Cryptography 2012, exercise 1, week 3

1. Cipher text

LDPFDHVDUDQGBRXDUHFOHYHU

have been done with Caesar method. Decrypt this message.

2. Analyse

OYFREEETRSPSORNCTRNIMOLTDPOOXRGCOIFO

Try to find some method to decrypt this message.

3. Hill’s method, which substitutes m-tuples of letters by multiplication with an m×m matrix, is easy to analyse, if cryptanalyst has some knowntext – ciphertext pairs. Solve the problem in the case that the knowntext is FRIDAY, the ciphertext is PQCFKU and m = 2.

4. The notations E_k and D_k, (k = 0, 1, 2,…, 26) mean that each letter is shifted according to the formulas

c = E_k(p) = (p+k) mod (26), c = D_k(p) = (p-k) mod (26).

Show that

E_kD_n = D_nE_k for all k,n = 0, 1, 2,…, 26.

Simplify the expression

E₃D₇E₆D₁₁E₄D₅.

5. Write an algorithm and a computer program which outputs all the candidates for

plaintest in the case of Caesar’s method. The input for the algorithm is the given

ciphertext.

6. It can be shown that in DES the 24 first bits of each subkey come from the set of 28 bits of the original key. Determine in which places in the original key these 28 bits are situated?