Substitution ciphers and transposition ciphers both belong to symmetric cryptographic system, where encryption key and decryption key are the same, or one can be deducted from the other.

**Substitution ciphers**

**Caeser cipher**

Ceaser cipher is simply substitute all letters to k letters afterwards, where k is the encryption and decryption key, if the plaintext is English then it will be a number between 0 to 25. Easy to use, very easy to break.

Example: ceaser -> fhdvhu, k = 3.

2.** Mono-alphabetic subsitution ciphers**

Give every letter in the alphabet a subsitution letter, every letter should be use once and only once. So there are 26! possibilities (considering English letters alphabet).

Example:

Plain: ABCDEFGHIJKLMNOPQRSTUVWXYZ

Cipher: DKVQFIBJWPESCXHTMYAUOLRGZN

Compared to Ceaser cipher, Mono-alphabetic subsitution is harder to break in terms of brute-force attack, but still very week because frequency of letters remains, for example the highest frequency letter is more likely to be letter E than any other letters because it is the most frequently used letter in English.

3. **Homophonic subsitution cipher**

Similar to Mono-alphabetic subsitution ciphers, but provides more than one possible ciphertexts to each plaintext letter.

Example: A = {x, y}, H(x) = {00, 10}, and H(y) = {01, 11}. Then the plaintext xy can be encrypted as 0001 or 1001 or 0011 or 1011.

Although frequency of single letter can be hide, diagram frequencies (pattern of multiple letter) still exist, especially in longer text. Because the provided subsitutes are finite will be reused, at some point some patterns shown before will show again in the ciphertext.

4. **Playfair cipher**

Make a 5×5 matrix, each box contains one letter (i and j in one box), by selecting a keyword, put the letters of the keyword in the boxes starting at the top left, and fill in the rest boxes with the rest letters.

Example: keyword MONARCHY, matrix as follows

M O N A R

C H Y B D

E F G I/J K

L P Q S T

U V W X Z

After constructing the matrix, break the plaintext into two letters each block, if number of letters are odd, add a selected letter at the end, for example X. Then the rule is:

If both letters fall in the same row, replace each with letter to right, wrapping back to start from end (e.g., “AR” is encrypted as “RM”).

If both letters fall in the same column, replace each with the letter below it, wrapping to top from bottom (e.g., “MU” is encrypted as “CM”).

Otherwise each letter is replaced by the letter in the same row and in the column of the other letter of the pair (e.g., “HS” becomes “BP” and “EA” becomes “IM”, or “JM”, as the encipherer wishes).

Playfair cipher is better than homophonic subsitution, but still the structure of the plaintext is left intact, and not very hard for computer to brute-froce.

5. **Polyalphabetic substitution ciphers (Vigenère cipher)**

Select a keyword, repeat the keyword until it is as long as the message, there we formed a key where each letter stands for a ceaser cipher, for example, d=3.

Example:

keyword: deceptive

key: deceptivedeceptivedeceptive

plaintext: wearediscoveredsaveyourself

ciphertext: ZICVTWQNGRZGVTWAVZHCQYGLMGJ

this is again better than playfair, but cryptoanalysis methods are still available, for example Kasiski method and Index of coincidence.

6. **Vernam cipher** **and one-time pad**

Needs a key as long as the plaintext in terms of bits, do XOR operation, and due to the feature of the XOR operation, when apply XOR to the ciphertext with the key again, plaintext is recovered.

One-time pad is to use the Vernam cipher method, use the key once, then discard and find another one to use.

One-time pad is absolutely safe because it is encrypted in the unit of bits, so no information contains in the ciphertext, and the key is only use once. But it is not to expensive to apply in real life.

**Transposition ciphers**

**Rail fence cipher**

The key of rail fence cipher is a number, the number of depth of the fence. Write the plaintext in the shape of V with the given depth (the key).

Example:

plaintext: WE ARE DISCOVERED FLEE AT ONCE

key: 3

W E C R L T E

E R D S O E E F E A O C

A I V D E N

cipher text:W E C R L T E E R D S O E E F E A O C A I V D E N

Rail fence use the same idea with the Scytale, very week to break.

2. **Rotating (turning) grille**

Much easier to illustrate with example.

Example:

Plaintext: The Lord is my shepherd. I shall not be in want.

Cut out 9 grid from a 6×6 square, select one from the four of each number to cut, each number should be cut once and only coce.

once prepared, fill the plantext letters in the empty grid one by one, then rotate the paper conterclockwise 90 degree, and continue filling in, until the grille is finished.

ciphertext: mtdhyeisthlbehoeapirhldnelwrainnostt.

Rotating grille is also easy to break since again the frequency of letters remains.

3. **Columnar transposition cipher**

write the message in a retangle row by row, give a number of sequence to each column and reorganize the text to get the ciphertext, the sequence is the key.

Example:

Key: 4 3 1 2 5 6 7

Plaintext:

a t t a c k p

o s t p o n e

d u n t i l t

w o a m x y z

Ciphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ