*16:17* [Pub][ePrint]
On the Phase Space of Block-Hiding Strategies, by Assaf Shomer
We calculate the probability of success of block-hiding mining strategies in bitcoin-like networks.These strategies involve building a secret branch of the block-tree and publishing it opportunistically, aiming to replace the top of the main branch and rip the reward associated with the secretly mined blocks. We identify two types of block-hiding strategies and chart the parameter space where those are more beneficial than the standard mining strategy described in Nakamoto\'s paper.

Our analysis suggests a generalization of the notion of the relative hashing power as a measure for a miner\'s influence on the network. Block-hiding strategies are beneficial only when this measure of influence exceeds a certain threshold.

*04:17* [Pub][ePrint]
Optimal Non-Perfect Uniform Secret Sharing Schemes, by Oriol Farràs and Torben Hansen and Tarik Kaced and Carles Padró
A secret sharing scheme is non-perfect if some subsets of participants cannot recover the secret value but have some information about it. This work is dedicated to the search of efficient non-perfect secret sharing schemes. The efficiency is measured by means of the information ratio, the ratio between the maximum length of the shares and the length of the secret value.In order to study perfect and non-perfect secret sharing schemes with all generality, we describe the structure of the schemes through their access function, a real function that measures the amount of information that every subset of participants knows about the secret value. We present new tools for the construction of secret sharing schemes. In particular, we construct a secret sharing scheme for every access function.

We extend the connections between polymatroids and perfect secret sharing schemes to the non-perfect ones to find new results on the information ratio. We find a new lower bound on the information ratio that is better than the ones previously known. In particular, this bound is tight for uniform access functions. The access function of a secret sharing scheme is uniform if all participants play the same role in a scheme (e.g. ramp secret sharing schemes). Moreover, we construct a secret sharing scheme with optimal information ratio for every rational uniform access function.

*04:17* [Pub][ePrint]
Algebraic Properties of Modular Addition Modulo a Power of Two, by S. M. Dehnavi and Alireza Rahimipour
Modular addition modulo a power of two, is one of the most applicable operators in symmetric cryptography; therefore, investigating cryptographic properties of this operator has a significant role in design and analysis of symmetric ciphers.Algebraic properties of modular addition modulo a power of two have been studied for two operands by Braeken in fse\'05. Also, the authors of this paper, have studied this operator, in some special cases, before. In this paper, taking advantage of previous researches in this area, we generalize the algebraic properties of this operator for more than two summands. More precisely, we

determine the algebraic degree of the component Boolean functions of modular addition of arbitrary number of summands modulo a power of two, as a vectorial Boolean function, along with the number of terms and variables in these component functions. As a result, algebraic degrees of the component Boolean functions of Generalized Pseudo-Hadamard Transforms are driven.

*04:17* [Pub][ePrint]
Efficient Three-Party Computation from Cut-and-Choose, by Seung Geol Choi and Jonathan Katz and Alex J. Malozemoff and Vassilis Zikas
With relatively few exceptions, the literature on efficient (practical) secure computation has focused on secure two-party computation~(2PC). It is, in general, unclear whether the techniques used to construct practical 2PC protocols---in particular, the \\emph{cut-and-choose} approach---can be adapted to the multi-party setting.In this work we explore the possibility of using cut-and-choose for practical secure \\emph{three-party} computation. The three-party case has been studied in prior work in the semi-honest setting, and is motivated by the observation that real-world deployments of multi-party computation are likely to involve few parties. We propose a constant-round protocol for three-party computation tolerating any number of malicious parties, whose computational cost is essentially only \\emph{twice} that of state-of-the-art two-party protocols.

*04:17* [Pub][ePrint]
How to Use Bitcoin to Design Fair Protocols, by Iddo Bentov and Ranjit Kumaresan
We study a model of fairness in secure computation in which an adversarial party that aborts on receiving output is forced to pay a mutually predefined monetary penalty. We then show how the Bitcoin network can be used to achieve the above notion of fairness in the two-party as well as the multiparty setting (with a dishonest majority). In particular, we propose new ideal functionalities and protocols for fair secure computation and fair lottery in this model. One of our main contributions is the definition of an ideal primitive, which we call $\\mathcal{F}_{\\mathrm{CR}}^\\star$ ($\\mathrm{CR}$ stands for ``claim-or-refund\'\'), that formalizes and abstracts the exact properties we require from the Bitcoin network to achieve our goals. Naturally, this abstraction allows us to design fair protocols in a hybrid model in which parties have access to the $\\mathcal{F}_{\\mathrm{CR}}^\\star$ functionality, and is otherwise independent of the Bitcoin ecosystem.

We also show an efficient realization of $\\mathcal{F}_{\\mathrm{CR}}^\\star$ that requires only two Bitcoin transactions to be made on the network.

Our constructions also enjoy high efficiency. In a multiparty setting, our protocols only require a constant number of calls to $\\mathcal{F}_{\\mathrm{CR}}^\\star$ per party on top of a standard multiparty secure computation protocol. Our fair multiparty lottery protocol improves over previous solutions which required a quadratic number of Bitcoin transactions.