Practical Cryptology

Examination tasks

1. Suppose that a and b are integers such that a ≡ 45 (mod 71) and b ≡ 53 (mod 71).
   Find an integer c such that 0 ≤ c < 71 such that (1 pts/task)
   (a) c ≡ a
   6
   · b
   −5
   (mod 71)
   (b) a ≡ b
   c
   (mod 71)
   (c) c ≡ 34(a
   5 − b
   2
   ) (mod 71)
   (d) 29c ≡ 41a + b
   7
   (mod 71)

Sample Solution