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arXiv:quant-ph/0006124 · Journal of Physics A Mathematical and General

A method of enciphering quantum states

Hiroo Azuma, Masashi Ban

Published Mar 26, 2001• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/0305-4470/34/13/305

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•Jan 1, 2012•0 citations
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.
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).
The quantum key distribution protocol BB84, published by C. H. Bennett and G. Brassard in 1984, describes how two spatially separated parties can generate a random bit string fully known only to them by transmission of single-qubit quantum states. Any attempt to eavesdrop on the protocol introduces disturbance which can be detected by the legitimate parties. In this Master's Thesis a novel modification to the BB84 protocol is analyzed. Instead of sending single particles one-by-one as in BB84, they are grouped and a non-local transformation is applied to each group before transmission. Each particle is sent to the intended receiver, always delaying the transmission until the receiver has acknowledged the previous particle on an authenticated classical channel, restricting eavesdropping to accessing the quantum transmission one particle at a time. Hence, an eavesdropper cannot undo the non-local transformation perfectly. Even if perfect cloning of quantum states was possible the state of the group could not be cloned. We calculate the maximal information on the established key provided by an intercept-resend attack and the induced disturbance for different transformations. We observe that it is possible to significantly reduce the eavesdropper's maximal information on the key--to one eighth of that in BB84 for a fixed, reasonable amount of disturbance. We also show that the individual access to the particles poses a fundamental restriction to the eavesdropper, and discuss a novel attack type against the proposed protocol.
We present and analyze a quantum key distribution protocol based on sending entangled NNN-qubit states instead of single-qubit ones as in the trail-blazing scheme by Bennett and Brassard 1984 (BB84). Since the qubits are sent and acknowledged individually, an eavesdropper is limited to accessing them one by one. In an intercept-resend attack, this fundamental restriction allows one to make the eavesdropper's information on the transmitted key vanish if even one of the qubits is not intercepted. The implied upper bound 1∕(2N)1∕(2N)1∕(2N) for this information is further shown not to be the lowest, as the information can be reduced to less than 30% of that in the BB84 scheme in the case N=2N=2N=2. In general, the protocol is at least as secure as BB84.
Transmitting message in secret is getting more and more important nowadays. In the classical world, the message we sent run the risk of being intercepted by an attacker. As a result, we have to encrypt the message, or send it using a private channel. However, if we transmit messages via such methods, there are still some ways to decipher the information. For example, a powerful computer can be used to decrypt the message or try to steal the message from the private channel. In quantum cryptography, entanglement can be used as a secure channel to transmit information with absolute secrecy. From this perspective, quantum entanglement pairs are equivalent to a quantum private key. However, like the classical key distribution problem, the entanglement has to be shared before it can be used. In this paper, we propose a protocol that can be used to distribute such entanglement pairs securely, so they can be subsequently used to transmit messages with perfect security. The security of this protocol is based on the laws of nature, instead of unproven mathematical hard problems.
Abstract. The BB84 protocol is used by Alice (the sender) and Bob (the receiver) to settle on a secret classical bit-string by communicating qubits over an insecure quantum channel where Eve (the Eavesdropper) can have access. In this paper, we revisit a well known eavesdropping technique against BB84. We claim that there exist certain gaps in understanding the existing eavesdropping strategyin terms of cryptanalytic view and we try to bridge those gaps in this paper. First we refer to the result where it is shown that in the six-state variant of the BB84 protocol (Bruß, Phys. Rev. Lett., 1998), the mutual information between Alice (the sender) and Eve (the eavesdropper) is higher when two-bit probe is used compared to the one-bit probe and hencethetwo-bitprobeprovidesastrongereavesdroppingstrategy.However, from cryptanalytic point of view, we show that Eve has the same success probability in guessing the bit transmitted by Alice in both the cases of the two-bit and the one-bit probe. Thus, we point out that having higher mutual information may not directly lead to obtaining higher probability in guessing the key bit. It is also explained in the work of Bruß that the six-state variant of the BB84 protocol is more secure than the traditional four-state BB84. We look into this point in more detail and identify that this advantage is only achieved at the expense of communicating more qubits in the sixstate protocol. In fact, we present different scenarios, where given the same number of qubits communicated, the security comparison of the four and six-state protocols is evaluated carefully.