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I just picked up cryptography and have some questions on RSA cryptosystem:

  1. Say there are two public keys (n, e1), (n, e2), e1 is coprime to e2. They share the same n. Is it possible to find the plaintext if both of them encrypt the same message if I have both 2 public keys and 2 ciphertexts?

  2. Usually, we use two primes p, q to construct modulo n = pq. I am wondering if we change n to pqr....... which is the multiplication of more than two primes, is the phi(n) equal to (p-1)(q-1)(r-1)..... and nothing else need to be changed to make RSA still work?

ChesterL
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1 Answers1

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1) Yes. This is the common modulus attack and has actually been answered many times on this forum.

2) Assuming $r$ is prime, yes. $\phi(n)$, (the totient of $n$) can be computed by subtracting 1 from each of $n$'s prime factors and multiplying them together.

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user13741
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