Cryptography

Symmetric-Key Cryptography

In symmetric-key cryptography, the same key is used by both parties.

The sender uses this key and an encryption algorithm to encrypt data; the receiver uses the same key and the corresponding decryption algorithm to decrypt the data

In symmetric-key cryptography, the algorithm used for decryption is the inverse of the algorithm used for encryption.

This means that if the encryption algorithm uses a combination of addition and multiplication, the decryption algorithm uses a combination of division and subtraction.

Traditional Ciphers

In the earliest and simplest ciphers, a character was the unit of data to be encrypted. These traditional ciphers involved either substitution or transposition.

Substitution Cipher

A cipher using the substitution method substitutes one symbol with another. If the symbols in the plaintext are alphabetic characters, we replace one character with another.

For example, we can replace character A with D and character T with Z. If the symbols are digits (0 to 9), we can replace 3 with 7 and 2 with 6.

We will concentrate on alphabetic characters. Substitution can be categorized as either monoalphabetic or polyalphabetic.

Monoalphabetic Substitution

In mono alphabetic substitution, a character in the plaintext is always changed to the same character in the ciphertext regardless of its position in the text.

For example, if the algorithm says that character A in the plaintext must be changed to character D, every character A is changed to character D, regardless of its position in the text.

The first recorded ciphertext was used by Julius Caesar and is still called the Caesar cipher.

Example

ATTACK becomes

DWWDFN

Polyalphabetic Substitution

In polyalphabetic substitution, each occurrence of a character can have a different substitute. The relationship between a character in the plaintext to a character in the ciphertext is one-to-many.

Character A can be changed to D in the beginning of the text, but it could be changed to N at the middle. We discuss a very simple one.

It is obvious that if the relationship between plaintext characters and ciphertext characters is one-to-many, the key must tell us which of the many possible characters can be chosen for encryption.

Let us define our key as "take the position of the character in the text, divide the number by 9, and let the remainder be the shift value."

With this scenario, the character at position 1 will be shifted one character, the character at position 2 will be shifted two characters, and the character in position 14 will be shifted four characters (14 mod 9 is 4).So now the word ATTACK becomes

A T T A C K -plaintext

B V W E H Q -encrypted

Transpositional Cipher

In a transpositional cipher, the characters retain their plaintext form but change their positions to create the ciphertext.

The text is organized into a two-dimensional table, and the columns are interchanged according to a key. The key defines which columns should be swapped.

As you have guessed, transpositional cryptography is not very secure either.

The character frequencies are preserved, and the attacker can find the plaintext through trial and error.

This method can be combined with other methods to provide more sophisticated ciphers.

Example

7 4 5 1 2 9 3 6 KEY

P L E A S E T R

A N S F E R O N

E M I L L I O N

D O L L A R S T plain text

O M Y S W I S S

B A N K A C C O

U N T S I X T W

O T W O A B C D

Plaintext

PLEASE TRANSFER ONE MILLION DOLLARS IN MY SWISS BANK ACCOUNT SIX TWO TWO.

Ciphertext

AFLLSKSOSELAWAIATOOSSCTCLNMOMANTESILYNTWRNNTSOWDPAEDOBUOERIRICXB

Block Cipher

Traditional ciphers used a character or symbol as the unit of encryption/decryption. Modem ciphers, on the other hand, use a block of bits as the unit of encryption/decryption.

Figure shows the concept of the block cipher; the plaintext and ciphertext are blocks of bits.

Operation Modes

Ciphers that operate on eight-character segments are too short now the question arises, Can we encrypt and decrypt longer messages (900 characters, e.g.)?

Several modes have been defined, and we briefly describe the most common one.

Electronic Code Block (ECB) Mode

In electronic code block (ECB) mode, we divide the long message into 64-bit blocks and encrypt each block separately, as shown in Figure.