Week 16

Question 1

Describe the three components of a digital signature scheme

Answer 1

1. Key generation
   randomised algorithm
   generates a keypair (secret signing key 𝒃 + public verification key 𝒗)
   also generates some public params
2. Signature generation
   possibly randomised algorithm
   takes public params, message 𝒎 and signing key 𝒃
   outputs a signature S(𝒎, 𝒃)
   (only the owner of secret signing key 𝒃 can generate signatures)
3. Signature verification
   algorithm that takes public params, message 𝒎, signature and public verification key 𝒃
   either accepts or rejects the claim that the signature is valid on the message by the owner of the verification/signing key 𝒃

Question 2

Describe the RSA signature scheme

Question 3

Use the RSA signature scheme to generate signatures and verify signatures

Question 4

Define the total break, selective forgery and existential forgery attack goals for a digital signature scheme

Question 5

Define the passive attack, known message attack and chosen message attack attack models for a digital signature scheme

Question 6

Appreciate that if the RSA problem is hard then RSA signatures are secure against selective forgery under a passive attack

Question 7

Describe how to create an existential forgery for the RSA signature scheme using a passive attack

Question 8

Describe how to create a selective forgery for the RSA signature scheme using a chosen message attack

Question 9

Appreciate that hash functions are a useful tool in cryptography

Question 10

Appreciate that SHA-256 is a hash function that is currently very widely used

Question 11

Define the security properties of collision resistance, preimage resistance and second preimage resistance for a hash function

Question 12

Describe the use of hash functions in a hash-then-sign signature scheme