On codes, matroids, and secure multiparty computation from linear secret-sharing schemes

Error-correcting codes and matroids have been widely used in the study of ordinary secret sharing schemes. In this paper, the connections between codes, matroids, and a special class of secret sharing schemes, namely, multiplicative linear secret sharing schemes (LSSSs), are studied. Such schemes are known to enable multiparty computation protocols secure against general (nonthreshold) adversaries.Two open problems related to the complexity of multiplicative LSSSs are considered in this paper. The first one deals with strongly multiplicative LSSSs. As opposed to the case of multiplicative LSSSs, it is not known whether there is an efficient method to transform an LSSS into a strongly multiplicative LSSS for the same access structure with a polynomial increase of the complexity. A property of strongly multiplicative LSSSs that could be useful in solving this problem is proved. Namely, using a suitable generalization of the well-known Berlekamp–Welch decoder, it is shown that all strongly multiplicative LSSSs enable efficient reconstruction of a shared secret in the presence of malicious faults. The second one is to characterize the access structures of ideal multiplicative LSSSs. Specifically, the considered open problem is to determine whether all self-dual vector space access structures are in this situation. By the aforementioned connection, this in fact constitutes an open problem about matroid theory, since it can be restated in terms of representability of identically self-dual matroids by self-dual codes. A new concept is introduced, the flat-partition, that provides a useful classification of identically self-dual matroids. Uniform identically self-dual matroids, which are known to be representable by self-dual codes, form one of the classes. It is proved that this property also holds for the family of matroids that, in a natural way, is the next class in the above classification: the identically self-dual bipartite matroids.

Metrics on diagram groups and uniform embeddings in a Hilbert space

"Vegeu el resum a l'inici del document del fitxer adjunt".

Tacit collusion and capacity withholding in repeated uniform price auctions

This paper contributes to the study of tacit collusion by analyzing infinitely repeated multiunit uniform price auctions in a symmetric oligopoly with capacity constrained firms. Under both the Market Clearing and Maximum Accepted Price rules of determining the uniform price, we show that when each firm sets a price-quantity pair specifying the firm's minimum acceptable price and the maximum quantity the firm is willing to sell at this price, there exists a range of discount factors for which the monopoly outcome with equal sharing is sustainable in the uniform price auction, but not in the corresponding discriminatory auction. Moreover, capacity withholding may be necessary to sustain this out-come. We extend these results to the case where firms may set bids that are arbitrary step functions of price-quantity pairs with any finite number of price steps. Surprisingly, under the Maximum Accepted Price rule, firms need employ no more than two price steps to minimize the value of the discount factor

Auctions for government securities: a laboratory comparison of uniform, discriminatory and spanish designs

The Bank of Spain uses a unique auction format to sell government bonds, which can be seen as a hybrid of a uniform and a discriminatory auction. For winning bids above the average winning bid, buyers are charged the average winning bid, otherwise they pay their respective bids. We report on an experiment that compares this auction format to the discriminatory format, used in most other countries, and to the uniform format. Our design is based on a common value model with multi-unit supply and two-unit demand. The results show significantly higher revenue with the Spanish and the uniform formats than with the discriminatory one, while volatility of prices over time is significantly lower in the discriminatory format than in the Spanish and uniform cases. Actual price dispersion is significantly larger in the discriminatory than in the Spanish. Our data also exhibit the use of bid-spreading strategies in all three designs.

Asymmetric demand information in uniform and discriminatory call auctions: an experimental analysis motivated by electricity markets

We study the outcomes of experimental multi-unit uniform and discriminatory auctions with demand uncertainty. Our study is motivated by the ongoing debate about market design in the electricity industry. Our main aim is to compare the effect of asymmetric demand-information between sellers on the performance of the two auction institutions. In our baseline conditions all sellers have the same information, whereas in our treatment conditions some sellers have better information than others. In both information conditions we find that average transaction prices and price volatility are not significantly different under the two auction institutions. However, when there is asymmetric information among sellers the discriminatory auction is significantly less efficient. These results are not in line with the typical arguments made in favor of discriminatory pricing in electricity industries; namely, lower consumer prices and less price volatility. Moreover, our results provide some indication that discriminatory auctions reduce technical efficiency relative to uniform auctions.

Infinite index subgroups and finiteness properties of intersections of geometrically finite groups

We explore which types of finiteness properties are possible for intersections of geometrically finite groups of isometries in negatively curved symmetric rank one spaces. Our main tool is a twist construction which takes as input a geometrically finite group containing a normal subgroup of infinite index with given finiteness properties and infinite Abelian quotient, and produces a pair of geometrically finite groups whose intersection is isomorphic to the normal subgroup.

Codes of best practice in competitive markets for managers

We study firms' corporate governance in environments where possibly heterogeneous shareholders compete for possibly heterogeneous managers. A firm, formed by a shareholder and a manager, can sign either an incentive contract or a contract including a Code of Best Practice. A Code allows for a better manager's control but makes manager's decisions hard to react when market conditions change. It tends to be adopted in markets with low volatility and in low-competitive environments. The firms with the best projects tend to adopt the Code when managers are not too heterogeneous while the best managers tend to be hired through incentive contracts when the projects are similar. Although the matching between shareholders and managers is often positively assortative, the shareholders with the best projects might be willing to renounce to hire the best managers, signing contracts including Codes with lower-ability managers.

On uniform conjugators in torsion-free hyperbolic groups

"Vegeu el resum a l'inici del document del fitxer adjunt."

Solidarity and uniform rules in bankruptcy problems

The idea of ensuring a guarantee (a minimum amount of the resources) to each agent has recently acquired great relevance, in both social and politi- cal terms. Furthermore, the notion of Solidarity has been treated frequently in redistribution problems to establish that any increment of the resources should be equally distributed taking into account some relevant characteris- tics. In this paper, we combine these two general concepts, guarantee and solidarity, to characterize the uniform rules in bankruptcy problems (Con- strained Equal Awards and Constrained Equal Losses rules). Keywords: Constrained Equal Awards, Constrained Equal Losses, Lower bounds, Bankruptcy problems, Solidarity. JEL classification: C71, D63, D71.

QRP: An improved secure authentication method using QR codes

This paper presents the design and implementation of QRP, an open source proof-of-concept authentication system that uses a two-factorauthentication by combining a password and a camera-equipped mobile phone, acting as an authentication token. QRP is extremely secure asall the sensitive information stored and transmitted is encrypted, but it isalso an easy to use and cost-efficient solution. QRP is portable and can be used securely in untrusted computers. Finally, QRP is able to successfully authenticate even when the phone is offline.

Reliable and persistent storage for CoDeS a distributed collaborative system

This research is aimed to find a solution for a distributed storage system adapted for CoDeS. By studying how DSSs work and how they are implemented, we can conclude how we can implement a DSS compatible with CoDeS requirements.

On fast-decodable space-time block codes

We focus on full-rate, fast-decodable space–time block codes (STBCs) for 2 x 2 and 4 x 2 multiple-input multiple-output (MIMO) transmission. We first derive conditions and design criteria for reduced-complexity maximum-likelihood (ML) decodable 2 x 2 STBCs, and we apply them to two families of codes that were recently discovered. Next, we derive a novel reduced-complexity 4 x 2 STBC, and show that it outperforms all previously known codes with certain constellations.

On high-rate full-diversity 2x2 space-time codes with low-complexity optimum detection

The 2×2 MIMO profiles included in Mobile WiMAX specifications are Alamouti’s space-time code (STC) fortransmit diversity and spatial multiplexing (SM). The former hasfull diversity and the latter has full rate, but neither of them hasboth of these desired features. An alternative 2×2 STC, which is both full rate and full diversity, is the Golden code. It is the best known 2×2 STC, but it has a high decoding complexity. Recently, the attention was turned to the decoder complexity, this issue wasincluded in the STC design criteria, and different STCs wereproposed. In this paper, we first present a full-rate full-diversity2×2 STC design leading to substantially lower complexity ofthe optimum detector compared to the Golden code with only a slight performance loss. We provide the general optimized form of this STC and show that this scheme achieves the diversitymultiplexing frontier for square QAM signal constellations. Then, we present a variant of the proposed STC, which provides a further decrease in the detection complexity with a rate reduction of 25% and show that this provides an interesting trade-off between the Alamouti scheme and SM.

Low-density parity-check codes for nonergodic block-fading channels

We design powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel. We first study the case of maximum-likelihood decoding, and show that the design criterion is rather straightforward. Since optimal constructions for maximum-likelihood decoding do not performwell under iterative decoding, we introduce a new family of full-diversity LDPC codes that exhibit near-outage-limit performance under iterative decoding for all block-lengths. This family competes favorably with multiplexed parallel turbo codes for nonergodic channels.

Generalized low-density codes with BCH constituents for full-diversity near-outage performance

A new graph-based construction of generalized low density codes (GLD-Tanner) with binary BCH constituents is described. The proposed family of GLD codes is optimal on block erasure channels and quasi-optimal on block fading channels. Optimality is considered in the outage probability sense. Aclassical GLD code for ergodic channels (e.g., the AWGN channel,the i.i.d. Rayleigh fading channel, and the i.i.d. binary erasure channel) is built by connecting bitnodes and subcode nodes via a unique random edge permutation. In the proposed construction of full-diversity GLD codes (referred to as root GLD), bitnodes are divided into 4 classes, subcodes are divided into 2 classes, and finally both sides of the Tanner graph are linked via 4 random edge permutations. The study focuses on non-ergodic channels with two states and can be easily extended to channels with 3 states or more.