Unbelievable Security Matching AES Security Using Public Key Systems

The Advanced Encryption Standard (AES) provides three levels of security: 128, 192, and 256 bits. Given a desired level of security for the AES, this paper discusses matching public key sizes for RSA and the ElGamal family of protocols. For the latter both traditional multiplicative groups of finite fields and elliptic curve groups are considered. The practicality of the resulting systems is commented upon. Despite the conclusions, this paper should not be interpreted as an endorsement of any particular public key system in favor of any other.