Section 3: Public Key, Digital Signature

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Presentation transcript:

Section 3: Public Key, Digital Signature Network Security Section 3: Public Key, Digital Signature

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.

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

RSA Adelman Shmir Rivest

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?

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!

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.

Symmetric-Key Signatures Store signature on valid institute (BB: Big Brother). What is the problem of this method? Do you trust Big Brother?

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?

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)

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

SHA-1 Secure Hash Algorithm Developed by NSA 160bit buffer

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