Blockchain Papers

Farid Ablayev, D. A. Bulychkov, D. A. Sapaev, Alexander Vasiliev · 5 authors

Bitcoin and blockchain in general is a hot topic nowadays. In the paper we propose a quantum empowering of this technology and show how to speed-up the mining procedure using the modified Grover's algorithm.

Kazuki Ikeda

No abstract is available for this record.

Kazuki Ikeda

A decentralized online quantum cash system, called qBitcoin, is given. We design the system which has great benefits of quantization in the following sense. Firstly, quantum teleportation technology is used for coin transaction, which prevents from the owner of the coin keeping the original coin data even after sending the coin to another. This was a main problem in a classical circuit and a blockchain was introduced to solve this issue. In qBitcoin, the double-spending problem never happens and its security is guaranteed theoretically by virtue of quantum information theory. Making a block is time consuming and the system of qBitcoin is based on a quantum chain, instead of blocks. Therefore a payment can be completed much faster than Bitcoin. Moreover we employ quantum digital signature so that it naturally inherits properties of peer-to-peer (P2P) cash system as originally proposed in Bitcoin.

E O Kiktenko, N O Pozhar, M N Anufriev, A S Trushechkin · 8 authors

Abstract Blockchain is a distributed database which is cryptographically protected against malicious modifications. While promising for a wide range of applications, current blockchain platforms rely on digital signatures, which are vulnerable to attacks by means of quantum computers. The same, albeit to a lesser extent, applies to cryptographic hash functions that are used in preparing new blocks, so parties with access to quantum computation would have unfair advantage in procuring mining rewards. Here we propose a possible solution to the quantum era blockchain challenge and report an experimental realization of a quantum-safe blockchain platform that utilizes quantum key distribution across an urban fiber network for information-theoretically secure authentication. These results address important questions about realizability and scalability of quantum-safe blockchains for commercial and governmental applications.

Jonathan Jogenfors

The digital currency Bitcoin has had remarkable growth since it was first proposed in 2008. Its distributed nature allows currency transactions without a central authority by using cryptographic methods and a data structure called the blockchain. In this paper we use the no-cloning theorem of quantum mechanics to introduce Quantum Bitcoin, a Bitcoin-like currency that runs on a quantum computer. We show that our construction of quantum shards and two blockchains allows untrusted peers to mint quantum money without risking the integrity of the currency. The Quantum Bitcoin protocol has several advantages over classical Bitcoin, including immediate local verification of transactions. This is a major improvement since we no longer need the computationally intensive and time-consuming method Bitcoin uses to record all transactions in the blockchain. Instead, Quantum Bitcoin only records newly minted currency which drastically reduces the footprint and increases efficiency. We present formal security proofs for counterfeiting resistance and show that a quantum bitcoin can be re-used a large number of times before wearing out - just like ordinary coins and banknotes. Quantum Bitcoin is the first distributed quantum money system and we show that the lack of a paper trail implies full anonymity for the users. In addition, there are no transaction fees and the system can scale to any transaction volume.

John H. Smith

Kant, Calculus, Consciousness, and the Mathematical Infinite in Us John H. Smith Der Begriff des Unendlichkleinen, darauf die Mathematik so öfters hinauskommt, wird mit einer angemaßten Dreistigkeit so geradezu als erdichtet verworfen, anstatt daß man eher vermuten sollte, daß man noch nicht genug davon verstände, um ein Urteil darüber zu fällen. Die Natur selbst scheint gleichwohl nicht undeutliche Beweistümer an die Hand zu geben, daß dieser Begriff sehr wahr sei. Denn wenn es Kräfte gibt, welche eine Zeit hindurch kontinuierlich wirken, um Bewegungen hervorzubringen, wie allem Ansehen nach die Schwere ist, so muß die Kraft, die sie im Anfangsaugenblicke oder in Ruhe ausübt, gegen die, welche sie in einer Zeit mitteilt, unendlich klein sein. Es ist schwer, ich gestehe es, in die Natur dieser Begriffe hineinzudringen; aber diese Schwierigkeit kann allenfalls nur die Behutsamkeit unsicherer Vermutungen, aber nicht entscheidende Aussprüche der Unmöglichkeit rechtfertigen.1 [The concept of the infinitely small, which comes up so often in mathematics, is rejected straight out with presumptuous audacity as a fiction, instead of assuming that it is not well enough understood to form a judgment about it. Nature itself seems, however, to provide clear proofs that there is truth to this concept. For if there are forces that work continuously through time in order to produce movements, as it would appear is the case with gravity, then the force that effects this movement in an initial instant (or rest) must be infinitely small as opposed to the one that imparts movement in time. It is difficult, I confess, to penetrate into the nature of these concepts; but this difficulty can at most justify cautiously avoiding unfounded suppositions and not claiming decisively that it is impossible.] The question that I address in this essay is simple: what is the mathematical infinite doing at crucial moments in Kant’s philosophy? By doing I mean the way that specific notions of the infinitely small—the infinitesimal, the differential, infinite approximation, continuity—serve as metaphors in a strong Aristotelian sense; that is, they attempt to “bring before the eyes” something abstract and thereby contribute a kind of intuition to the unintuitable.2 And yet, there is something doubly ironic going on in this effort. On the one hand, although mathematics and the mathematization of nature have been criticized by Husserl for abstracting modern thought from the concrete life-world of experience, I will look to places where there is a turn to the mathematical infinite in order to be concrete.3 On the other hand, the clear [End Page 95] intuitions associated with the mathematical infinite can easily get caught up in contradictions that undermine the initial clarity.4 By exploring these moments of metaphoric and paradoxical representation, we can see how major thinkers grappled with a notion of the “immanence of the infinite” that characterizes the epochal turn of modernity.5 First, let me give a general sense of what is at stake in the notion of the mathematical infinite and the issues of representation associated with infinitesimal calculus, which was up through the nineteenth century arguably the most powerful tool for understanding the physical world. Although Kant rarely addresses calculus as such, this tool has particular relevance for him given the fundamental role that both its inventors, Leibniz and Newton, play in the development of his critical project. Consider the problem of a line tangent to a curve—that is, a straight line that touches any curved line at precisely one point. As I hope and expect has just occurred in the mind of any reader at this point, a somewhat-clear image has taken shape. This image can be rendered mathematically precise thanks to the technique of calculus; indeed, calculus was developed in large part to address this problem. The reason is that such a tangent can be considered the rate of change of the curve at any instant, which can be calculated given the curve’s function. Thus, say, a soaring baseball defines a parabolic arc at a changing rate of speed (fast at first, slowing at the peak, then ever faster as it returns to the ground). The tangents at any point indicate...

Juan-Hong Tian, Jian-Zhong Zhang, Yan-Ping Li

No abstract is available for this record.

Naya Nagy, Marius Nagy

No abstract is available for this record.

Yang Liu, Yuan Cao, Marcos Curty, Sheng‐Kai Liao · 16 authors

Bit commitment is a fundamental cryptographic task that guarantees a secure commitment between two mutually mistrustful parties and is a building block for many cryptographic primitives, including coin tossing, zero-knowledge proofs, oblivious transfer and secure two-party computation. Unconditionally secure bit commitment was thought to be impossible until recent theoretical protocols that combine quantum mechanics and relativity were shown to elude previous impossibility proofs. Here we implement such a bit commitment protocol. In the experiment, the committer performs quantum measurements using two quantum key distribution systems and the results are transmitted via free-space optical communication to two agents separated with more than 20 km. The security of the protocol relies on the properties of quantum information and relativity theory. We show that, in each run of the experiment, a bit is successfully committed with less than 5.68*10^-2 cheating probability. Our result demonstrates unconditionally secure bit commitment and the experimental feasibility of relativistic quantum communication.

Patrick Hayden, Kevin R. Milner, Mark M. Wilde

Suppose that a polynomial-time mixed-state quantum circuit, described as a sequence of local unitary interactions followed by a partial trace, generates a quantum state shared between two parties. One might then wonder, does this quantum circuit produce a state that is separable or entangled? Here, we give evidence that it is computationally hard to decide the answer to this question, even if one has access to the power of quantum computation. We begin by exhibiting a two-message quantum interactive proof system that can decide the answer to a promise version of the question. We then prove that the promise problem is hard for the class of promise problems with 'quantum statistical zero knowledge' (QSZK) proof systems by demonstrating a polynomial-time Karp reduction from the QSZK-complete promise problem 'quantum state distinguish ability' to our quantum separability problem. By exploiting Knill's efficient encoding of a matrix description of a state into a description of a circuit to generate the state, we can show that our promise problem is NP-hard with respect to Cook reductions. Thus, the quantum separability problem (as phrased above) constitutes the first nontrivial promise problem decidable by a two-message quantum interactive proof system while being hard for both NP and QSZK. We also consider a variant of the problem, in which a given polynomial-time mixed-state quantum circuit accepts a quantum state as input, and the question is to decide if there is an input to this circuit which makes its output separable across some bipartite cut. We prove that this problem is a complete promise problem for the class QIP of problems decidable by quantum interactive proof systems. Finally, we show that a two-message quantum interactive proof system can also decide a multipartite generalization of the quantum separability problem. © 2013 IEEE.

Wang Yu-wu, Wei Xiang-he, Zhu Zhao-Hui

In the paper, we present a kind of quantum voting protocol, which is based on controlled quantum teleportation of local unitary operations in non-symmetric quantum channel. In this protocol, the umpire CA with zero knowledge proof quantum identity authentication ensures voter’s anonymous identity authentication. The counting institution Bob generates a high-dimensional Greenberger-Horne-Zeilinger entangled state to establish a high-dimensional quantum communication channel. Performing the local unitary operation on their low-dimensional quantum ballot, voter’s quantum vote is teleportated by asymmetric matrix measurement and scrutineer Charlie auxiliary measuring. With the scrutineer Charlie’s help, Bob achieves the voting result by the output of unitary operation. Compared with other general quantum operation teleportation quantum voting protocol, the protocol utilizes the quantum information and transmission of quantum channel, which have different dimensions, so single particle information cannot be stolen, and can prevent forgery. The electoral process is fair and undeniable, owing to Charlie’s supervision. Since the success probability of quantum teleportation of local unitary operations is 1, the quantum voting is reliable.

José Cláudio do Nascimento, Rubens Viana Ramos

No abstract is available for this record.

Wang Yu-wu, You-Bang Zhan, (1)淮阴师范学院计算机科学系,淮安 223300; (2)淮阴师范学院物理系,淮安 223300

A theoretical scheme for zero-knowledge proof quantum identity authentication is proposed by the absolutely impartial third party CA， which has been realized based on remote state preparation and assisted cloning controlled means. In the process of identification， only CA knows the information of quantum identity card and the first party Alice and the second party Bob can accomplish the quantum identity authentication without knowing it. We discuss the probability of accomplishing this job. The security of this scheme is unconditional and it is guaranteed by quantum mechanism.

José Cláudio do Nascimento, Rubens Viana Ramos

Zero-knowledge proof system is an important protocol that can be used as a basic block for construction of other more complex cryptographic protocols. An intrinsic characteristic of a zero-knowledge systems is the assumption that is impossible for the verifier to show to a third part that he has interacted with the prover. However, it has been shown that using quantum correlations the impossibility of transferring proofs can be successfully attacked. In this work we show two new protocols for proof transference, being the first one based on teleportation and the second one without using entangled states.

David Avis, Hiroshi Imai, Tsuyoshi Ito

The cut polytope of a graph arises in many fields. Although much is known about facets of the cut polytope of the complete graph, very little is known for general graphs. The study of Bell inequalities in quantum information science requires knowledge of the facets of the cut polytope of the complete bipartite graph or, more generally, the complete k-partite graph. Lifting is a central tool to prove certain inequalities are facet inducing for the cut polytope. In this paper we introduce a lifting operation, named triangular elimination, applicable to the cut polytope of a wide range of graphs. Triangular elimination is a specific combination of zero-lifting and Fourier-Motzkin elimination using the triangle inequality. We prove sufficient conditions for the triangular elimination of facet inducing inequalities to be facet inducing. The proof is based on a variation of the lifting lemma adapted to general graphs. The result can be used to derive facet inducing inequalities of the cut polytope of various graphs from those of the complete graph. We also investigate the symmetry of facet inducing inequalities of the cut polytope of the complete bipartite graph derived by triangular elimination.

John Watrous

In this paper we propose a definition for (honest verifier) quantum statistical zero-knowledge interactive proof systems and study the resulting complexity class, which we denote QSZK. We prove several facts regarding this class that establish close connections between classical statistical zero-knowledge and our definition for quantum statistical zero-knowledge, and give some insight regarding the effect of this zero-knowledge restriction on quantum interactive proof systems.

Diederik Aerts, Frank Valckenborgh

We consider the situation of a physical entity that is the compound entity consisting of two ‘separated ’ quantum entities. In earlier work it has been proved by one of the authors that such a physical entity cannot be described by standard quantum mechanics. More precisely, it was shown that two of the axioms of traditional quantum axiomatics are at the origin of the impossibility for standard quantum mechanics to describe this type of compound entity. One of these axioms is equivalent with the superposition principle, which means that separated quantum entities put the linearity of quantum mechanics at stake. We analyze the conceptual steps that are involved in this proof, and expose the necessary material of quantum axiomatics to be able to understand the argument. 1

Hoi‐Kwong Lo, H. F. Chau

There had been well known claims of unconditionally secure quantum protocols for bit commitment. However, we, and independently Mayers, showed that all proposed quantum bit commitment schemes are, in principle, insecure because the sender, Alice, can almost always cheat successfully by using an Einstein-Podolsky-Rosen (EPR) type of attack and delaying her measurements. One might wonder if secure quantum bit commitment protocols exist at all. We answer this question by showing that the same type of attack by Alice will, in principle, break any bit commitment scheme. The cheating strategy generally requires a quantum computer. We emphasize the generality of this ``no-go theorem'': Unconditionally secure bit commitment schemes based on quantum mechanics---fully quantum, classical or quantum but with measurements---are all ruled out by this result. Since bit commitment is a useful primitive for building up more sophisticated protocols such as zero-knowledge proofs, our results cast very serious doubt on the security of quantum cryptography in the so-called ``post-cold-war'' applications. We also show that ideal quantum coin tossing is impossible because of the EPR attack. This no-go theorem for ideal quantum coin tossing may help to shed some lights on the possibility of non-ideal protocols.