Can you sign a quantum state?

Cryptography with quantum states exhibits a number of surprising and counterintuitive features. In a 2002 work, Barnum et al. argue that these features imply that digital signatures for quantum states are impossible (Barnum et al., FOCS 2002). In this work, we ask: can all forms of signing quantum data, even in a possibly weak sense, be completely ruled out? We give two results which shed significant light on this basic question.First, we prove an impossibility result for digital signatures for quantum data, which extends the result of Barnum et al. Specifically, we show that no nontrivial combination of correctness and security requirements can be fulfilled, beyond what is achievable simply by measuring the quantum message and then signing the outcome. In other words, only classical signature schemes exist.We then show a positive result: a quantum state can be signed with the same security guarantees as classically, provided that it is also encrypted with the public key of the intended recipient. Following classical nomenclature, we call this notion quantum signcryption. Classically, signcryption is only interesting if it provides superior performance to encypt-then-sign. Quantumly, it is far more interesting: it is the only signing method available. We develop "as-strong-as-classical" security definitions for quantum signcryption and give secure constructions based on post-quantum public-key primitives. Along the way, we show that a natural hybrid method of combining classical and quantum schemes can be used to "upgrade" a secure classical scheme to the fully-quantum setting, in a wide range of cryptographic settings including signcryption, authenticated encryption, and CCA security.

Representation and aggregation of crisp and fuzzy ordered structures: applications to social choice

The present memory is structured as follows: after the Introduction, in the Chapter 2 of preliminaries, we will pay attention to the three areas which sustain the development of this thesis. These are, binary relations, Social Choice and Fuzzy sets. Chapter 3 is devoted to the study of fuzzy Arrovian models. First, it is introduced the concept of a fuzzy preference. Next, we define fuzzy aggregation rules and all of the restrictions of common sense, which are inspired by the restrictions that come from the classic Arrovian model. Next, different models are defined in the fuzzy setting. Their definitions depend on the particular nuances and features of a preference (choosing a transitivity type and a connectedness type) and the restrictions on an aggregation function (choosing an independence of irrelevant alternatives property,an unanimity property, etc). Different possibility and impossibility theorems have been proved depending on the set of definition and restrictions. In Chapter 4 it is studied the problem of the decomposition of fuzzy binary relations. There, it is defined clearly the problem of setting suitable decomposition rules. That is, we analyze how to obtain a strict preference and an indifference from the weak preference in a fuzzy approach. In this chapter, the existence and the uniqueness of certain kind of decomposition rules associated to fuzzy unions are characterized. In Chapter 5, the decomposition rules studied in Chapter 4 are used to achieve a new impossibility result. It is important to point out that in the proof of the main result in this chapter it is introduced a new technique. In this proof, fuzzy preferences are framed through an auxiliary tuple of five crisp binary relations, that we name a pseudofuzzy preference. An aggregation model à la Arrow of pseudofuzzy preferences is also studied,but the main result is about the aggregation of fuzzy preferences that come from decompositions.Chapters 3, 4 and 5 constitute the main body of this memory. Then a section of conclusions is included. It contains suggestions for further studies, open problems and several final comments. Finally, an Appendix has been added in order to give an account of the work done within these three years, that can not be included in the body of the present memory.

An impossibility result on methodological individualism

Methodological individualists often claim that any social phenomenon can ultimately be explained in terms of the actions and interactions of individuals. Any Nagelian version of methodological individualism requires that there be bridge laws that translate social statements into individualistic ones. We show that Nagelian individualism can be put to logical scrutiny by making the relevant social and individualistic languages fully explicit and mathematically precise. In particular, we prove that the social statement that a group of (at least two) agents performs a deontically admissible group action cannot be expressed in a well-established deontic logic of agency that models every combination of actions, omissions, abilities, and obligations of finitely many individual agents.

Fair Allocation of Indivisible Goods: Improvement

We study the problem of fair allocation for indivisible goods. We use the maximin share paradigm introduced by Budish [Budish E (2011) The combinatorial assignment problem: Approximate competitive equilibrium from equal incomes. J. Political Econom. 119(6):1061–1103.] as a measure of fairness. Kurokawa et al. [Kurokawa D, Procaccia AD, Wang J (2018) Fair enough: Guaranteeing approximate maximin shares. J. ACM 65(2):8.] were the first to investigate this fundamental problem in the additive setting. They showed that in delicately constructed examples, not everyone can obtain a utility of at least her maximin value. They mitigated this impossibility result with a beautiful observation: no matter how the utility functions are made, we always can allocate the items to the agents to guarantee each agent’s utility is at least 2/3 of her maximin value. They left open whether this bound can be improved. Our main contribution answers this question in the affirmative. We improve their approximation result to a 3/4 factor guarantee.

The halting problem and security’s language-theoretic approach: Praise and criticism from a technical historian

The term ‘Halting Problem’ arguably refers to computer science’s most celebrated impossibility result and to the core notion underlying the language-theoretic approach to security. Computer professionals often ignore the Halting Problem however. In retrospect, this is not too surprising given that several advocates of computability theory implicitly follow Christopher Strachey’s alleged 1965 proof of his Halting Problem (which is about executable – i.e., hackable – programs) rather than Martin Davis’s correct 1958 version or his 1994 account (each of which is solely about mathematical objects). For the sake of conceptual clarity, particularly for researchers pursuing a coherent science of cybersecurity, I will scrutinize Strachey’s 1965 line of reasoning – which is widespread today – both from a charitable, historical angle and from a critical, engineering perspective.

Strategic Issues in One-to-One Matching with Externalities

We consider strategic issues in one-to-one matching with externalities. We show that no core (stable) mechanism is strategy-proof, extending an impossibility result of [Roth, A. E. [1982] The economics of matching: Stability and incentives, Math. Oper. Res. 7(4), 617–628] obtained in the absence of externalities. Moreover, we show that there are no limits on successful manipulation of preferences by coalitions of men and women, in contrast with the result of [Demange, G., Gale, D. and Sotomayor, M. [1987] A further note on the stable matching problem, Discrete Appl. Math. 16(3), 217–222] obtained in the absence of externalities.

Incentives, Optimization, and Democratic Planning: A Socialist Primer

Socialism has traditionally been identified with central, top-down planning, which is seen as impossible and irrational. The only alternative is “the market,” identified with capitalism. The 20th-century socialist experience, by contrast, put forward a multilevel (central–local) model, in which enterprises form their own detailed plans, under incentives to plan both ambitiously and realistically. The incentive design literature in Western economics has suggested an “impossibility” result: there is no way to incentivize local agents to tell the truth about their actual possibilities and therefore to contribute to efficient central plans. However, under modern conditions, a Collective Morale Function operates: planning requires activist mobilization of, and critical understanding among, workers. If an enterprise is to organize production successfully, it must attain high levels of morale, which in turn requires truth-telling and ambitious planning. This constitutes a path toward mature socialism, breaking the one-dimensional binary: either authoritarian planning, or the “market.”

Distributed Systems

Chapter 5 considers distributed systems by their properties. The first section studies the classification of software systems, which is usually distinguished in centralized, decentralized and distributed systems. It studies the differences between these three major approaches, showing there is a rather multidimensional classification instead of a linear one. The most important case are distributed systems that enable spreading of computational tasks across several autonomous, independently acting computational entities. A very important result of this case is the CAP theorem that considers the trade-off between consistency, availability and partition tolerance. The last section deals with the possibility to reach consensus in distributed systems, discussing how fault tolerant consensus mechanisms enable mutual agreement among the individual entities in presence of failures. One very special case are so-called Byzantine failures that are discussed in great detail. The main result is the so-called FLP Impossibility Result which states that there is no deterministic algorithm that guarantees solution to the consensus problem in the asynchronous case. The chapter concludes by considering practical solutions that circumvent the impossibility result in order to reach consensus.