This paper introduces the concepts of divertibility and atomic proxy cryptography. Divertibility is a property of 2-party protocols that allows an intermediary (warden) to transform communication without breaking the protocol. The warden randomizes messages so that the intended protocol succeeds, but subtle deviations are obliterated. The paper defines protocol divertibility as a 2-party protocol property, distinct from zero-knowledge or other protocol properties. A sufficiency criterion for divertibility is proposed, which is satisfied by many existing protocols, including Diffie-Hellman key exchange. Atomic proxy cryptography is introduced, where an atomic proxy function, along with a public proxy key, converts ciphertexts for one key into ciphertexts for another. Proxy keys can be made public and used in untrusted environments. The paper presents atomic proxy functions for discrete-log-based encryption, identification, and signature schemes. It discusses the relationship between divertibility and proxy cryptography, showing that they are closely related. The paper also discusses new examples of diverted protocols, including blind signatures and key exchange. It demonstrates that the Diffie-Hellman key exchange protocol is computationally divertible. The paper further explores the security of proxy schemes, showing that publishing proxy keys does not compromise messages or secret keys. It also discusses the practical utility of proxy functions in key management and secure communication. The paper concludes that divertibility and proxy cryptography are both defined in terms of effectiveness and security properties. While divertibility ensures that no subliminal messages are communicated through the warden, proxy cryptography ensures that the proxy key does not release more information than the original protocol. The paper highlights the potential of atomic proxy cryptography as a natural extension of public-key cryptography and raises questions about the existence of atomic proxy schemes for other public-key cryptosystems.This paper introduces the concepts of divertibility and atomic proxy cryptography. Divertibility is a property of 2-party protocols that allows an intermediary (warden) to transform communication without breaking the protocol. The warden randomizes messages so that the intended protocol succeeds, but subtle deviations are obliterated. The paper defines protocol divertibility as a 2-party protocol property, distinct from zero-knowledge or other protocol properties. A sufficiency criterion for divertibility is proposed, which is satisfied by many existing protocols, including Diffie-Hellman key exchange. Atomic proxy cryptography is introduced, where an atomic proxy function, along with a public proxy key, converts ciphertexts for one key into ciphertexts for another. Proxy keys can be made public and used in untrusted environments. The paper presents atomic proxy functions for discrete-log-based encryption, identification, and signature schemes. It discusses the relationship between divertibility and proxy cryptography, showing that they are closely related. The paper also discusses new examples of diverted protocols, including blind signatures and key exchange. It demonstrates that the Diffie-Hellman key exchange protocol is computationally divertible. The paper further explores the security of proxy schemes, showing that publishing proxy keys does not compromise messages or secret keys. It also discusses the practical utility of proxy functions in key management and secure communication. The paper concludes that divertibility and proxy cryptography are both defined in terms of effectiveness and security properties. While divertibility ensures that no subliminal messages are communicated through the warden, proxy cryptography ensures that the proxy key does not release more information than the original protocol. The paper highlights the potential of atomic proxy cryptography as a natural extension of public-key cryptography and raises questions about the existence of atomic proxy schemes for other public-key cryptosystems.