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Quantum Information and Computation

Quantum vernam cipher

Debbie Leung

Published Jan 1, 2002• 19 citations
Publisher

Abstract

We discuss aspects of secure quantum communication by proposing and analyzing a quantum analog of the Vernam cipher (one-time-pad). The quantum Vernam cipher uses entanglement as the key to encrypt quantum information sent through an insecure quantum channel. First, in sharp contrast with the classical Vernam cipher, the quantum key can be recycled securely. We show that key recycling is intrinsic to the quantum cipher-text, rather than using entanglement as the key. Second, the scheme detects and corrects for arbitrary transmission errors, and it does so using only local operations and classical communication (LOCC) between the sender and the receiver. The application to quantum message authentication is discussed. Quantum secret sharing schemes with similar properties are characterized. We also discuss two general issues, the relation between secret communication and secret sharing, the classification of secure communication protocols.

DOI
10.26421/qic2.1-2

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We discuss aspects of secure quantum communication by proposing and analyzing a quantum analog of the Vernam cipher (one-time-pad). The quantum Vernam cipher uses entanglement as the key to encrypt quantum information sent through an insecure quantum channel. First, in sharp contrast with the classical Vernam cipher, the quantum key can be recycled securely. We show that key recycling is intrinsic to the quantum cipher-text, rather than using entanglement as the key. Second, the scheme detects and corrects for arbitrary transmission errors, and it does so using only local operations and classical communication (LOCC) between the sender and the receiver. The application to quantum message authentication is discussed. Quantum secret sharing schemes with similar properties are characterized. We also discuss two general issues, the relation between secret communication and secret sharing, the classification of secure communication protocols.
We discuss aspects of secure quantum communication by proposing and analyzing a quantum analog of the Vernam cipher (one-time-pad). The quantum Vernam cipher uses entanglement as the key to encrypt quantum information sent through an insecure quantum channel. First, in sharp contrast with the classical Vernam cipher, the quantum key can be recycled securely. We show that key recycling is intrinsic to the quantum cipher-text, rather than using entanglement as the key. Second, the scheme detects and corrects for arbitrary transmission errors, and it does so using only local operations and classical communication (LOCC) between the sender and the receiver. The application to quantum message authentication is discussed. Quantum secret sharing schemes with similar properties are characterized. We also discuss two general issues, the relation between secret communication and secret sharing, the classification of secure communication protocols.
We discuss aspects of secret quantum communication by proposing and analyzing a quantum analog of the Vernam cipher (one-time-pad). The quantum Vernam cipher uses entanglement as the key to encrypt quantum information sent through an insecure quantum channel. First, in sharp contrast with the classical Vernam cipher, the quantum key can be recycled securely. We show that key recycling is intrinsic to the quantum cipher-text, rather than using entanglement as the key. Second, the scheme detects and corrects for arbitrary transmission errors, and it does so using only local operations and classical communication (LOCC) between the sender and the receiver. Quantum secret sharing schemes with similar properties are characterized. We also discuss two general issues, the relation between secret communication and secret sharing, and the classification of secure communication protocols.
Cryptographic protocols can be classified by the type of security against eavesdropping which they provide. There exist mathematically secure schemes whose security relies on mathematical proofs (like the Vernam cipher discussed below) or conjectures (like public key RSA encryption) about the complexity of deciphering the message without possessing the correct key. The majority of current secure public Internet connections rely on such schemes. Alternatively, a cryptographic setup may provide a physically secure method for communicating. In these setups the security is provided by the physical laws governing the communication protocol. Here we first discuss a provably secure classical communication protocol and then quantum methods for distributing the necessary keys. The BB84 protocol relies on the impossibility of perfectly distinguishing non-orthogonal quantum states from one copy of the quantum system. The scheme was invented in 1984 and is the first of its kind. In contrast, the Ekert91 protocol makes use of Bell correlations between entangled pairs of photons. These correlations are destroyed when Eve attempts to make a measurement on one of the particles but also when imperfections, such as decoherence processes, affect the scheme. As long as no such “elements of reality” are introduced, and Bell correlations violating local realism can be generated by Alice and Bob, no eavesdropper can be present. One-time pads and the Vernam cipher The Vernam cipher is a cryptographic protocol which allows the encryption and decryption protocol to be publicly known. The security of the protocol relies entirely on the key which is private and not publicly known. Alice and Bob share identical n -bit secret key strings (one-time pad).
Assuming an insecure quantum channel and an authenticated classical channel, we propose an unconditionally secure scheme for encrypting classical messages under a shared key, where attempts to eavesdrop the ciphertext can be detected. If no eavesdropping is detected, we can securely re-use the entire key for encrypting new messages. If eavesdropping is detected, we must discard a number of key bits corresponding to the length of the message, but can re-use almost all of the rest. We show this is essentially optimal. Thus, provided the adversary does not interfere (too much) with the quantum channel, we can securely send an arbitrary number of message bits, independently of the length of the initial key. Moreover, the key-recycling mechanism only requires one-bit feedback. While ordinary quantum key distribution with a classical one time pad could be used instead to obtain a similar functionality, this would need more rounds of interaction and more communication.
Quantum information is a valuable resource which can be encrypted in order to protect it. We consider the size of the one-time pad that is needed to protect quantum information in a number of cases. The situation is dramatically different from the classical case: we prove that one can recycle the one-time pad without compromising security. The protocol for recycling relies on detecting whether eavesdropping has occurred, and further relies on the fact that information contained in the encrypted quantum state cannot be fully accessed. We prove the security of recycling rates when authentication of quantum states is accepted, and when it is rejected. We note that recycling schemes respect a general law of cryptography which we introduce relating the size of private keys, sent qubits, and encrypted messages. We discuss applications for encryption of quantum information in light of the resources needed for teleportation. Potential uses include the protection of resources such as entanglement and the memory of quantum computers. We also introduce another application: encrypted secret sharing and find that one can even reuse the private key that is used to encrypt a classical message. In a number of cases, one finds that the amount of private key needed for authentication or protection is smaller than in the general case.