Lecture 1 in Public key ciphers

5.1 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 every one 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 5.1 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 every one 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 meaning users have their