Discrete Mathematical Structures: Theory and Applications 1 Cryptography (advanced extra curricular topic)  Cryptography (from the Greek words Kryptos,

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Presentation transcript:

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 Cryptography  The 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 Cryptography  RSA 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