Symmetric-key cryptography refers to encryption methods in which both the sender and receiver share the same key.Symmetric key ciphers are implemented as either block ciphers or stream ciphers. They are usually used for the pre 1976 encryption schemes.
Asymmetric-key cryptography refers to encryption methods in which the sender and receiver have different keys. That is different keys are used for encryption and decryption.
It is a type of substitution cipher in which each letter in the plaintext is replaced by a letter some fixed number of positions down the alphabet.
En(x) = (x + n) mod {26}.
Decryption is performed similarly,
Dn(x) = (x - n) mod {26}.
Suppose Alice wishes to send the message "HELLO" to Bob. Assume two pads of paper containing identical random sequences of letters were somehow previously produced and securely issued to both. Alice chooses the appropriate unused page from the pad. The way to do this is normally arranged for in advance, as for instance 'use the 12th sheet on 1 May', or 'use the next available sheet for the next message'.
The material on the selected sheet is the key for this message. Each letter from the pad will be combined in a predetermined way with one letter of the message. (It is common, but not required, to assign each letter a numerical value, e.g., "A" is 0, "B" is 1, and so on.)
In this example, the technique is to combine the key and the message using modular addition. The numerical values of corresponding message and key letters are added together, modulo 26. So, if key material begins with "XMCKL" and the message is "HELLO", then the coding would be done as follows (encryption):
H E L L O message
7 (H) 4 (E) 11 (L) 11 (L) 14 (O) message
+ 23 (X) 12 (M) 2 (C) 10 (K) 11 (L) key
= 30 16 13 21 25 message + key
= 4 (E) 16 (Q) 13 (N) 21 (V) 25 (Z) message + key (mod 26)
E Q N V Z → ciphertext
If a number is larger than 26, then the remainder after subtraction of 26 is taken in modular arithmetic fashion. This simply means that if the computations "go past" Z, the sequence starts again at A.
The ciphertext to be sent to Bob is thus "EQNVZ". Bob uses the matching key page and the same process, but in reverse, to obtain the plaintext. Here the key is subtracted from the ciphertext, again using modular arithmetic (decryption):
E Q N V Z ciphertext
4 (E) 16 (Q) 13 (N) 21 (V) 25 (Z) ciphertext
- 23 (X) 12 (M) 2 (C) 10 (K) 11 (L) key
= -19 4 11 11 14 ciphertext – key
= 7 (H) 4 (E) 11 (L) 11 (L) 14 (O) ciphertext – key (mod 26)
H E L L O → message
Similar to the above, if a number is negative then 26 is added to make the number zero or higher. Thus Bob recovers Alice's plaintext, the message "HELLO". Both Alice and Bob destroy the key sheet immediately after use, thus preventing reuse and an attack against the cipher
The Vigenère cipher consists of several Caesar ciphers in sequence with different shift values.
To encrypt, a table of alphabets can be used, termed a tabula recta, Vigenère square, or Vigenère table. It consists of the alphabet written out 26 times in different rows, each alphabet shifted cyclically to the left compared to the previous alphabet, corresponding to the 26 possible Caesar ciphers. At different points in the encryption process, the cipher uses a different alphabet from one of the rows. The alphabet used at each point depends on a repeating keyword.[citation needed]
For example, suppose that the plaintext to be encrypted is:
ATTACKATDAWN
The person sending the message chooses a keyword and repeats it until it matches the length of the plaintext, for example, the keyword "LEMON":
LEMONLEMONLE
Each row starts with a key letter. The remainder of the row holds the letters A to Z (in shifted order). Although there are 26 key rows shown, you will only use as many keys (different alphabets) as there are unique letters in the key string, here just 5 keys, {L, E, M, O, N}. For successive letters of the message, we are going to take successive letters of the key string, and encipher each message letter using its corresponding key row. Choose the next letter of the key, go along that row to find the column heading that matches the message character; the letter at the intersection of [key-row, msg-col] is the enciphered letter.
For example, the first letter of the plaintext, A, is paired with L, the first letter of the key. So use row L and column A of the Vigenère square, namely L. Similarly, for the second letter of the plaintext, the second letter of the key is used; the letter at row E and column T is X. The rest of the plaintext is enciphered in a similar fashion:
Plaintext: ATTACKATDAWN
Key: LEMONLEMONLE
Ciphertext: LXFOPVEFRNHR
Decryption is performed by going to the row in the table corresponding to the key, finding the position of the ciphertext letter in this row, and then using the column's label as the plaintext. For example, in row L (from LEMON), the ciphertext L appears in column A, which is the first plaintext letter. Next we go to row E (from LEMON), locate the ciphertext X which is found in column T, thus T is the second plaintext letter.
Brute force - Try all possible keys
Frequency analysis - In a simple substitution cipher, each letter of the plaintext is replaced with another, and any particular letter in the plaintext will always be transformed into the same letter in the ciphertext. For instance, if all occurrences of the letter e turn into the letter X, a ciphertext message containing numerous instances of the letter X would suggest to a cryptanalyst that X represents e.
The basic use of frequency analysis is to first count the frequency of ciphertext letters and then associate guessed plaintext letters with them.
Check out this link for standard frequency distributions
https://www.math.cornell.edu/~mec/2003-2004/cryptography/subs/frequencies.html