Lecture6 of Information Security for Diploma 2018-2019

Lecture 6 Title : Public Key Ciphers

Lecture Outlines:
6.1 Introduction
6.2 One Way Hash Function
6.3 Public Key Cryptography
6.4 Exponential Cipher
6.5 Pohlig-Hellman Ciphers
6.6 RSA Cipher System
6.7 Knapsack Cipher

Objectives:
After studying this lecture, you will be able to discuss

??Main concepts of public key system.
??Terminologies used in asymmetric encryption
??Differences between symmetric and asymmetric encryption
??Function of public key system
??Application of public key systems
??Requirements of public key systems













6.1 Introduction
In the real world, key management is the hardest part of cryptology. Cryptanalysts often attack cipher system through their key management. One of the problems facing symmetric cipher systems is key distribution. Keys must be distributed in secret, since knowledge of the key gives knowledge of the massage. From the other side, keys are shared by pairs, and could work well in small networks ,but raised tremendously as network grows up , since every pair of users must exchange keys.
The total numbers of key exchanges required in n-person network is n(n-1)/2. In six person network , 15 key exchange are required, in 1000 – person network ,nearly 500,000 key exchanges are required. Public key system are invented to overcome the problems of key distribution faced by symmetric (one - key) cipher systems. We summarize the mentioned problems as follows :
• First key must be distributed in secret.
• Second: If key is compromised, then stranger can share the system as member.
• Third: number of key increases rapidly as users increased.

Public key cryptography based on one-way hash function (Trap-door function), that is depend on two keys public key used for encryption process and it is available for everyone in the network, the second key is the secret key which is used for decryption processes, and every person in the network has his own secret keys .In another meaning users have their own secret keys and share others with public keys .Since public key is known for everyone, then A can communicate with B as follows:
• A gets public key of B from database.
• A encrypt his message using B public key and send it.
• B decrypt the message using his own secret key.

6.2 One Way Hash Function
The notion of one-way function is central to public key cryptography. One-way function is easy to compute, but it is significantly hard (computationally) to reverse. That is given x, it is easy to compute f(x), but given f(x), it is hard to compute x. Breaking plate is a good example of a one-way hash function, it is easy to smash a plate into thousands of tiny pieces back together into a plate. One-way functions are not useful in public key cryptography, in public key.
We need a special type of one –way function, that is trap-door one-way function, which has a secret door (secret key) used to reverse the other direction .i.e. giving f(x) and some secret value we can deduce.