A Quantum Mechanical Proof of Insecurity of the Theoretical QKD Protocols

Abstract

Cryptography is crucial to communication security. In 1984, a well-known QKD (quantum key distribution) protocol, BB84, was published by Bennett and Brassard. The BB84 Protocol was followed by the QKD protocols published by Ekert (1991) (E91) and Bennett (1992) (B92). Some authors proved security of the theoretical QKD protocols in different theoretical frameworks by defining security of QKD protocols differently. My argument is that the previous proofs of security are neither unique nor exhaustive for each theoretical QKD protocol, which means that proof of security of the theoretical QKD protocols has not been completed or achieved. The non-uniqueness and the non-exhaustiveness of the proofs will lead to more proofs. However, a coming "proof" of security of the theoretical QKD protocols is possible to be a disproof. The research by quantum mechanics in this paper disproves security of the theoretical QKD protocols, by establishing the theoretical framework of quantum mechanical proof, defining security of QKD protocols, establishing the quantum state of the final key of the theoretical protocols from their information leakages, and applying Grover's fast quantum mechanical algorithm for database search to the quantum state of the final key to result in the Insecurity Theorem. This result is opposite to those of the previous proofs where the theoretical QKD protocols were secure. It is impossible for Alice and Bob to protect their communications from information leakage by stopping or canceling the protocols. The theoretical QKD keys are conventional and basically insecure. Disproof of security of the theoretical QKD protocols is logical.

On Security of Quantum Cryptography by Probabilistic Analysis

“…Solving Equation ( 3) is to search P (expressed by Equation ( 2)) for the j p whose bit string, p j , satisfies Equation (3). Bob can use Grover's fast quantum mechanical algorithm for database search for his searching to find p t [20]. Bob succeeds with the probability bigger than 1/2.…”

“…Zhao argued that the previous proofs were neither unique nor exhaustive, which meant that proof of security of the theoretical QKD protocols was not completed or achieved [20]. The research proved, by quantum mechanics, that the theoretical QKD protocols were insecure in an updated theoretical framework with an updated definition of security of QKD protocols [20].…”