Network Security

1
Network Security

• Section 3 Public Key,
• Digital Signature

2
New Algorithm Requirements

• Definitions
• E Encryption Key
• D Decryption Key
• New Requirements
• D(E(P)) P
• E gt D
• E not crack-able by known texts attack.

3
Example
Alice Ea, Da
Bob Eb,Db
4
RSA
Adelman
Shmir
Rivest
5
RSA

• One of the public key algorithms
• RSA Algorithm
• Chose two number p q (1024bit)
• npq and z(p-1)(q-1)
• Choose a number d that is relatively prime to z
• e ed mod z 1
• Divde P to blocks, 0 lt block length lt n
• C Pe mod n
• Exit.
• OK. Where is the security location?

6
RSA Example

• p 3, q 11
• n 33, z 20, d 7, e 3

No more cryptography algorithms PLEASE!
7
Digital Signatures

• Why do we use signatures?
• Authorization and Validity
• What is the problem of signature in digital
  world?
• Authorize sender
• Message must be undeniable from senders
  prospective.
• Receiver can not produce fake messages.

8
Symmetric-Key Signatures

• Store signature on valid institute (BB Big
  Brother).
• What is the problem of this method?

Do you trust Big Brother?
9
Public-Key Signatures
E(D(P)) P D(E(P)) P
Yes! How?

1. Be lost Da!!
2. Changing Da!!

Can Alice evade message P?
No! Why?
10
Message Digests

• Digital Signature do both authorization and
  confidentiality of message
• Message Digests only authorize messages.
• MD features
• Easy Calculation of MD(P)
• MD(P) gt P
• MD(P) MD(Q)
• MD(P) MD(P1)

11
MD5

• MD5 5th Message Digest. 128bit buffer
• md5(apple) 1f3870be274f6c49b3e31a0c6728957f

12
SHA-1

• Secure Hash Algorithm
• Developed by NSA
• 160bit buffer

13
The Birthday attack

• Problem If it is easy to find two random
  messages that map to the same signature then a
  birthday attack is easy
• Example the probability of 2 people having the
  same birthday in a group of 23 people is more
  than 0.5