Cryptography / spring 2012

Exercise 5, week 7

1. Modify the digital signature techniques represented on page 100 in cases 1 and 2 to enable the receiver to verify the signature.

2. Modify the digital signature techniques represented on page 100 in case 3 to avoid triple encryption of the entire message.

3. Consider the following hash function. Messages are in the form of decimal

numbers M = (a₁, a₂, …, a_k). The hash value h is calculated as

(a₁+ a₂ + …+ a_k) mod n

for some predefined value n. Does this hash function satisfy any of the

requirements for a hash function?

4. Consider the list of names: Matti, Pekka, John, Charles, Juha, Eetu, Kim, Sari, Mary, Saara. Define hash function

h(c₁ c₂… c_n) = (asc(c₁) + asc(c₂) + … + asc(c_n)) mod 10,

where asc(c_i) is the Ascii code of the i’th letter c_i of the name. How many collisions do you find?

5. For SHA-512, show the equation for the values W₁₆, W₁₇, W₁₈, W₁₉.

6. Needham-Schroeder’s authentication protocol uses authentication centre X and is working as follows:

a) A -> X: R_A ◦ I_A ◦ I_B

b) X -> A: E_KAX( R_A ◦ I_B ◦ K_AB ◦ E_KBX(I_A ◦ K_AB))

c) A -> B: E_KBX(I_A ◦ K_AB)◦ E_KAB(R’_A)

d) B -> A: E_KAB(R’_A - 1) ◦ R_B

e) A -> B: E_KAB(R_B - 1)

Deduce how the protocol is working.