I'm stuck with this problem: Assume Alice and Bob are using RSA to communicate each other. Given Bob's public key $(217,7)$, Alice send the ciphertext $c=53$ to Bob through RSA encryption. Now, Eve can read the ciphertext $c$, how can Eve decrypt the ciphertext and read plaintext $m$?
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Some examples of answers to similar questions:
- Theoretical decryption of RSA
- https://crypto.stackexchange.com/questions/31433/how-to-decrypt-a-rsa-encrypted-text-file-when-only-public-key-is-known
Hint: $N = 217 =\ ?\ \times\ ?$
In the public key, $e$ is the exponent and $N$ is modulus, therefore $e < N$.
If $m$ is your message, $m^e \mod N = c$ is the cipher.
To decipher you need to find $d$, such as: $d \times e = 1 \mod \phi(N)$.
You will then be able to find $m$: $c^d \mod N = m$
