Introduction to Cryptology

Fall 2007

Definitions Digital encryption techniques are used to protect data in

two ways: to maintain privacy and to prove integrity [1] Cryptography comes from the Greek words

Kryptos, meaning hidden, Graphen, meaning to write.

Cryptography is the art of communicating confidentially through an insecure channel

Cryptanalysis is the art of deciphering those communications when one is not the legitimate receiver.

Cryptology is the union of these two domains. Cryptology is actually the study of codes and ciphers.

Definitions Plaintext the original message that is to be changed into a

secret form Cipher, Cryptosystem, Encryption Method is a procedure

for converting the plaintext message into encrypted message – ciphertext

The word cipher originates from the Hebrew word "Saphar," meaning "to number."

Decryption - the process that conducted by the intended receiver to recover original message (plaintext) from the encrypted message (ciphertext)

Key - keeps the message secret

Encryption-Decryption

Plaintext Ciphertext

Encryption Method

Encryption key

Ciphertext Plaintext

Decryption method

Decryption Key

Symmetric and Asymmetric Ciphers

Symmetric Cipher – knowledge of encryption key is equivalent to knowledge of the decryption key, or the same key is used for encryption and decryption.

Asymmetric Cipher (Public-Key Cryptosystem) the knowledge of encryption key give little information about the decryption key and vice versa

Early History of Cryptology

Polybius’ Checkboard 205 – 123 B.C.

Plaintext POLYBIUS produces the ciphertext

3534315412244543

ZYXWV5

UTSRQ4

PONML3

KIJHGF2

EDCBA1

54321

Julius Caesar Cipher

The letters of the alphabet are coded as:A B C D ... Z0 1 2 3 ... 25

Caesar Cipher One of the simplest examples of a substitution or

shift cipher Have been used by Julius Caesar to communicate

with his army Caesar is considered to be one of the first persons

to have ever employed encryption for the sake of securing messages

Caesar Cipher

• Caesar decided that shifting each letter in the message would be his standard algorithm

• Caesar simply replaced each letter in a message with the letter that is three places further down the alphabet - encryption 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

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

Caesar Cipher

Ciphertext may be deciphered or decrypted by replacing each letter by the third previous letter.

Example: Plaintext: dog Ciphertext: GRJ

Example: Ciphertext: BDQD Plaintext: yana

Caesar Cipher

Remember: we think of each letter as corresponding to a number from 0 to 25

To encrypt, we map numbers according to C ( P + 3 )(mod 26)

To decrypt, we map numbers according to P (C – 3) (mod 26)

Substitution and Affine Ciphers

General Substitution Cipher: To encrypt: C = (P + K) (mod 26), K is the KEY To decrypt: P = (C - K) (mod 26), K is the SAME

KEY Affine Cipher:

To encrypt: C = (AP + B) (mod 26), A and B are KEYS. A is relatively prime to 26

To decrypt: P = A-1 (C - B) (mod 26) A-1 is multiplicative inverse of A mod 26