1. Digital Signatures
Last Updated: Oct 14, 2017

2. Digital Signatures
Diagram illustrating how to digitally sign a message
Why do we use a one-way hash?
How does this relate to a collision or 2nd pre-image attack?

3. Digital Signatures What assurances do we get with a digital signature?
Authentication
Confidentiality
Integrity
Non-repudiation
MAC vs. Digital Signature
MAC does not offer non-repudiation. Why?
With a MAC, either Alice or Bob could have generated the mac.

4. Message Authentication
Three approaches
Benefits of each?
Drawbacks?
Third option is broken, use HMAC

5. HMAC Government standard for HMAC H(K || H(K || M))
Prevents extension attack

6. Public Key Distribution Problem
Symmetric encryption – exponential key distribution problem (n^2 key pairs for group of size n)
Public keys – we all distribute our own public key (n keys)
How can I trust that I have received your public key?
Trusted third party hands out signed documents containing user ID and public key
Signed documents are known as certificates

7. Digital Certificates Who has a digital certificate?
Which private key is used to sign a certificate?
Whose public key is in the certificate?
What are common uses for certificates?

8. Performance of Crypto Primitives

9. Performance Test
Goal: figure out the relative computing time for algorithms (one block)
SHA-1
AES
RSA Encrypt
RSA Signature
Order the above, fastest to slowest

10. Performance Test Average of 10, 000 iterations SHA-1 – 0.0017 ms
AES – ms
RSA encrypt – ms
3515x slower than a hash
RSA signature – ms
8x slower than a hash
215x slower than a hash
26x slower than AES
421x slower than AES
16x slower than RSA enc.

11. Or: “How RSA should really be used”
RSA Padding
Or: “How RSA should really be used”
(See PKCS #1)

12. RSA Primitives RSA Encryption : me = c (mod n)
RSA Decryption : cd = m (mod n)
Pitfalls of using RSA
What if m is very small? Remember that e is usually small.
Take the e’th root of c
Brute force the domain of m
Solution: RSA Padding
Before encrypting/signing a key/hash, pad it so that it is a large number and comparable to the modulus n
Implementation flaws – timing attacks
Insert constant delays or binding
RSA Labs publishes the standards for using RSA
Public Key Cryptography Standard #1 (PKCS #1)