If $m$ is less than say $2^ N_i$ then we can always construct such a value via the CRT since for $m < N_i$ it holds that $m^e < N_1N_2. Poof goes confidentiality if the message is a name on the class roll, a guessable password. They simply encipher a guess of $m$ with $(N_i,e)$ and check it against $c_i$. It severely limits the size of the message (to less than 128 octets).Ī guess of the message can be checked by anyone with a public key $(N_i,e)$ and the ciphertext $c_i$, which by a standard assumption in cryptography includes adversaries. not using the multiple public keys, and the answer likely thought at 5. ![]() This has dire consequences, including the following (with 1./2./3. In the question, the same message is directly encrypted to three different public keys using textbook RSA.
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