On Competition and the Strategic Management of Intellectual Property in Oligopoly

An innovative firm with private information about its indivisible process innovation chooses strategically whether to apply for a patent with probabilistic validity or rely on secrecy. By doing so, the firm manages its rivals’ beliefs about the size of the innovation, and affects the incentives in the product market. A Cournot competitor tends to patent big innovations, and keep small innovations secret, while a Bertrand competitor adopts the reverse strategy. Increasing the number of firms gives a greater (smaller) patenting incentive for Cournot (Bertrand) competitors. Increasing the degree of product substitutability increases the incentives to patent the innovation

Secret Sharing Schemes with a large number of players from Toric Varieties

A general theory for constructing linear secret sharing schemes over a finite field \Fq from toric varieties is introduced. The number of players can be as large as $(q-1)^r-1$ for $r\geq 1$. We present general methods for obtaining the reconstruction and privacy thresholds as well as conditions for multiplication on the associated secret sharing schemes. In particular we apply the method on certain toric surfaces. The main results are ideal linear secret sharing schemes where the number of players can be as large as $(q-1)^2-1$. We determine bounds for the reconstruction and privacy thresholds and conditions for strong multiplication using the cohomology and the intersection theory on toric surfaces.Comment: 15 pages, 4 figures. arXiv admin note: text overlap with arXiv:1203.454

Intersection sets, three-character multisets and associated codes

In this article we construct new minimal intersection sets in ${\mathrm{AG}}(r,q^2)$ sporting three intersection numbers with hyperplanes; we then use these sets to obtain linear error correcting codes with few weights, whose weight enumerator we also determine. Furthermore, we provide a new family of three-character multisets in ${\mathrm{PG}}(r,q^2)$ with $r$ even and we also compute their weight distribution.Comment: 17 Pages; revised and corrected result

Function and secret sharing extensions for Blakley and Asmuth-Bloom secret sharing schemes

Ankara : The Department of Computer Engineering and the Institute of Engineering and Science of Bilkent University, 2009.Thesis (Master's) -- Bilkent University, 2009.Includes bibliographical references leaves 65-69.Threshold cryptography deals with situations where the authority to initiate or perform cryptographic operations is distributed amongst a group of individuals. Usually in these situations a secret sharing scheme is used to distribute shares of a highly sensitive secret, such as the private key of a bank, to the involved individuals so that only when a sufficient number of them can reconstruct the secret but smaller coalitions cannot. The secret sharing problem was introduced independently by Blakley and Shamir in 1979. They proposed two different solutions. Both secret sharing schemes (SSS) are examples of linear secret sharing. Many extensions and solutions based on these secret sharing schemes have appeared in the literature, most of them using Shamir SSS. In this thesis, we apply these ideas to Blakley secret sharing scheme. Many of the standard operations of single-user cryptography have counterparts in threshold cryptography. Function sharing deals with the problem of distribution of the computation of a function (such as decryption or signature) among several parties. The necessary values for the computation are distributed to the participants using a secret sharing scheme. Several function sharing schemes have been proposed in the literature with most of them using Shamir secret sharing as the underlying SSS. In this work, we investigate how function sharing can be achieved using linear secret sharing schemes in general and give solutions of threshold RSA signature, threshold Paillier decryption and threshold DSS signature operations. The threshold RSA scheme we propose is a generalization of Shoup’s Shamir-based scheme. It is similarly robust and provably secure under the static adversary model. In threshold cryptography the authorization of groups of people are decided simply according to their size. There are also general access structures in which any group can be designed as authorized. Multipartite access structures constitute an example of general access structures in which members of a subset are equivalent to each other and can be interchanged. Multipartite access structures can be used to represent any access structure since all access structures are multipartite. To investigate secret sharing schemes using these access structures, we used Mignotte and Asmuth-Bloom secret sharing schemes which are based on the Chinese remainder theorem (CRT). The question we tried to asnwer was whether one can find a Mignotte or Asmuth-Bloom sequence for an arbitrary access structure. For this purpose, we adapted an algorithm that appeared in the literature to generate these sequences. We also proposed a new SSS which solves the mentioned problem by generating more than one sequence.Bozkurt, İlker NadiM.S