Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

/pdf/the-knowledge-complexity-of-interactive-proof-systems-31apre0ecf.pdf

The knowledge complexity of interactive proof-systems

Communications of the ACM (CACM for short, not the best sounding acronym around) is the ACM’s flagship magazine. Started in 1957, CACM is handy for keeping up to date on current research being carried out across all topics of computer science and realworld applications. CACM has had an illustrious past with many influential pieces of work and debates started within its pages. These include Hoare’s presentation of the Quicksort algorithm; Rivest, Shamir and Adleman’s description of the first publickey cryptosystem RSA; and Dijkstra’s famous letter against the use of GOTO. In addition to the print edition, which is released monthly, there is a fantastic website (http://cacm.acm. org/) that showcases not only the most recent edition but all previous CACM articles as well, readable online as well as downloadable as a PDF. In addition, the website lets you browse for articles by subject, a handy feature if you want to focus on a particular topic. CACM is really essential reading. Pretty much guaranteed to contain content that is interesting to anyone, it keeps tabs on the latest in computer science. It is a valuable asset for us students, who tend to delve deep into a particular area of CS and forget everything that is happening around us. — Daniel Gooch U ndergraduate research is like a box of chocolates: You never know what kind of project you will get. That being said, there are still a few things you should know to get the most out of the experience.

Communications of the ACM

In this paper we discuss quantum computational restrictions on the types of thought experiments recently used by Almheiri, Marolf, Polchinski, and Sully to argue against the smoothness of black hole horizons. We argue that the quantum computations required to do these experiments would take a time which is exponential in the entropy of the black hole under study, and we show that for a wide variety of black holes this prevents the experiments from being done. We interpret our results as motivating a broader type of nonlocality than is usually considered in the context of black hole thought experiments, and claim that once this type of nonlocality is allowed there may be no need for firewalls. Our results do not threaten the unitarity of black hole evaporation or the ability of advanced civilizations to test it.

Quantum Computation vs. Firewalls

This paper investigates the powers and limitations of quantum entanglement in the context of cooperative games of incomplete information. We give several examples of such nonlocal games where strategies that make use of entanglement outperform all possible classical strategies. One implication of these examples is that entanglement can profoundly affect the soundness property of two-prover interactive proof systems. We then establish limits on the probability with which strategies making use of entanglement can win restricted types of nonlocal games. These upper bounds may be regarded as generalizations of Tsirelson-type inequalities, which place bounds on the extent to which quantum information can allow for the violation of Bell inequalities. We also investigate the amount of entanglement required by optimal and nearly optimal quantum strategies for some games.

https://arxiv.org/pdf/quant-ph/0404076.pdf

Consequences and Limits of Nonlocal Strategies

The area of property testing tries to design algorithms that can efficiently
handle very large amounts of data: given a large object that either has a
certain property or is somehow "far" from having that property, a tester should
efficiently distinguish between these two cases. In this survey we describe
recent results obtained for quantum property testing. This area naturally falls
into three parts. First, we may consider quantum testers for properties of
classical objects. We survey the main examples known where quantum testers can
be much (sometimes exponentially) more efficient than classical testers.
Second, we may consider classical testers of quantum objects. This is the
situation that arises for instance when one is trying to determine if quantum
states or operations do what they are supposed to do, based only on classical
input-output behavior. Finally, we may also consider quantum testers for
properties of quantum objects, such as states or operations. We survey known
bounds on testing various natural properties, such as whether two states are
equal, whether a state is separable, whether two operations commute, etc. We
also highlight connections to other areas of quantum information theory and
mention a number of open questions.

/pdf/a-survey-of-quantum-property-testing-140jv260hs.pdf

A Survey of Quantum Property Testing

In the past few years secure messaging has become mainstream, with over a billion active users of end-to-end encryption protocols such as Signal. The Signal Protocol provides a strong property called post-compromise security to its users. However, it turns out that many of its implementations provide, without notification, a weaker property for group messaging: an adversary who compromises a single group member can read and inject messages indefinitely. We show for the first time that post-compromise security can be achieved in realistic, asynchronous group messaging systems. We present a design called Asynchronous Ratcheting Trees (ART), which uses tree-based Diffie-Hellman key exchange to allow a group of users to derive a shared symmetric key even if no two are ever online at the same time. ART scales to groups containing thousands of members, while still providing provable security guarantees. It has seen significant interest from industry, and forms the basis for two draft IETF RFCs and a chartered working group. Our results show that strong security guarantees for group messaging are practically achievable in a modern setting.

https://dl.acm.org/doi/pdf/10.1145/3243734.3243747

On Ends-to-Ends Encryption: Asynchronous Group Messaging with Strong Security Guarantees

Most of the world’s power grids are controlled remotely. Their control messages are sent over potentially insecure channels, driving the need for an authentication mechanism. The main communication mechanism for power grids and other utilities is defined by an IEEE standard, referred to as DNP3; this includes the Secure Authentication v5 (SAv5) protocol, which aims to ensure that messages are authenticated. We provide the first security analysis of the complete DNP3: SAv5 protocol. Previous work has considered the message-passing sub-protocol of SAv5 in isolation, and considered some aspects of the intended security properties. In contrast, we formally model and analyse the complex composition of the protocol’s three sub-protocols. In doing so, we consider the full state machine, and the possibility of cross-protocol attacks. Furthermore, we model fine-grained security properties that closely match the standard’s intended security properties. For our analysis, we leverage the Tamarin prover for the symbolic analysis of security protocols.

/pdf/secure-authentication-in-the-grid-a-formal-analysis-of-dnp3-26xoo8wadf.pdf

Secure Authentication in the Grid:A Formal Analysis of DNP3: SAv5

We identify a formal connection between physical problems related to the detection of separable (unentangled) quantum states and complexity classes in theoretical computer science. In particular, we show that to nearly every quantum interactive proof complexity class (including BQP, QMA, QMA(2), and QSZK), there corresponds a natural separability testing problem that is complete for that class. Of particular interest is the fact that the problem of determining whether an isometry can be made to produce a separable state is either QMA-complete or QMA(2)-complete, depending upon whether the distance between quantum states is measured by the one-way LOCC norm or the trace norm. We obtain strong hardness results by proving that for each n-qubit maximally entangled state there exists a fixed one-way LOCC measurement that distinguishes it from any separable state with error probability that decays exponentially in n.

/pdf/quantum-interactive-proofs-and-the-complexity-of-34suckq8ku.pdf

Quantum interactive proofs and the complexity of separability testing

/pdf/secure-authentication-in-the-grid-a-formal-analysis-of-dnp3-abv3lpyj0p.pdf

Secure authentication in the grid: A formal analysis of DNP3 SAv5

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 distinguishability" 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.

Kevin Milner

Papers

On Ends-to-Ends Encryption: Asynchronous Group Messaging with Strong Security Guarantees

Secure Authentication in the Grid:A Formal Analysis of DNP3: SAv5

Quantum interactive proofs and the complexity of separability testing

Secure authentication in the grid: A formal analysis of DNP3 SAv5

Two-message quantum interactive proofs and the quantum separability problem