## Beginner Guide to Classic Cryptography

Cryptography:  It is a technique of scrambling message using mathematical logic to keep the information secure. It preserve the scrambled message from being hacked when transport over unsecure network. Since it convert the readable message in unreadable text.

Plaintext: It is the content of data which is in readable form that need to share over insecure network.

Encrypting key: It is random string of bits created particularly to scramble the plaintext information into unreadable text using mathematical logic. There are two types of encryption key symmetric key and asymmetric key.

Cipher text: The output of encryption produce cipher text which in not readable by human beings.

Decrypting key: It is the key which use to decipher the cipher text into again plaintext using symmetric or asymmetric key to read original message. Functionality of cryptosystem

• Authentication: It is the process of verification of the identity of the valid person through his username and password that communicates over a network.
• Authorization: It refers to the process of granting or denying access to a network resource or service. Most of the computer security systems that we have today are based on a two-step mechanism. The first step is authentication, and the second step is authorization or access control, which allows the user to access various resources based on the user’s identity.
• Confidentiality or privacy: It means the assurance that only authorized users can read or use confidential information. When cryptographic keys are used on plaintext to create cipher text, privacy is assigned to the information.
• Integrity: Integrity is the security aspect that confirms that the original contents of information have not been altered or corrupted. There should be not any kind of modification with information while it transport over network.
• Non repudiation: Non repudiation makes sure that each party is liable for its sent message. Someone can communicate and then later either falsely deny the communication entirely or claim that it occurred at a different time, or even deny receiving any piece of information.

Classical Cryptographic Algorithms types

### Caesar Cipher

Caesar cipher is a type of substitution cipher in which each letter of the alphabet is swap by a letter a certain distance away from that letter.

Algorithm

Step 0: Mathematically, map the letters to numbers (i.e., A = 1, B = 2, and so on).

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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

Step 1: Select an integer key K in between 1 and 25 (i.e., there are total 26 letters in the English language) let say shift right 3 alphabets where A +3 = D, B+3 = E and so on.

 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

Step 2: The encryption formula is “Add k mod 26”; that is, the original letter L becomes (L + k)%26.

For example encryption of “IGNITE” will like as:

C = E (L+K) %26

Here L= I and K = 3

C = E (I+3) % 26

C = E (9+3) % 26

C = E (12) % 26

C = E (L)

Hence encryption of IGNITE: LJQLWH

 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

 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

 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

 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

 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

 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

Step 3: The deciphering is “Subtract k mod 26”; that is, the encrypted letter L becomes (L – k) %26.

For example Decryption of “LJQLWH” will like as:

C = D (L-K) %26

C = D (L-3) % 26

C = D (12-3) % 26

C = D (9) % 26

C = D (I)

Hence decryption of LJQLWH: IGNITE

Limitation: Caesar cipher is vulnerable to brute-force attack because it depends on a single key with 25 possible values if the plaintext is written in English. Consequently, by trying each option and checking which one results in a meaningful word, it is possible to find out the key. Once the key is found, the full cipher text can be deciphered accurately.

### Monoalphabetic Cipher

It is also a type of substitution cipher in which each letter of the alphabet is swap by using some permutation of the letters in alphabet. Hence permutations of 26 letters will be 26! (Factorial of 26) and that is equal to 4×1026. This technique uses a random key for every single letter for encryption and which makes the monoalphabetic cipher secure against brute-force attack.

The sender and the receiver decide on a randomly selected permutation of the letters of the alphabet. For example in word “HACKING” replace G from “J” and N from “W” hence permutation key is 2! i.e. factorial of 2 and HACKING will become “HACKJIW”.

Algorithm

Step 0: Generate plaintext–cipher text pair by mapping each plaintext letter to a different random cipher text letter IJKLQR——–GFE.

 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 I J K L Q R S T U V W D C B A Z Y X P O N M H G F E

Step 1: To encipher, for each letter in the original text, replace the plaintext letter with a cipher text letter.

Hence encryption of “IGNITE” will be as shown below:

 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 I J K L Q R S T U V W D C B A Z Y X P O N M H G F E

 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 I J K L Q R S T U V W D C B A Z Y X P O N M H G F E

 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 I J K L Q R S T U V W D C B A Z Y X P O N M H G F E

 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 I J K L Q R S T U V W D C B A Z Y X P O N M H G F E

 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 I J K L Q R S T U V W D C B A Z Y X P O N M H G F E

 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 I J K L Q R S T U V W D C B A Z Y X P O N M H G F E

Step 2: For deciphering, reverse the procedure in step 1.

Hence decryption of “USBUOQ” will be “IGNITE”

Limitations

Despite its advantages, the random key for each letter in monoalphabetic substitution has some downsides too. It is very difficult to remember the order of the letters in the key, and therefore, it takes a lot of time and effort to encipher or decipher the text manually. Monoalphabetic substitution is vulnerable to frequency analysis.

### Playfair Cipher

It encrypts digraphs or pairs of letters rather than single letters like the plain substitution cipher

In this cipher a table of alphabet is 5×5 grids is created which contain 25 letters instead of 26. One alphabet “J” (or any other) is omitted. One would first fill in the spaces in the table with the letters of the keyword (dropping any duplicate letters), then fill the remaining spaces with the rest of the letters of the alphabet in order. If the plaintext () contains J, then it is replaced by I.

Algorithm

Step 0: Split the plaintext into pair, if number of letters are odd then add “X” with last letter of plaintext

For example “TABLE” is our plaintext split it into pair as: TA BL EX

Step 1: Set the 5 × 5 matrix by filling the first positions with the key. Fill the rest of the matrix with other letters. Let assume “ARTI” is our key for encryption.

 A R T I B C D E F G H K L M N O P Q S U V W X Y Z

Step 2: For encryption it involves three rules:

If both letters fall in the same row, substitute each with the letter to its right in a circular pattern. TA—–> IR

 A R T I B C D E F G H K L M N O P Q S U V W X Y Z

If both letters fall in the different row and column, form a rectangle with the two letters and take the letters on the horizontal opposite corner of the rectangle. BL—–> TN

 A R T I B C D E F G H K L M N O P Q S U V W X Y Z

If both letters fall in the same column, substitute each letter with the letter below it in a circular pattern. EX—–> LT

 A R T I B C D E F G H K L M N O P Q S U V W X Y Z

Hence encryption of word “TABLE” is “IR TN LT”.

Step 3: For decryption receiver use same key to decipher the text by reversing above three rules used in step 2.

Limitations:

Playfair is considerably complicated to break; it is still vulnerable to frequency analysis because in the case of Playfair, frequency analysis will be applied on the 25*25 = 625 possible digraphs rather than the 25 possible monographs (monoalphabetic)

### Polyalphabetic Cipher

A polyalphabetic substitution cipher is a series of simple substitution ciphers. It is used to change each character of the plaintext with a variable length. The Vigenere cipher is a special example of the polyalphabetic cipher.

Algorithm

Step 0: Decide a encrypting key to change plaintext into cipher, for example take “HACKING” as encryption key whose numerical representation is “7, 0 ,2 ,10, 8, 13, 6 “

 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 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

Step 1: To encrypt, the numeric number of first letter of the key encrypts the first letter of the plaintext, the second numeric number of second letter of the key encrypts the second letter of the plaintext, and so on.

For example plaintext is “VISIT TO HACKING ARTICLES” and key is “HACKING: 7 0 2 10 8 13 6”

 V I S I T T O H A C K I N G A R T I C L E S 7 0 2 10 8 13 6 7 0 2 10 8 13 6 7 0 2 10 8 13 6 7

Step 2: The encryption formula is “Add k mod 26”; that is, the original letter L becomes (L + k)%26

C = E (L+K) %26

Here L=V and K =7

C = E (V+7) %26

C = E (21+7) %26

C = E (28) %26

C = E (2)

C = E (C)

Hence encryption of “VISIT TO HACKING ARTICLES” is “CIUSBGUOAEUQAMHRVSKYKZ”

 V I S I T T O H A C K I N G A R T I C L E S 7 0 2 10 8 13 6 7 0 2 10 8 13 6 7 0 2 10 8 13 6 7 C I U S B G U O A E U Q A M H R V S K Y K Z

Step 3: The deciphering is “Subtract k mod 26”; that is, the encrypted letter L becomes (L – k) %26.

For example Decryption of “CIUSBGUOAEUQAMHRVSKYKZ” will like as:

C = D (L-K) %26

Here L=C and K =7

C = E (C-7) %26

C = E (21)

C = E (V)

Hence decryption of “CIUSBGUOAEUQAMHRVSKYKZ” is “VISIT TO HACKING ARTICLES”

Limitation

The main limitation of the Vigenère cipher is the repeating character of its key. If a cryptanalyst properly estimate the length of the key, then the cipher text can be treated as link Caesar ciphers, which can be easily broken separately.

### Rotation Cipher

In rotation cipher generates cipher text on the behalf of block size and angle of rotation of plain text in the direction of following angles: 90o 1800 270

Algorithm

Step 0: Decide the size of block for plaintext “CRYPTOGRAPHY”, let assume 6 as block size for it.

 CRYPTO GRAPHY

Step 1: For encryption arrange plaintext in any direction among these angles 90o 1800 270o   as shown below:

In 90o Rotation place starting letter downwards vertically from G to C and so on.

 CRYPTO GRAPHY

In 180o Rotation place letter right to left horizontally from O to C and so on.

 CRYPTO OTPYRC GRAPHY YHPARG

In 270o Rotation place last letter top to bottom vertically from O to Y and so on.

 CRYPTO GRAPHY

Hence cipher text will arrange in following ways:

 90o 1800 270o GC RR AY PP HT YO OTPYRC YHPARG OY TH PP YA RR CG

Step 2: arrange letter according their angles represents:

90  rotated cipher “GCRRAYPPHTYO”

180  rotated cipher “YHPARGOTPYRC”

270  rotated cipher “OYTHPPYARRCG”

Step 3: for decryption using block size and angle of rotation among all above three cipher texts can be decrypt.

### Transposition Cipher

In transposition cipher plaintext are rearrange without replacing original letter from other as compare to above cipher techniques.

Algorithm

Step 0: Decide the keyword that will be represent the number of column of a table which store plain text inside it, and help in generating cipher text, let suppose we choose CIPHER as key.

Step 1: store plaintext “classical cryptography” in a table from left to right cell.

 C I P H E R C L A S S I C A L C R Y P T O G R A P H Y

Step 2: for encryption arrange all letters according to columns from in ascending order of keyword “CIPHER” will be CEHIPR as:

 C E H I P R C S S L A I C R C A L Y P R G T O A P H Y

Column 1: CCCPP

Column2: ESRR

Column 3: HSCG

Column 4: PALOY

Column 5: RIYA

Hence the cipher obtain will be “CCCPPESRRHSCGPALOYRIYA

Step 3: for decryption receiver use key to rearrange 26 cipher letters according to its column in 6*5 matrix.

Limitation

It was very easy to rearrange cipher letter if correct key is guesses.

### Rail fence Cipher

The ‘rail fence cipher’ also called a zigzag cipher is a form of transposition cipher the plain text is written downwards and diagonally on successive “rails” of an imaginary fence, then moving up when we reach the bottom rail.

Algorithm

Step 0: choose the number rails which will act as key for plotting the plaintext on it. Here 3 rails is decided as key for encryption

Step 1: plot plaintext “RAJ CHANDEL” on the rail in zigzag form, in direction top to bottom (downwards and diagonally) and then bottom to up (upwards and diagonally)

 R H E A C A D L J N

Step 2: for encryption place all letter horizontally starting form row 1 to row 3 as:

Row 1: RHE

Row 2: ACADL

Row 3: JN

Hence encryption for “RAJCHANDEL” is “RHEACADLJN”

Step 3: for decryption generate the matrix by multiplying total cipher text with number of rail, here

Total 10 letters are in cipher text “RHEACADELJN” and 3 rails, hence matrix will of 10*3.

 1 5 9 2 4 6 8 10 3 7

Transverse the above rule use in encryption and place the cipher text as

Row 1: RHE

 R H E 2 4 6 8 10 3 7

Row 2: ACADL

 R H E A C A D L 3 7

Row 3: JN

 R H E A C A D L J N

Limitations

The rail fence cipher is not very strong; the number of practical keys (the number of rails) is small enough that a cryptanalyst can try them all by hand.

Author: AArti Singh is a Researcher and Technical Writer at Hacking Articles an Information Security Consultant Social Media Lover and Gadgets. Contact here

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