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An identity-based non-interactive public key distribution system is presented that is based on a novel trapdoor one-way function allowing a trusted authority to compute the discrete logarithm of a given number modulo a publicly known composite number rn while this is infeasible for an adversary not knowing the factorization of m. Without interaction with a key distribution center or with the recipient of a given message a user can generate a mutual secure cipher key based solely on the recipient's identity and his own secret key and send the message, encrypted with the generated cipher key using a conventional cipher, over an insecure channel to the recipient. Unlike in previously proposed identity-based systems, no public keys, certificates for public keys or other information need to be exchanged and thus the system is suitable for many applications such as electronic mail that do not allow for interaction. 'A more detailed version of this paper has been submitted to the IEEE 'Jlansactions on Information Theory. *Work performed while consulting for Omnisec AG, Switzerland, prior to joining Princeton Univereity.

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An additive privacy homomorphism is an encryption function in which the decryption of a sum (or possibly some other operation) of ciphers is the s u m of the corresponding messages. Rivest, Adleman, and Dertouzos have proposed four different additive privacy homomorphisms. In this paper, we show that two of them are insecure under a ciphertext only attack and the other two can be broken by a known plaintext attack. We also introduce the notion of an R -additive privacy homomorphism, which is essentially an additive privacy homomorphism in which only at most R messages need to be added together. We give an example of an R -additive privacy homomorphism that appears to be secure against a ciphertext only attack.

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