Answer Happy

6. Alice gets lazy and use the same RSA set of public and private keys for both RSA digital signatures and RSA encryption. Specifically, this means Alice has private key d and public key e for RSA encryp- tion/decryption, while having private signing key s = d and public verification key v = e for RSA digital signatures. Suppose that Alice

occasionally signs messages for other people automatically (for exam- ple, Alice runs an online server where people give her messages and she signs them using RSA digital signatures). Show that Eve can do some "bad" things.