This paper introduces the concepts of protocol divertibility and atomic proxy cryptography. Protocol divertibility is defined as a property of two-party protocols, where an intermediary (referred to as a warden) can randomize messages to ensure the underlying protocol succeeds while preventing subtle deviations from the protocol from being observed. The paper proposes a criterion for protocol divertibility and demonstrates its applicability to various protocols, including blind signature protocols and Diffie-Hellman key exchange. Atomic proxy cryptography involves the use of proxy keys to convert ciphertexts encrypted for one key into ciphertexts for another without revealing secret decryption keys or cleartext messages. The paper presents atomic proxy functions for encryption, identification, and signature schemes, and discusses the security and practical utility of these schemes. It also explores the relationship between protocol divertibility and proxy cryptography, highlighting that both concepts share a common effectiveness property but differ in their security requirements. The paper concludes by discussing the existence and potential of atomic proxy functions in various public-key cryptosystems.This paper introduces the concepts of protocol divertibility and atomic proxy cryptography. Protocol divertibility is defined as a property of two-party protocols, where an intermediary (referred to as a warden) can randomize messages to ensure the underlying protocol succeeds while preventing subtle deviations from the protocol from being observed. The paper proposes a criterion for protocol divertibility and demonstrates its applicability to various protocols, including blind signature protocols and Diffie-Hellman key exchange. Atomic proxy cryptography involves the use of proxy keys to convert ciphertexts encrypted for one key into ciphertexts for another without revealing secret decryption keys or cleartext messages. The paper presents atomic proxy functions for encryption, identification, and signature schemes, and discusses the security and practical utility of these schemes. It also explores the relationship between protocol divertibility and proxy cryptography, highlighting that both concepts share a common effectiveness property but differ in their security requirements. The paper concludes by discussing the existence and potential of atomic proxy functions in various public-key cryptosystems.