Impossibility of Three Pass Protocol using Public Abelian Groups
This result addresses a foundational problem in cryptography by showing a limitation in key transport protocols, preventing potential misuse in secure communications.
The paper proves that it is impossible to use public Abelian groups to implement the three-pass protocol for secret key transport, which would have enabled information-theoretic security in post-quantum cryptography without relying on computational hardness.
Key transport protocols are designed to transfer a secret key from an initiating principal to other entities in a network. The three-pass protocol is a key transport protocol developed by Adi Shamir in 1980 where Alice wants to transport a secret message to Bob over an insecure channel, and they do not have any pre-shared secret information. In this paper, we prove the impossibility of secret key transportation from a principal to another entity in a network by using the three pass protocol over public Abelian groups. If it were possible to employ public Abelian groups to implement the three-pass protocol, we could use it in post-quantum cryptography for transporting keys providing information theoretic security without relying on any computationally difficult problem.