# Certificate == signed public key

For primes p and q used to create a keypair, I understand that the following operation is used to create a signature:

$M^d (\bmod\ N)$

where d and N have their usual meanings and M is the message. In this case, however you need to possess the public key in order to verify the signature S as follows :-

$S^e (\bmod\ N)$

In the case of a certificate (CA signed or self signed), is the plaintext public key part of it?

• This is NOT a secure signature scheme. If you have two messages signed, you can compute a signature of their product simply multiplying their signatures. Apr 29 '13 at 8:52
• In addition, the word "plaintext" is used in contrast with "ciphertext", that we do not have in the case of signatures. To answer your question, the message is not part of the certificate, while the public key used to verify the signatures is. Apr 29 '13 at 8:58

To sign a message $M$ under RSA, one should NOT build the signature as $\mathcal{Sign}(M)=M^d\bmod N$, for several reasons:
• either that limits to messages $M$ in range $[0..N-1]$, or that allows forgeries of the form $\hat M=M+k\cdot N$, because $\mathcal{Sign}(\hat M)=\mathcal{Sign}(M)$;
• that allows forgeries of the form $\hat M=R^e\cdot\prod{M_j}^{a_j}$ because $\mathcal{Sign}(\hat M)=R\cdot\prod{\mathcal{Sign}(M_j)}^{a_j}\bmod N$.