Public-Key Encryption in a Multi-user Setting: Security Proofs and Improvements

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.