Network Security – Part 2 Public Key Cryptography Spring 2007 V.T. Raja, Ph.D., Oregon State University

Network Security – Part 2 Outline –Public Key Cryptography Public keys and Private keys RSA Algorithm –Authentication Authentication Protocol (ap) –ap 1.0, 2.0, 3.0, 3.1, 4.0, 5.0 –Exchanging Public Keys Man (Woman) in the middle-attack

Introduction - Public Key Cryptography Disadvantage of symmetric key cryptography? Until 1970s encryption involved symmetric key Is it possible for two parties to communicate using encryption/decryption without using a shared secret key? A radically different and marvelously elegant approach towards encryption/decryption Public key cryptography is useful not only for encryption/decryption, but also for authentication and digital signatures as well.

Basic Idea of Public Key Cryptography Each participant has a private key (known only to the participant) and a public key. The public key is created with one’s private key. Public key is made available to others and could be posted even on a website which is accessible by the rest of the world. Public key of recipient is used by sender to encrypt message. Recipient decrypts message using recipient’s private key.

Basic Idea of Public Key Cryptography Example: –Alice wishes to send a message to Bob. –Alice fetches Bob’s public key. –Alice uses Bob’s public key to encrypt message –Alice sends encrypted message to Bob. –Bob decrypts cipher text with Bob’s private key.

Notation and Choice of Keys Assume Alice’s plain text message, (which has to be encrypted and then sent to Bob) is denoted as m. Assume Bob’s public key is denoted as K B + and his private key is denoted as K B -. These keys are chosen such that: K B - (K B + (m)) = K B + (K B - (m)) = m

RSA Algorithm How does RSA work? Class Participation Exercise on RSA application Why does RSA work? (See MS Word handout for answers to above questions)

RSA Algorithm Even for small p and q, as seen in the participation exercise, we had to deal with extremely large numbers. If we follow the suggestion of RSA labs and select p and q to be several hundred bits long, then the following practical issues come to mind: –How to choose large prime numbers p and q? –How to choose e and d? –How to perform exponentiation with large numbers? (For those who are interested in this area, refer to Kaufman 1995 for answers to the above mentioned questions).

RSA and DES/AES DES is at least 100 times faster than RSA. In practice, RSA is often used in combination with DES or AES. How? (Alice encrypts DES key with Bob’s public key. Bob decrypts and obtains DES key with his private key. The data is encrypted using DES key, which now both Alice and Bob have access to in order to encrypt/decrypt data).

Security of RSA The security of RSA relies on the fact that there are no known algorithms for quickly factoring a number (n), into the primes p and q. If one knew p and q, then given e, one could then easily compute the secret key d. It is not known whether or not there exist fast algorithms for factoring a number, and in this sense the security of RSA is not guaranteed.

Authentication ap 1.0 ap 2.0 ap 3.0 ap 3.1 ap 4.0 ap 5.0

Exchanging Public Keys Why should public key be publicly available? Wouldn’t it be better for Alice and Bob to exchange their respective public keys via , after authenticating each other? –Due to possibility of “man (woman) in the middle attack.”

Man (Woman) in the Middle Attack