We introduce a new cryptographic technique that we call universal re-encryption. A conventional cryptosystem that permits reencryption, such as ElGamal, does so only for a player with knowledge of the public key corresponding to a given ciphertext. In contrast, universal re-encryption can be done without knowledge of public keys. We propose an asymmetric cryptosystem with universal re-encryption that is half as efficient as standard ElGamal in terms of computation and storage. While technically and conceptually simple, universal re-encryption leads to new types of functionality in mixnet architectures. Conventional mixnets are often called upon to enable players to communicate with one another through channels that are externally anonymous, i.e., that hide information permitting traffic-analysis. Universal re-encryption lets us construct a mixnet of this kind in which servers hold no public or private keying material, and may therefore dispense with the cumbersome requirements of key g...