1. Section 3: Public Key, Digital Signature
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 #> D
E not crack-able by “known texts” attack.

3. Example ABCDEFGHI P Eb Eb(P) ****************** Send to Bob Alice
Ea, Da Ea
Bob reads P
D(Eb(P))
ABCDEFGHI
******************
Eb(P)
Bob
Eb,Db

4. RSA
Adelman
Shmir
Rivest

5. RSA One of the public key algorithms RSA Algorithm:
Chose two number p & q (1024bit)
n=p×q and z=(p-1)×(q-1)
Choose a number d that is relatively prime to z
e: e×d mod z = 1
Divde P to blocks, 0 <= block length < 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 HOOORAY! OK!
Lets finish cryptography algorithms
HOOORAY!
p = 3, q = 11
n = 33, z = 20, d = 7, e = 3
No more cryptography algorithms PLEASE!

7. Authorization and Validity
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 sender’s 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
Public-Key Signatures
Yes! How?
Be lost Da!!
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) #> P
MD(P) # MD(Q)
MD(P) # MD(P+1)

11. MD5 MD5: 5th Message Digest. 128bit buffer
md5(apple) = 1f3870be274f6c49b3e31a0c f

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