1. @Yuan Xue (yuan.xue@vanderbilt.edu)CS 285: Network Security CS 285 Network Security Digital Signature Yuan Xue Fall 2012

2. @Yuan Xue (yuan.xue@vanderbilt.edu)CS 285 Network Security Digital Signature Overview Message Authentication Code Data integrity Source authentication Issue  Source can successfully claim they did not create a message Reason  Source and destination share the same key (same knowledge) Digital Signature Message authentication + non-repudiation Solution  Use of asymmetric key

3. @Yuan Xue (yuan.xue@vanderbilt.edu)CS 285 Network Security Digital Signature Two approaches Encryption of hash value via private key provides digital signature Any asymmetric encryption algorithm could be used  E.g. RSA Many asymmetric encryption algorithms have export restriction DSA (digital signature algorithm)-based approach

4. @Yuan Xue (yuan.xue@vanderbilt.edu)CS 285 Network Security Primitives for Digital Signature Algorithm Elgamal Digital Signature Based on discrete log operation  primitive root Signature has two components a is a primitive root of prime number p then a mod p, a 2 mod p, …, a p-1 mod p are distinct and consist of the integers from 1 through p-1 For any b and a primitive root a of p, unique exponent I can be found such that b = a i mod p (0<=i <= p-1)

5. @Yuan Xue (yuan.xue@vanderbilt.edu)CS 285 Network Security Digital Signature Algorithm An asymmetric key algorithm Can not be used for encryption Can ONLY be used for digital signature Algorithm Based on discrete log operation Global variables  p, q, g  Private key x  Public key y = g x mod p User per-msg secret num k Generate a random per-message value k where 0 < k < q Calculate r = (g k mod p) mod q Calculate s = (k −1 (H(m) + x·r)) mod q The signature is (r, s) Calculate w = s −1 mod q Calculate u1 = H(m)·w mod q Calculate u2 = r·w mod q Calculate v = ((g u1 ·y u2 ) mod p) mod q The signature is valid if v = r

6. @Yuan Xue (yuan.xue@vanderbilt.edu)CS 285 Network Security Digital Signature Algorithm

7. @Yuan Xue (yuan.xue@vanderbilt.edu)CS 285 Network Security Public-Key Algorithm Summary Encryption/ Decryption Digital Signature Key Exchange RSAYYY Diffie- Hellman NNY DSSNYN

8. @Yuan Xue (yuan.xue@vanderbilt.edu)CS 285 Network Security MAC and DS Summary Message Authentication Code CBC-based Hash-based  Encrypt the hash code  Hash the message + key HMAC CMAC and more.. Digital Signature Encrypt the hash code Digital signature standard Symmetric Key Encryption Asymmetric Key Encryption

9. @Yuan Xue (yuan.xue@vanderbilt.edu)CS 285 Network Security Comparison Computation efficiency Hash > symmetric encryption > asymmetric encryption Message Authentication Code CBC-based Hash-based  Encrypt the hash code  Hash the message + key HMAC Digital Signature Encrypt the hash code Digital signature standard faster