Answer Happy

Suppose a community of RSA users share the same encryption exponent e but each user i has their own encryption modulus n. Furthermore, suppose that distinct n are pairwise relatively prime. Now, let us assume that Alice sends the same message x(0 < x < n₂ for all i) to k different entities in the community, i.e., Alice sends y₁ = x² (mod n,) (0 < y; <n;) to user i for 1 ≤ i ≤k. Show that if k> e, then a cryptanalyst can recover the plaintext z without factoring any of the nį.