On the Composability of Statistically Secure Random Oblivious Transfer

We show that random oblivious transfer protocols that are statistically secure according to a definition based on a list of information-theoretical properties are also statistically universally composable. That is, they are simulatable secure with an unlimited adversary, an unlimited simulator, and an unlimited environment machine. Our result implies that several previous oblivious transfer protocols in the literature that were proven secure under weaker, non-composable definitions of security can actually be used in arbitrary statistically secure applications without lowering the security

Towards Characterizing Securely Computable Two-Party Randomized Functions

A basic question of cryptographic complexity is to combinatorially characterize all randomized functions which have information-theoretic semi-honest secure 2-party computation protocols. The corresponding question for deterministic functions was answered almost three decades back, by Kushilevitz (FOCS 1989). In this work, we make progress towards understanding securely computable `randomized\u27 functions. We bring tools developed in the study of completeness to bear on this problem. In particular, our characterizations are obtained by considering only symmetric functions with a combinatorial property called `simplicity\u27 (Maji et al. Indocrypt 2012). Our main result is a complete combinatorial characterization of randomized functions with `ternary output\u27 kernels, that have information-theoretic semi-honest secure 2-party computation protocols. In particular, we show that there exist simple randomized functions with ternary output that do not have secure computation protocols. (For deterministic functions, the smallest output alphabet size of such a function is 5, due to an example given by Beaver, DIMACS Workshop on Distributed Computing and Cryptography 1989.) Also, we give a complete combinatorial characterization of randomized functions that have `2-round\u27 information-theoretic semi-honest secure 2-party computation protocols. We also give a counter-example to a natural conjecture for the full characterization, namely, that all securely computable simple functions have secure protocols with a unique transcript for each output value. This conjecture is in fact true for deterministic functions, and -- as our results above show -- for ternary functions and for functions with 2-round secure protocols

Modes of Truth

The aim of this volume is to open up new perspectives and to raise new research questions about a unified approach to truth, modalities, and propositional attitudes. The volume’s essays are grouped thematically around different research questions. The first theme concerns the tension between the theoretical role of the truth predicate in semantics and its expressive function in language. The second theme of the volume concerns the interaction of truth with modal and doxastic notions. The third theme covers higher-order solutions to the semantic and modal paradoxes, providing an alternative to first-order solutions embraced in the first two themes. This book will be of interest to researchers working in epistemology, logic, philosophy of logic, philosophy of language, philosophy of mathematics, and semantics

Doing the best one can (while trying to do better)

The thesis explores the question of how should a rational moral agent reason and make choices when he finds himself accepting inconsistent moral judgments. It is argued that it is both conceptually and psychologically justified to describe such an agent as suffering from uncertainty. Such uncertainty, however, is not uncertainty regarding the truth of some descriptive claim, but rather uncertainty regarding the truth of a normative claim. Specifically it is uncertainty regarding the truth of a moral judgement. In the literature this is sometimes called “moral uncertainty”. Two different lines of philosophical literatures that explore the idea of moral uncertainty are discussed. The first line – the one that originated from David Lewis‟ argument against the “Desire as Belief Thesis” – explores the mere possibility of moral uncertainty, while the second line explores the question how ought a rational moral agent choose in face of moral uncertainty. The discussion of these two lines of research leads to the conclusion that a consistent account of moral decision making under conditions of moral uncertainty that will be applicable to the kind of cases that the thesis explores, must make use of degrees of beliefs in comparative moral judgements (i.e. judgements of the form “act a is morally superior to act b”) and of them alone. Specifically, no references to degrees of moral value should be made. An attempt to present such an account in the framework of an extension of Leonard Savage‟s model for decision making is carried out. This attempt leads to a problematic result. Several implications of the result to ethic and meta-ethics are discussed as well as possible ways to avoid it. The conclusion is partly positive and partly negative: While a plausible account of moral decision making under conditions of moral uncertainty is presented, an account of moral reasoning that aims at finding a complete moral theory (i.e. a moral theory that gives a prescription to every possible moral choice) is shown to be a very difficult – if not impossible - aim to achieve