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Homework answers / question archive / Let p and q be primes

Let p and q be primes. Let E and D be an encryptor and decryptor that work for

the RSA encoding process with N = pq.

Now consider RSA encoding with N = pq, and encryptor E

2

. Prove that D2

is a

decryptor for this encryptor.

Note: This question is describing the following situation: suppose you “doubly”

encode the message M by encoding once using E (obtaining ME) and then again

using E (obtaining

ME

E

). You are asked to show that by using D2 you can decode

the doubly encrypted message in one step, instead of doing so in two steps. In other

words, “doubly” encoding your message adds no additional security.