# Beginner Guide to Classic Cryptography

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

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

**Encrypting key:** It is a 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.

**Ciphertext:** The output of encryption produce ciphertext which is not readable by human beings.

**Decrypting key:** It is the key which use to decipher the ciphertext into again plaintext using the symmetric or asymmetric key to read the 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 ciphertext, 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 its transport over the 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).

**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.

**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**

**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 ciphertext 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 an alphabet. Hence permutations of 26 letters will be 26! (Factorial of 26) and that is equal to 4×10^{26}. 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 plain text letter to a different random cipher text letter **IJKLQR——–GFE.**

**Step 1**: To encipher, for each letter in the original text, replace the plain text letter with a ciphertext letter.

Hence encryption of “IGNITE” will be as shown below

**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 the 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 a pair, if the number of letters is odd then add “X” with the last letter of the plaintext

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

**Step 1**: Set the 5 × 5 matrices 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.

**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**

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**

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

**Step 3**: For decryption, the receiver uses the same key to decipher the text by reversing above three rules used in step 2. Hence encryption of word “TABLE” is “IR TN LT”.

**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 an 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 “

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

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

**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”

**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 estimates the length of the key, then the ciphertext can be treated as link Caesar ciphers, which can be easily broken separately.

**Rotation Cipher**

In the rotation, cipher generates ciphertext on the behalf of block size and angle of rotation of plain text in the direction of following angles: 90^{o }180^{0 }270^{o }

**Algorithm **

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

CRYPTO |

GRAPHY |

**Step 1:** For encryption arrange plaintext in any direction among these angles 90^{o }180^{0 }270^{o }as shown below:

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

CRYPTO |

GRAPHY |

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

CRYPTO |
OTPYRC |

GRAPHY |
YHPARG |

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

CRYPTO |

GRAPHY |

Hence ciphertext will arrange in the following ways:

**Step 2:** arrange a letter according to their angles represents:

90^{o } rotated cipher “GCRRAYPPHTYO”

180^{o } rotated cipher “YHPARGOTPYRC”

270^{o } rotated cipher “OYTHPPYARRCG”

**Step 3:** for decryption using block size and angle of rotation among all above three ciphertexts can be decrypted.

**Transposition Cipher**

In transposition, cipher plaintext is rearranged without replacing original letter from others as compare to above cipher techniques.

**Algorithm**

Step 0: Decide the keyword that will be representing the number of column of a table which stores 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.

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

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 the 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 of rails which will act as **a key **for plotting the plaintext on it. Here **3 rails** are 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 the bottom to up (upwards and diagonally)

**Step 2:** for encryption place all letter horizontally starting from 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 ciphertext with the number of rails, here

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

**
**Transverse the above rule use in encryption and place the ciphertext as

**Row 1: RHE**

**Row 2: ACADL**** **

** ****Row 3: JN**

**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.** **

**Reference:**

Wikipedia.org

Practical cryptography algorithm and implement (by Saiful Azad , Al-Sakib Khan)

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