Out of 42 points 1: (6pt) m2l = c2r xor c1r xor m1l = 832B4AF7 2: (2pt each) A) repeated outputs B) right rotate of bits C) b0 | b1 | b2 -> ~b2 | .. | b0 xor b1 xor b2 (also accepted answers based on differential analysis) 3: (3pt each) A) x^{(p-1)(q-1) - 1} B) 22 C) 105^235 mod 391 = 41 D) ed = k(p-1)(q-1) + 1 = k(n/q -1)(q-1) + 1 = k(n - q -n/q -1) + 1 k <= 3 (for e = 3) solve for q by trying each k 4: (3pt each) A) (2,3) B) 6 C) 10 is not a generator for 11 In fact, in general (p-1)^k mod p will only generate 1 and -1 since p-1 = -1 mod p in modular arithmetic. 5: (3pt and 6pt) A) 39, 58, 53, 37, 60, 58, 53, ... 1, 0, 1, 1, 0, 0, 1, ... B) (p-1)(q-1)/4 got full credit if explained. In particular since (p-1) and (q-1) are each divisible by 2 2^i mod (p-1)(q-1) will generate at most (p-1)(q-1)/4 + 2 values. (p-1)(q-1) and (p-1)(q-1)/2 got partial credit.