Let n be the product of two large primes. Alice wants to send a message m to Bob, where gcd(m, n) = 1. Alice and Bob choose integers a and b that are relatively prime to Φ(n). Alice computes c ≡ ma (mod n) and sends c to Bob. Bob computes d ≡ cb (mod n) and sends d back to Alice. Since Alice knows a, she finds a1 such that aa1 ≡ 1 (mod Φ(n)). Then she computes e ≡ da1 (mod n) and sends e to Bob. Explain what Bob must do to obtain m and show that this works.

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A:

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