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Fortschritte der Physik

The Impossibility of Keyless Communication in Quantum Cryptography

Daniel M. Greenberger, Mark Hillary

Published May 1, 2000• 0 citations
Publisher

Abstract

We define a keyless communication as a message sent from one party (Alice) to another (Bob), such that the message is totally secure. This means that if a third party (Eve) is trying to eavesdrop, she will receive only random bits. She cannot understand the content of the message, even if she is able to intercept it in such away that Alice and Bob do not know it has been intercepted. For such a totally secure message, Alice and Bob do not need to set up any key beforehand, as it can add no further security. Starting with a system that we felt sure met such criteria, we were shocked to find out that it could be broken in at least two ways, by a semi-classical method and by a quantum method, such that Eve could read a message and Alice and Bob would not know it. Alice and Bob can counter such eavesdropping, but only by sending out test messages. This will enable them to ascertain that Eve is on the line, but then she can still occasionally pick up snippets of their conversation. In that case, in order to be totally secure, it is better to establish an unbreakable key beforehand. We postulate and give plausibility arguments that in general it is impossible to establish keyless communication between two parties.

DOI
10.1002/(sici)1521-3978(200005)48:5/7<523::aid-prop523>3.0.co;2-w

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We define a keyless communication as a message sent from one party (Alice) to another (Bob), such that the message is totally secure. This means that if a third party (Eve) is trying to eavesdrop, she will receive only random bits. She cannot understand the content of the message, even if she is able to intercept it in such away that Alice and Bob do not know it has been intercepted. For such a totally secure message, Alice and Bob do not need to set up any key beforehand, as it can add no further security. Starting with a system that we felt sure met such criteria, we were shocked to find out that it could be broken in at least two ways, by a semi-classical method and by a quantum method, such that Eve could read a message and Alice and Bob would not know it. Alice and Bob can counter such eavesdropping, but only by sending out test messages. This will enable them to ascertain that Eve is on the line, but then she can still occasionally pick up snippets of their conversation. In that case, in order to be totally secure, it is better to establish an unbreakable key beforehand. We postulate and give plausibility arguments that in general it is impossible to establish keyless communication between two parties.
Consider two parties: Alice and Bob and suppose that Bob is given a qubit system in a quantum state ϕ , unknown to him. Alice knows ϕ and she is supposed to convince Bob that she knows ϕ sending some test message. Is it possible for her to convince Bob providing him "zero knowledge" i. e. no information about ϕ he has? We prove that there is no "zero knowledge" protocol of that kind. In fact it turns out that basing on Alice message, Bob (or third party - Eve - who can intercept the message) can synthetize a copy of the unknown qubit state ϕ with nonzero probability. This "no-go" result puts general constrains on information processing where information about quantum state is involved.
In quantum key distribution (QKD), Alice selects a sequence of characters from a finite alphabet and transmits the corresponding signals, each described by a quantum state, to Bob. Between Alice and Bob, Eve---with her own receiver and transmitter---can eavesdrop. Eve is assumed to know beforehand all the possible states from among which Alice chooses. The central question is: Can Eve gain significant information about the key without influencing what Bob receives in ways that Alice and Bob can detect? This formulation implies that many options are available to Eve. It is the purpose here to discuss one of these options, where extensive use is made of the Schrodinger equation with spatial variables. This procedure of Eve---which consists of letting the quantum state of Alice scatter from a quantum memory and then, using the information thus obtained, sending a suitably chosen quantum state to Bob---is discussed in detail. Furthermore, there are ways for Alice to defeat this procedure by an unusual choice of her quantum states. This counter-measure is also presented and discussed.
Consider two parties: Alice and Bob and suppose that Bob is given a qubit system in a quantum state phi\\phiphi, unknown to him. Alice knows phi\\phiphi and she is supposed to convince Bob that she knows phi\\phiphi sending some test message. Is it possible for her to convince Bob providing him "zero knowledge" i. e. no information about phi\\phiphi he has? We prove that there is no "zero knowledge" protocol of that kind. In fact it turns out that basing on Alice message, Bob (or third party - Eve - who can intercept the message) can synthetize a copy of the unknown qubit state phi\\phiphi with nonzero probability. This "no-go" result puts general constrains on information processing where information {\\it about} quantum state is involved.
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).
In this paper, we propose a method of enciphering quantum states of two-state systems (qubits) for sending them in secrecy without entangled qubits shared by two legitimate users (Alice and Bob). This method has the following two properties. First, even if an eavesdropper (Eve) steals qubits, she can extract information from them with only a certain probability at most. Second, Alice and Bob can confirm that the qubits are transmitted between them correctly by measuring a signature. If Eve measures m qubits one by one from n enciphered qubits and sends alternative ones (the intercept/resend attack), the probability that Alice and Bob do not notice Eve's action is equal to (3/4) m or less. Passwords for decryption and the signature are given by classical binary strings and they are disclosed through a public channel. Enciphering classical information by this method is equivalent to the one-time pad method with distributing a classical key (random binary string) by the BB84 protocol. If Eve takes away qubits, Alice and Bob lose the original quantum information. If we apply our method to a state in iteration, Eve's success probability decreases exponentially. We cannot examine security against the case that Eve makes an attack using entanglement. This remains to be solved in the future.
While secure communication between two quantum parties has been shown possible theoretically, what is the possible direct communication between a full quantum capability sender Alice and a limited quantum capability receiver Bob? This is called Semi- Quantum Direct Communication (SQDC). Several protocols have been proposed for secure SQDC. However, they all need a pre-shared key and at least linear entanglement preservation time, as well as a linear number of quantum bit registers, with respect to message length. Besides, complex hardware implementation (including quantum bit permutations) decreases the transmission efficiency. This paper introduces a no-key SQDC protocol requiring only constant entanglement preservation time and a fixed number of quantum bit registers by adding an authentic public classical channel. The quantum circuit complexity of Alice decreases considerably as well as the number of quantum bits transmitted for sending a fixed length message. Moreover, the protocol is provably secure if some precondition is satisfied.