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arXiv:0910.3131

Cryptographic encryption scheme for solving the trusted courier problem based on metastable excited nuclei

Thomas Durt, Α. Hermanne

Published Oct 16, 2009• 0 citations
arXivHTMLPDF

Abstract

Quantum cryptography makes it possible to expand a short shared key (of e.g. 256 bits[1]) into an arbitrary long shared key. The novelty of quantum cryptography is that whenever a spy tries to eavesdrop the communication he causes disturbances in the transmission of the message. Ultimately this unavoidable disturbance is a consequence of Heisenberg's uncertainty principle that limits the joint knowledge of complementary observables. Now, a problem remains: in order to initialize quantum key distribution, Alice and Bob need to share a short shared key in order to be able to identify each other unambiguously. Therefore a trusted courier is needed. We propose in this paper a solution to the trusted courrier problem that was inspired by quantum cryptography. The idea is to encode the key that Alice sends to Bob into unstable nuclei in such a way that the message gets revealed only after the courrier has delivered it to Bob. In this approach, we replace Heisenberg uncertainties by another type of uncertainty, that characterizes the knowledge of the time at which an unstable nucleus decays. As we shall show, this scheme makes it possible to refresh a key even in the case that we do not trust the courier who carries the key.

DOI
10.48550/arxiv.0910.3131

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Quantum cryptography makes it possible to expand a short shared key (of e.g. 256 bits[1]) into an arbitrary long shared key. The novelty of quantum cryptography is that whenever a spy tries to eavesdrop the communication he causes disturbances in the transmission of the message. Ultimately this unavoidable disturbance is a consequence of Heisenberg's uncertainty principle that limits the joint knowledge of complementary observables. Now, a problem remains: in order to initialize quantum key distribution, Alice and Bob need to share a short shared key in order to be able to identify each other unambiguously. Therefore a trusted courier is needed. We propose in this paper a solution to the trusted courrier problem that was inspired by quantum cryptography. The idea is to encode the key that Alice sends to Bob into unstable nuclei in such a way that the message gets revealed only after the courrier has delivered it to Bob. In this approach, we replace Heisenberg uncertainties by another type of uncertainty, that characterizes the knowledge of the time at which an unstable nucleus decays. As we shall show, this scheme makes it possible to refresh a key even in the case that we do not trust the courier who carries the key.
a cryptographic key, enabling Alice to scramble her messages in a way only Bob, knowing the same key, could unscramble. Privacy thus appeared to be generally unavailable to users lacking the means and foresight by which diplomats and spies share secret keys with their intended correspondents. Classical cryptography offered no purely mathematical solution to this "key distribution problem ". Meanwhile the only solution to the discreet communications problem appeared to be for Alice and Bob to confide their secrets in a trusted intermediary, who might later choose to blackmail them. All this was changed by PKC. The idea of PKC is for each user (eg Alice) to randomly choose a pair of mutually inverse transformations---a scrambling transformation and an unscrambling transformation---and to publish the directions for performing the former but not the latter. Anyone, including Bob, can then use Alice's public scrambling algorithm to prepare a message that only she can unscramble. Si
Present paper provides a conceptual framework on the proposed C-QUBITS Key exchange algorithm, which is used as a base for the data security through quantum computing. In the first phase a detailed description of the BB84 Cryptographic protocol is given, from which the first algorithm based on the quantum cryptography has been derived. In this the emphasis is on the loopholes present in this algorithm which makes it less effective. In the next phase the focus is made on the CQUBITS algorithm, which can be used for the exchange of key between the sender and the receiver. Thereafter, the key is used for the encryption of the data to be transferred between the two entities. This algorithm makes use of the concepts of quantum physics like polarization and more importantly C-NOT gate which is mainly used in case of qubits (quantum bits). Complete experimental set-up of the whole process involved in the algorithm has been presented and all possible cases have been discussed. Mathematical solution is derived which proves that data security through C-QUBITS algorithm is more effective and secure than other algorithms based on quantum approach. Quantum Cryptography was born in the early seventies when Stephen Wiesner wrote Conjugate Coding, which unfortunately took more than ten years to see the light of print 1 . In the mean time, Charles H Bennett (who knew of Wiesner's idea) and Gilles Brassard picked up the subject and brought it to fruition in a series of papers that culminated with the demonstration of an experimental prototype that established the technological feasibility of the concept 2 . Quantum cryptographic systems take advantage of Heisenberg's uncertainty principle, according to which measuring a quantum system in general disturbs it and yields incomplete information about its state before the measurement. Eavesdropping on a quantum communication channel therefore causes an unavoidable disturbance, alerting the legitimate users. This yields a cryptographic system for the distribution of a secret random cryptographic key between two parties initially sharing no secret information that is secure against an eavesdropper having at her disposal unlimited computing power. Once this secret key is established, it can be used together with classical cryptographic techniques such as the one-time-pad to allow the parties to communicate meaningful information in absolute secrecy.
Unclonable Encryption, introduced by Gottesman in 2003 [Quantum Inform. Comput. 3 (2003) 581], 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 client device is resource constrained and/or located in a hostile environment. Our protocol makes use of a bidirectional quantum channel in a manner similar to the two-way protocol LM05 [Phys. Rev. Lett. 94 (2005) 140501]. Bob sends random qubit states to Alice. Alice flips the states in a way that depends on the message and a shared key, and sends the resulting states back to Bob. Bob recovers Alice’s message by measuring the flips. We prove that our protocol satisfies the definition of unclonable encryption and additionally that the message remains secure even if all of Alice’s keys leak after the protocol. Furthermore, we show that some of the key materials can be safely re-used. Our security proof is formulated in terms of diamond norms, which makes it composable, and allows for noisy quantum channels. We work out the details only for the asymptotics in the limit of long messages. As a side result, we construct a two-way QKD scheme with a high key rate. We show that its key rate is higher than the rate of the two-way QKD scheme LM05 proven by Beaudry et al. [Phys. Rev. A 88 (2013) 062302] for the case of independent channel noise.
Secure communication that allows only the sender and intended recipient of a message to view its content has a long history. Quantum objects, such as single photons are ideal carriers for secure information transmission because, according to the no-cloning theorem [1], it is impossible to create an identical and independent copy of an arbitrary quantum state while its detection leads to the information distortion. BB84 [2,3] is the first quantum cryptography protocol for a quantum key generation and distribution, based on single photon sources. This quantum key is used for coding and decoding of classical information. We propose completely different protocol based on a stochastic decay of an ensemble of radioactive nuclei randomly emitting a stream of gamma-photons. We experimentally demonstrate a method how to transmit classical information containing binary bits (0 or 1) with the help of this stream. Transmission is organized such that eavesdropping is impossible since the presence of information in the stream of randomly emitted gamma-photons can be hidden. Reading of this information needs precise knowledge of the repetition rate of its sending in advance. It is unrealistic for the eavesdropper to disclose this rate, and without knowledge of this parameter it is impossible to make the transmitted information visible.
The secure distribution of the secret random bit sequences known as `key' material, is an essential precursor to their use for the encryption and decryption of confidential communications. Quantum cryptography is an emerging technology for secure key distribution with single-photon transmissions: Heisenburg's uncertainty principle ensures that an adversary can neither successfully tap the key transmissions, nor evade detection (eavesdropping raises the key error rate above a threshold value). We have developed experimental quantum cryptography systems based on the transmission of non-orthogonal single-photon states to generate shared key material over multi-kilometer optical fiber paths and over line-of-sight links. In both cases, key material is built up using the transmission of a single- photon per bit of an initial secret random sequence. A quantum-mechanically random subset of this sequence is identified, becoming the key material after a data reconciliation stage with the sender. In our optical fiber experiment we have performed quantum key distribution over 24-km of underground optical fiber using single-photon interference states, demonstrating that secure, real-time key generation over `open' multi-km node-to-node optical fiber communications links is possible.
Alice has made a decision in her mind. While she does not want to reveal it to Bob at this moment, she would like to convince Bob that she is committed to this particular decision and that she cannot change it at a later time. Is there a way for Alice to get Bob's trust? Until recently, researchers had believed that the above task can be performed with the help of quantum mechanics. And the security of the quantum scheme lies on the uncertainty principle. Nevertheless, such optimism was recently shattered by Mayers and by us, who found that Alice can always change her mind if she has a quantum computer. Here, we survey this dramatic development and its implications on the security of other quantum cryptographic schemes.