Alice and her three friends are all users of the RSA cryptosystem. Her friends have public keys (Ni, ei = 3), i = 1, 2, 3, where as always, Ni = piqi for randomly chosen n-bit primes pi, qi. Show that if Alice sends the same n-bit message M (encrypted using RSA) to each of her friends, then anyone who intercepts all three encrypted messages will be able to efficiently recover M. (Hint: It helps to have solved problem 1.37 first.)
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