Using quantum oblivious transfer to cheat sensitive quantum bit commitment

It is well known that unconditionally secure bit commitment is impossible even in the quantum world. In this paper a weak variant of quantum bit commitment, introduced independently by Aharonov et al. [STOC, 2000] and Hardy and Kent [Phys. Rev. Lett. 92 (2004)] is investigated. In this variant, the parties require some nonzero probability of detecting a cheating, i.e. if Bob, who commits a bit b to Alice, changes his mind during the revealing phase then Alice detects the cheating with a positive probability (we call this property binding); and if Alice gains information about the committed bit before the revealing phase then Bob discovers this with positive probability (sealing). In our paper we give quantum bit commitment scheme that is simultaneously binding and sealing and we show that if a cheating gives epsilon advantage to a malicious Alice then Bob can detect the cheating with a probability Omega(epsilon^2). If Bob cheats then Alice's probability of detecting the cheating is greater than some fixed constant lambda>0. This improves the probabilities of cheating detections shown by Hardy and Kent and the scheme by Aharonov et al. who presented a protocol that is either binding or sealing, but not simultaneously both. To construct a cheat sensitive quantum bit commitment scheme we use a protocol for a weak quantum one-out-of-two oblivious transfer

Quantum Cryptography Beyond Quantum Key Distribution

Quantum cryptography is the art and science of exploiting quantum mechanical effects in order to perform cryptographic tasks. While the most well-known example of this discipline is quantum key distribution (QKD), there exist many other applications such as quantum money, randomness generation, secure two- and multi-party computation and delegated quantum computation. Quantum cryptography also studies the limitations and challenges resulting from quantum adversaries---including the impossibility of quantum bit commitment, the difficulty of quantum rewinding and the definition of quantum security models for classical primitives. In this review article, aimed primarily at cryptographers unfamiliar with the quantum world, we survey the area of theoretical quantum cryptography, with an emphasis on the constructions and limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference

Possibility, Impossibility and Cheat-Sensitivity of Quantum Bit String Commitment

Unconditionally secure non-relativistic bit commitment is known to be impossible in both the classical and the quantum worlds. But when committing to a string of n bits at once, how far can we stretch the quantum limits? In this paper, we introduce a framework for quantum schemes where Alice commits a string of n bits to Bob in such a way that she can only cheat on a bits and Bob can learn at most b bits of information before the reveal phase. Our results are two-fold: we show by an explicit construction that in the traditional approach, where the reveal and guess probabilities form the security criteria, no good schemes can exist: a+b is at least n. If, however, we use a more liberal criterion of security, the accessible information, we construct schemes where a=4log n+O(1) and b=4, which is impossible classically. We furthermore present a cheat-sensitive quantum bit string commitment protocol for which we give an explicit tradeoff between Bob's ability to gain information about the committed string, and the probability of him being detected cheating.Comment: 10 pages, RevTex, 2 figure. v2: title change, cheat-sensitivity adde

Cryptographic Randomized Response Techniques

We develop cryptographically secure techniques to guarantee unconditional privacy for respondents to polls. Our constructions are efficient and practical, and are shown not to allow cheating respondents to affect the ``tally'' by more than their own vote -- which will be given the exact same weight as that of other respondents. We demonstrate solutions to this problem based on both traditional cryptographic techniques and quantum cryptography.Comment: 21 page

Secure bit commitment from relativistic constraints

We investigate two-party cryptographic protocols that are secure under assumptions motivated by physics, namely relativistic assumptions (no-signalling) and quantum mechanics. In particular, we discuss the security of bit commitment in so-called split models, i.e. models in which at least some of the parties are not allowed to communicate during certain phases of the protocol. We find the minimal splits that are necessary to evade the Mayers-Lo-Chau no-go argument and present protocols that achieve security in these split models. Furthermore, we introduce the notion of local versus global command, a subtle issue that arises when the split committer is required to delegate non-communicating agents to open the commitment. We argue that classical protocols are insecure under global command in the split model we consider. On the other hand, we provide a rigorous security proof in the global command model for Kent's quantum protocol [Kent 2011, Unconditionally Secure Bit Commitment by Transmitting Measurement Outcomes]. The proof employs two fundamental principles of modern physics, the no-signalling property of relativity and the uncertainty principle of quantum mechanics.Comment: published version, IEEE format, 18 pages, 8 figure

Can relativistic bit commitment lead to secure quantum oblivious transfer?

While unconditionally secure bit commitment (BC) is considered impossible within the quantum framework, it can be obtained under relativistic or experimental constraints. Here we study whether such BC can lead to secure quantum oblivious transfer (QOT). The answer is not completely negative. On one hand, we provide a detailed cheating strategy, showing that the "honest-but-curious adversaries" in some of the existing no-go proofs on QOT still apply even if secure BC is used, enabling the receiver to increase the average reliability of the decoded value of the transferred bit. On the other hand, it is also found that some other no-go proofs claiming that a dishonest receiver can always decode all transferred bits simultaneously with reliability 100% become invalid in this scenario, because their models of cryptographic protocols are too ideal to cover such a BC-based QOT.Comment: Published version. This paper generalized some results in Sec. V of arXiv:1101.4587, and pointed out the limitation of the proof in arXiv:quant-ph/961103

Quantum cryptography: key distribution and beyond

Uniquely among the sciences, quantum cryptography has driven both foundational research as well as practical real-life applications. We review the progress of quantum cryptography in the last decade, covering quantum key distribution and other applications.Comment: It's a review on quantum cryptography and it is not restricted to QK