Discrete Mathematical Structures: Theory and Applications 1

Cryptography (advanced extra curricular topic)

Cryptography (from the Greek words Kryptos, meaning hidden, and graphein, meaning to write) is the study of sending and receiving secret messages.

The message to be sent is called plaintext. The disguised message is called ciphertext.

The process of converting from plaintext to ciphertext is called encryption, while the reverse process of changing from ciphertext back to plaintext is called decryption.

Discrete Mathematical Structures: Theory and Applications 2

CryptographyThe function used in the process of encryption

and decryption is called an encryption function.

The encryption function f is called the encryption key and f −1 is called the decryption key. Ideally, only the sender and the receiver know

these two keys.If f is known then f −1 is known, so there is only

one key and both the sender and the receiver have this key.

Discrete Mathematical Structures: Theory and Applications 3

Cryptography

RSA Cryptosystem

Discrete Mathematical Structures: Theory and Applications 4

Cryptography

Discrete Mathematical Structures: Theory and Applications 5

CryptographyRSA Cryptosystem

This pair is the public key for B and B that keeps the pair (n, d) = (8633, 1207) secret. Notice that B does not make public the prime numbers p, q and also keeps the pair (n, d) = (8633, 1207) secret.

This pair (n, d) is the decryption key for B, and the pair (n, k) is the encryption key for anyone who wants to send the message to B. A will encrypt the message by using this encryption key.

Discrete Mathematical Structures: Theory and Applications 6

Mathematical Foundations of Cryptography

Discrete Mathematical Structures: Theory and Applications 7

Cryptography