In this Paper, we investigate the security of Zhang, Li and Guo quantum key distribution via quantum encryption protocol [$\text{Phys. Rev. A} \textbf{64}, 24302 (2001)$] and show that it is not secure against some of Eve's attacks and with the probability one half she gets all of keys without being detected by the two parties. The main defect in this protocol is that there is an attack strategy by which Eve can change the previously shared Bell state between Alice and Bob to two Bell states among herself and Alice and Bob. Hence, we show that with probability $1/d$ its generalization to $d$-dimension systems is not secure and show that its extension to the case of more partners based on the reusable GHZ states is not secure and with probability one half Eve gets all of keys without being detected by the two parties. In what follows, we show how in going to higher dimensions those protocols can be repaired.
We present a quantum probabilistic encryption algorithm for a private-key encryption scheme based on conjugate coding of the qubit string. A probabilistic encryption algorithm is generally adopted in public-key encryption protocols. Here we consider the way it increases the unicity distance of both classical and quantum private-key encryption schemes. The security of quantum probabilistic private-key encryption schemes against two kinds of attacks is analyzed. By using the no-signalling postulate, we show that the scheme can resist attack to the key. The scheme's security against plaintext att…
The standard definition of quantum state randomization, which is the quantum analog of the classical one-time pad, consists in applying some transformation to the quantum message conditioned on a classical secret key $k$. We investigate encryption schemes in which this transformation is conditioned on a quantum encryption key state $ρ_k$ instead of a classical string, and extend this symmetric-key scheme to an asymmetric-key model in which copies of the same encryption key $ρ_k$ may be held by several different people, but maintaining information-theoretical security. We find bounds on the mes…
We propose a definition for the information theoretic security of a quantum public-key encryption scheme, and present bit-oriented and two-bit-oriented encryption schemes satisfying our security definition via the introduction of a new public-key algorithm structure. We extend the scheme to a multi-bitoriented one, and conjecture that it is also information theoretically secure, depending directly on the structure of our new algorithm.
A quantum key distribution protocol based on quantum encryption is presented in this Brief Report. In this protocol, the previously shared Einstein-Podolsky-Rosen pairs act as the quantum key to encode and decode the classical cryptography key. The quantum key is reusable and the eavesdropper cannot elicit any information from the particle Alice sends to Bob. The concept of quantum encryption is also discussed.
In the classical setting, public-key encryption requires randomness in order to be secure against a forward search attack, whereby an adversary compares the encryption of a guess of the secret message with that of the actual secret message. We show that this is also true in the information-theoretic setting -- where the public keys are quantum systems -- by defining and giving an example of a forward search attack for any deterministic quantum-public-key bit-encryption scheme. However, unlike in the classical setting, we show that any such deterministic scheme can be used as a black box to bui…
We re-visit Unclonable Encryption as introduced by Gottesman in 2003. We look at the combination of Unclonable Encryption and Key Recycling, while aiming for low communication complexity and high rate. We introduce a qubit-based prepare-and-measure Unclonable Encryption scheme with re-usable keys. Our scheme consists of a single transmission by Alice and a single classical feedback bit from Bob. The transmission from Alice to Bob consists entirely of qubits. The rate, defined as the message length divided by the number of qubits, is higher than what can be achieved using Gottesman's scheme. We…
The thesis is mainly about the construction and implementation of cyclic mutually unbiased bases, dealing with different entanglement structures by discussing the related group structures. A recursive construction for Fermat number dimensions is given and related to Wiedemann's conjecture for systems with more than 2048 qubits. The second part of the thesis analyses a quantum public-key encryption scheme.
In the paper [Zhang, Li and Guo, Phys. Rev. A 64, 024302 (2001)], a quantum key distribution protocol based on quantum encryption was proposed, in which the quantum key can be reused. However, it is shown that, if Eve employs a special strategy to attack, this protocol becomes insecure because of the reused quantum key. That is, Eve can elicit partial information about the key bits without being detected. Finally, a possible improvement of the Zhang-Li-Guo protocol is proposed.
Shannon presented the concept `unicity distance' for describing the security of secret key encryption protocols against various ciphertext-only attacks. We develop this important concept of cryptanalysis into the quantum context, and find that there exist quantum encryption protocols reusing a short key have infinite unicity distance.
In this paper, we consider a quantum key distribution protocol (QKD) with two-way classical communication that is assisted by one-time pad encryption. We propose a two-way preprocessing that uses one-time pad encryption by previously shared secret key, and the net key rate of the QKD with proposed preprocessing exceeds the key rate of the QKD without it. The preprocessing is reduced to the entanglement distillation protocol with two-way classical communication and previously shared EPR pairs (two-way breeding protocol), and the security of QKD with the preprocessing is guaranteed in the same w…
In this paper, we first define the quantum discrete logarithm problem (QDLP)which is similar to classical discrete logarithm problem. But, this problem cannot be solved by Shor's quantum algorithm. Based on quantum discrete logarithm problem, we present a novel quantum secret key encryption algorithm. The receiver constructs his quantum channel using their secret key. Then, the sender can use the receiver's quantum channel to encrypt the message. Finally, the receiver dencrypts the ciphertext by using secret key. In our algorithm, the quantum system will be broken after transferring messages. …
We present several quantum public-key encryption (QPKE) protocols designed with conjugate coding single-photon string, thus may be realized in laboratory with nowadays techniques. Two of these schemes are orienting one-bit message, and are extended to two kinds of QPKE schemes orienting multi-bits. The novel structure of these protocols ensures they are information-theoretically secure with, probably, a bound greater than any given polynomial of $n$. Finally, we describe a way to conceal the classical part of the public key with quantum state, this idea is expected to enhance a scheme to be in…
Exploring the symmetries underlying a previously proposed encryption scheme which relies on single-qubit rotations, we derive an improved upper bound on the maximum information that an eavesdropper might extract from all the available copies of the public key. Subsequently, the robustness of the scheme is investigated in the context of attacks that address each public-key qubit independently. The attacks under consideration make use of projective measurements on single qubits and their efficiency is compared to attacks that address many qubits collectively and require complicated quantum opera…
Quantum cryptography -- the application of quantum computing techniques to cryptography has been extensively investigated. Two major directions of quantum cryptography are quantum key distribution (QKD) and quantum encryption, with the former focusing on secure key distribution and the latter focusing on encryption using quantum algorithms. In contrast to the success of the QKD, the development of quantum encryption algorithms is limited to designs of mostly one-time pads (OTP) that are unsuitable for most communication needs. In this work we propose a non-OTP quantum encryption scheme utilizi…
We report on the design and performance of a point-to-point classical symmetric encryption link with fast key renewal provided by a Continuous Variable Quantum Key Distribution (CVQKD) system. Our system was operational and able to encrypt point-to-point communications during more than six months, from the end of July 2010 until the beginning of February 2011. This field test was the first demonstration of the reliability of a CVQKD system over a long period of time in a server room environment. This strengthens the potential of CVQKD for information technology security infrastructure deployme…
We present a classification of quantum public-key encryption protocols. There are six elements in quantum public-key encryption: plaintext, ciphertext, public-key, private-key, encryption algorithm and decryption algorithm. According to the property of each element which is either quantum or classical, the quantum public-key encryption protocols can be divided into 64 kinds. Among 64 kinds of protocols, 8 kinds have already been constructed, 52 kinds can be proved to be impossible to construct and the remaining 4 kinds have not been presented effectively yet. This indicates that the research o…
We demonstrate high-rate randomized data-encryption through optical fibers using the inherent quantum-measurement noise of coherent states of light. Specifically, we demonstrate 650Mbps data encryption through a 10Gbps data-bearing, in-line amplified 200km-long line. In our protocol, legitimate users (who share a short secret-key) communicate using an M-ry signal set while an attacker (who does not share the secret key) is forced to contend with the fundamental and irreducible quantum-measurement noise of coherent states. Implementations of our protocol using both polarization-encoded signal s…
A novel technique is devised to perform orthogonal state quantum key distribution. In this scheme, entangled parts of a quantum information carrier are sent from Alice to Bob through two quantum channels. However before the transmission, the orders of the quantum information carrier in one channel is reordered so that Eve can not steal useful information. At the receiver's end, the order of the quantum information carrier is restored. The order rearrangement operation in both parties is controlled by a prior shared control key which is used repeatedly in a quantum key distribution session.
It has been pointed out that current protocols for device independent quantum key distribution can leak key to the adversary when devices are used repeatedly and that this issue has not been addressed. We introduce the notion of an insider-proof channel. This allows us to propose a means by which devices with memories could be reused from one run of a device independent quantum key distribution protocol to the next while bounding the leakage to Eve, under the assumption that one run of the protocol could be completed securely using devices with memories.
The classification of quantum symmetric-key encryption protocol is presented. According to five elements of a quantum symmetric-key encryption protocol: plaintext, ciphertext, key, encryption algorithm and decryption algorithm, there are 32 different kinds of them. Among them, 5 kinds of protocols have already been constructed and studied, and 21 kinds of them are proved to be impossible to construct, the last 6 kinds of them are not yet presented effectively. That means the research on quantum symmetric-key encryption protocol only needs to consider with 5 kinds of them nowadays.
Suppose some data have been encrypted, can you compute with the data without decrypting them? This problem has been studied as homomorphic encryption and blind computing. We consider this problem in the context of quantum information processing, and present the definitions of quantum homomorphic encryption (QHE) and quantum fully homomorphic encryption (QFHE). Then, based on quantum one-time pad (QOTP), we construct a symmetric QFHE scheme, where the evaluate algorithm depends on the secret key. This scheme permits any unitary transformation on any $n$-qubit state that has been encrypted. Comp…
Unclonable Encryption, introduced by Gottesman in 2003, is a quantum protocol that guarantees the secrecy of a successfully transferred classical message even when all keys leak at a later time. We propose an Unclonable Encryption protocol with the additional property that the sender's key material is allowed to leak even in the case of an unsuccessful run. This extra feature makes it possible to achieve secure quantum encryption even when one of the parties is unable to protect its keys against after-protocol theft. Such an asymmetry occurs e.g. in case of server-client scenarios, where the c…
Non-malleability is an important security property for public-key encryption (PKE). Its significance is due to the fundamental unachievability of integrity and authenticity guarantees in this setting, rendering it the strongest integrity-like property achievable using only PKE, without digital signatures. In this work, we generalize this notion to the setting of quantum public-key encryption. Overcoming the notorious "recording barrier" known from generalizing other integrity-like security notions to quantum encryption, we generalize one of the equivalent classical definitions, comparison-base…
Quantum states cannot be cloned. I show how to extend this property to classical messages encoded using quantum states, a task I call "uncloneable encryption." An uncloneable encryption scheme has the property that an eavesdropper Eve not only cannot read the encrypted message, but she cannot copy it down for later decoding. She could steal it, but then the receiver Bob would not receive the message, and would thus be alerted that something was amiss. I prove that any authentication scheme for quantum states acts as a secure uncloneable encryption scheme. Uncloneable encryption is also closely…
Our main result is a quantum public-key encryption scheme based on the Extrapolated Dihedral Coset problem (EDCP) which is equivalent, under quantum polynomial-time reductions, to the Learning With Errors (LWE) problem. For limited number of public keys (roughly linear in the security parameter), the proposed scheme is information-theoretically secure. For polynomial number of public keys, breaking the scheme is as hard as solving the LWE problem. The public keys in our scheme are quantum states of size $\tilde{O}(n)$ qubits. The key generation and decryption algorithms require $\tilde{O}(n)$ …
We perform quantum key distribution (QKD) in the presence of 4 classical channels in a C-band dense wavelength division multiplexing (DWDM) configuration using a commercial QKD system. The classical channels are used for key distillation and 1 Gbps encrypted communication, rendering the entire system independent from any other communication channel than a single dedicated fibre. We successfully distil secret keys over fibre spans of up to 50 km. The separation between quantum channel and nearest classical channel is only 200 GHz, while the classical channels are all separated by 100 GHz. In ad…
Quantum public-key encryption [Gottesman; Kawachi et al., Eurocrypt'05] generalizes public-key encryption (PKE) by allowing the public keys to be quantum states. Prior work indicated that quantum PKE can be constructed from assumptions that are potentially weaker than those needed to realize its classical counterpart. In this work, we show that quantum PKE can be constructed from any quantum-secure one-way function. In contrast, classical PKE is believed to require more structured assumptions. Our construction is simple, uses only classical ciphertexts, and satisfies the strong notion of CCA s…
This paper investigates a quantum version of McEliece public-key encryption (PKE) scheme, and analyzes its security. As is well known, the security of classical McEliece PKE is not stronger than the onewayness of related classical one-way function. We prove the security of quantum McEliece PKE ranks between them. Moreover, we propose the double-encryption technique to improve its security, and the security of the improved scheme is proved to be between the original scheme and the quantum one-time pad.
Fully homomorphic encryption enables arbitrary computation on encrypted data without decrypting the data. Here it is studied in the context of quantum information processing. Based on universal quantum circuit, we present a quantum fully homomorphic encryption (QFHE) scheme, which permits arbitrary quantum transformation on an encrypted data. The QFHE scheme is proved to be perfectly secure. In the scheme, the decryption key is different from the encryption key, however, the encryption key cannot be public. Moreover, the evaluate algorithm of the scheme is independent of the encryption key, so…
The lack of perfect randomness can cause significant problems in securing communication between two parties. McInnes and Pinkas proved that unconditionally secure encryption is impossible when the key is sampled from a weak random source. The adversary can always gain some information about the plaintext, regardless of the cryptosystem design. Most notably, the adversary can obtain full information about the plaintext if he has access to just two bits of information about the source (irrespective on length of the key). In this paper we show that for every weak random source there is a cryptosy…
We realize shamir's no-key protocol via quantum computation of Boolean permutation and private quantum channel. The quantum no-key (QNK) protocol presented here is one with mutual authentications, and proved to be unconditionally secure. An important property of this protocol is that0 its authentication key can be reused permanently.
We propose a bit-oriented quantum public-key scheme which uses Boolean function as private-key and randomly changed pairs of quantum state and classical string as public-keys. Contrast to the typical classical public-key scheme, one private-key in our scheme corresponds to an exponential number of public-keys. The goal of our scheme is to achieve information-theoretic security, and the security analysis is also given.
One of the simplest security proofs of quantum key distribution is based on the so-called complementarity scenario, which involves the complementarity control of an actual protocol and a virtual protocol [M. Koashi, e-print arXiv:0704.3661 (2007)]. The existing virtual protocol has a limitation in classical postprocessing, i.e., the syndrome for the error-correction step has to be encrypted. In this paper, we remove this limitation by constructing a quantum circuit for the virtual protocol. Moreover, our circuit with a shield system gives an intuitive proof of why adding noise to the sifted ke…
Quantum encryption is a well studied problem for both classical and quantum information. However, little is known about quantum encryption schemes which enable the user, under different keys, to learn different functions of the plaintext, given the ciphertext. In this paper, we give a novel one-bit secret-key quantum encryption scheme, a classical extension of which allows different key holders to learn different length subsequences of the plaintext from the ciphertext. We prove our quantum-classical scheme secure under the notions of quantum semantic security, quantum entropic indistinguishab…
We investigate the definition of security for encryption scheme in quantum context. We systematically define the indistinguishability and semantic security for quantum public-key and private-key encryption schemes, and for computational security, physical security and information-theoretic security. Based on our definition, we present a necessary and sufficient condition that leads to information-theoretic indistinguishability for quantum encryption scheme. The equivalence between the indistinguishability and semantic security of quantum encryption scheme is also proved.
Broadbent and Islam (TCC '20) proposed a quantum cryptographic primitive called quantum encryption with certified deletion. In this primitive, a receiver in possession of a quantum ciphertext can generate a classical certificate that the encrypted message is deleted. Although their construction is information-theoretically secure, it is limited to the setting of one-time symmetric key encryption (SKE), where a sender and receiver have to share a common key in advance and the key can be used only once. Moreover, the sender has to generate a quantum state and send it to the receiver over a quant…
Quantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the security of classical cryptographic schemes against quantum attacks. In this work, we initiate the study of another relevant topic: the encryption of quantum data in the computational setting. In this direction, we establish quantum versions of several fundamental classical results. First, we develop natural definitions for private-key and public-key encryption schemes for quantum data. We then define notio…
A quantum encryption scheme (also called private quantum channel, or state randomization protocol) is a one-time pad for quantum messages. If two parties share a classical random string, one of them can transmit a quantum state to the other so that an eavesdropper gets little or no information about the state being transmitted. Perfect encryption schemes leak no information at all about the message. Approximate encryption schemes leak a non-zero (though small) amount of information but require a shorter shared random key. Approximate schemes with short keys have been shown to have a number of …
We propose a homomorphic search protocol based on quantum homomorphic encryption, in which a client Alice with limited quantum ability can give her encrypted data to a powerful but untrusted quantum server and let the server search for her without decryption. By outsourcing the interactive key-update process to a trusted key center, Alice only needs to prepare and encrypt her original data and to decrypt the ciphered search result in linear time. Besides, we also present a compact and perfectly secure quantum homomorphic evaluation protocol for Cliford circuits, where the decryption key can be…
Inspired by Fujita's analysis [Quantum inf. & comput. 12(3&4), 2012], we suggest a twice-encryption scheme to improve the security of the original quantum McEliece public-key encryption algorithm.
This paper presents a multi-stage, multi-photon quantum key distribution protocol based on the double-lock cryptography. It exploits the asymmetry in the detection strategies between the legitimate users and the eavesdropper. The security analysis of the protocol is presented with coherent states under the intercept-resend attack, the photon number splitting attack, and the man-in-the-middle attack. It is found that the mean photon number can be much larger than one. This complements the recent interest in multi-photon quantum communication protocols that require a pre-shared key between the l…
In 2020, Kuang and Bettenburg proposed Quantum Public Key Distribution (QPKE) which utilized the randomized phase shift gate. Since then, it has been implemented both theoretically through simulations and experimentally over existing fiber optical networks. QPKE can be compared to an RSA-type scheme but in the optical analogue domain. Later on, it was renamed Quantum Encryption in Phase Space (QEPS) to emphasize the encryption of coherent states in phase space. However, the phase shift gate used in QEPS is limited to data modulation schemes with phase shift keying such as quadrature phase shif…
