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Network Security

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. ABCDEFGHI. ******************. P. Eb(P). Send to Bob. Eb. Ea.

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Network Security

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  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 #> D • E not crack-able by “known texts” attack.

  3. ABCDEFGHI ****************** P Eb(P) Send to Bob Eb Ea Bob reads P ABCDEFGHI ****************** D(Eb(P)) Eb(P) 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) • 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. OK! Lets finish cryptography algorithms HOOORAY! 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 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. 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) = 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

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