the key for the integer. So what we do here is we multiply our integer value for the plaintext letter
by a, and then add b. In the end we take this modulus m (that is we take the remainder when the
solution is divided by m, or we take away the length of the alphabet until we get a number less
than this length.
Decryption
For deciphering the us do the reverse .We perform the opposite (or inverse) functions on the
cipher text to retrieve the plaintext. So at first we do is to convert each of the cipher text letters
into their integer values. We must now perform the following calculation on each integer
D(x) = c(x - b) mod m
Where c is the modular multiplicative inverse of a. where a x c = 1 mod m (c is the number such
that when you multiply a by it, and keep taking away the length of the alphabet, you get to 1). [8]
Rotation Cipher
Another type of transposition cipher technique is Rotation cipher. It mainly works on the rotation
angle and the block size. Rotation angle can be rotated to the left, right by 90°, 180° or 270°.
Encryption: If we want to encrypt the text ‘’ I love Cryptography;’’ with 90° and block size of 5
we get the encrypted text as ‘’ apeipt hoclygroryv’’
Ilove
Crypt
Ograp
hy
Depending on the rotation angle the encrypted text will be different.
Since the security of this cipher depends on the block size and if it’s small block size it’s easy to
break in.

Hill Cipher
The Hill cipher was developed in 1929 by Lester S. Hill. It’s a polygraphic substitution cipher based
on linear algebra. Hill used matrices and matrix multiplication to mix up the plaintext.
The Hill cipher was the first cipher purely based on mathematics (linear algebra). First, each
character is assigned to a number, usually from the range of 00-25 for the characters A-Z.
Encryption : To encode a message utilizing the Hill Cipher we should first transform our decisive
word into a key network (a 2 x 2 grid for working with digraphs, a 3 x 3 framework for working with
trigraphs, and so forth). We additionally transform the plaintext into digraphs (or trigraphs) and
each of these into a section vector. We then perform network augmentation modulo the letters in
order's length (i.e. 26) on every vector. These vectors are then changed over once more into
letters to deliver the ciphertext.
Decryption: To decode a ciphertext encoded utilizing the Hill Cipher, we must locate the reverse
framework. When we have the opposite grid, the procedure is the same as encoding. That is we
reproduce the backwards key lattice by the section vectors that the ciphertext is part into, take
the outcomes modulo the letter set's length, lastly change over the numbers back to letters. [9]
Beaufort Cipher
The cipher was developed by the Briton Sir Francis Beaufort. It uses same table(tabula recta)
for enciphering the plaintext as vigener cipher which is shown below
Fig-5: tabula recta

Encryption: If we want to encipher plaintext ‘ I love Cryptography’ with the keyword ‘parves’
We repeat the keyword beneath the plaintext as follows:
Ilovecryptography
Parvesparvesparv
Now we take the letter we will be encoding, and find the column on the tableau. Then, we move
down the 'D' column of the tableau until we come to the key letter. This way we get the ciphertext
as
Ilovecryptography
Parvesparvesparv
Hpdaaqycccqmyacog
Deciphering is performed in an identical fashion, i.e. encryption and decryption using the
beaufort cipher uses exactly the same algorithm. [9]
So thus far we tried have look at what are the technique that classical cryptography era used
which used mostly like transposition/permutation, substitution cipher. This classical cryptography
is the basis of modern cryptography upon which the foundation of modern cryptography has been
laid.
References:
1. "Introduction to Cryptography." Web. 15 Sept. 2015.
<http://www.cs.columbia.edu/~hgs/teaching/security/slides/crypto2.pdf>.
2. Cohen, F (1990). A short history of cryptography. Retrieved May 4, 2009, from
http://www.all.net/books/ip/Chap2-1.html New World Encyclopedia (2007).
3. "Route Cipher." Crypto Corner. Web. 16 Sept. 2015. <http://crypto.interactive-
maths.com/route-cipher.html>.
4. "Classic Cryptography Methods." CryptoGraphy Chapter 2. Web. 16 Sept. 2015.
<http://staff.neu.edu.tr/~fahri/cryptography_Chapter_2.pdf>.
5. "Codes and Ciphers - ADFGVX Cipher." Codes and Ciphers - ADFGVX Cipher. Web. 16
Sept. 2015. <http://www.srcf.ucam.org/~bgr25/cipher/adfgvx.php>.
6. Matthews, R. (1993). THE USE OF GENETIC ALGORITHMS IN CRYPTANALYSIS.
Cryptologia, 17(2), 187-201. doi:10.1080/0161-119391867863
7. Classical Encryption Techniques. (2015). Retrieved 19 September 2015, from
http://ir.nuk.edu.tw:8080/bitstream/310360000Q/11325/2/Ch02ClassicEncrTech-Rev.pdf

8. Lecture 2 Classical Cryptosystems. (2015). Retrieved 19 September 2015, from
https://www.lri.fr/~fmartignon/documenti/systemesecurite/2-ClassicalCryptosystems.pdf
9. Practicalcryptography.com,. (2015). Practical Cryptography. Retrieved 19 September 2015,
from http://practicalcryptography.com/ciphers/hill-cipher/

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