This paper addresses the security of public-key cryptosystems in a multi-user" setting, namely in the presence of attacks involving the encryption of related messages under di erent public keys, as exempli ed by H astad's classical attacks on RSA. We prove that security in the single-user setting implies security in the multi-user setting as long as the former is interpreted in the strong sense of indistinguishability," thereby pin-pointing many schemes guaranteed to be secure against H astad-type attacks. We then highlight the importance, in practice, of considering and improving the concrete security of the general reduction, and present such improvements for two Di e-Hellman based schemes, namely El Gamal and Cramer-Shoup.
For a theoretical treatment of public-key encryption in the multi-user setting, we refer to Bellare et al. REF .
Public-key encryption in a multi-user setting: Security proofs and improvements
EUROCRYPT
Computer Science