1. Exercises 2013-03-21 Information Security Course Eric Laermans – Tom Dhaene

2. Information Security Vakgroep Informatietechnologie – IBCN – Eric Laermans p. 2 Exercise 1 DES are there (different) DES keys K1 and K2 such that E K1 [M]=D K2 [M] (for all messages M)?  what (sufficient) condition can you derive for those?  can you give an example of such a key pair? are threre DES keys K for which E K [M]=D K [M] (for all messages M)?  what (sufficient) condition can you derive for those?  can you give an example of such a key?

3. Information Security Vakgroep Informatietechnologie – IBCN – Eric Laermans p. 3 Exercise 2 3-DES Given:  the reason why 3-DES with only 2 keys (112 bits) is used instead of 2-DES, is a so-called “meet-in-the- middle” attack Question:  what is the impact of this attack on the strength of 3- DES with 3 keys (168 bits)?

4. Information Security Vakgroep Informatietechnologie – IBCN – Eric Laermans p. 4 Exercise 3 RC4 Given:  RC4 has “families” of weak keys; these are keys for which the sum of the first two bytes: K[0]+K[1]=0 mod 256 Question:  what is, in this case, the most likely value of S[2] after the initialisation algorithm?

5. Information Security Vakgroep Informatietechnologie – IBCN – Eric Laermans p. 5 Exercise 4 RSA Given  2 persons use a common modulus n (albeit with different key pairs)  a same message is sent twice, encrypted using the public keys of both these users Question  how can an outsider (who doesn’t know the private keys) decipher the contents of the message (with a reasonable probability)?

6. Information Security Vakgroep Informatietechnologie – IBCN – Eric Laermans p. 6 Exercise 5 RSA Compare (approximately) the required computation time for the generation of a digital signature using RSA with a 1024 bit modulus and using RSA with a 2048 bit modulus Compare (approximately) the required computation time for verifying a digital signature using RSA with a 1024 bit modulus and using RSA with a 2048 bit modulus

7. Information Security Vakgroep Informatietechnologie – IBCN – Eric Laermans p. 7 Exercise 6 DSA There are now DSA versions using a 2048 bit prime number. Which hash function would you choose?  OPM.: the goal is to avoid that the hash function would weaken the algorithm, but “overkill” isn’t desirable either

8. Information Security Vakgroep Informatietechnologie – IBCN – Eric Laermans p. 8 Exercise 7 Rabin-encryption Given:  n = p q (with p and q two different prime numbers)  {n} is the public key, {p, q} is the private key  encryption: C = M 2 mod n  decryption: C p = C mod p; C q = C mod q –from which M p = M mod p; M q = M mod q (and therefore M using the CRT; or, more accurately, four possible values) Question:  set up a “chosen ciphertext” attack against this scheme