An Introduction to Secret-Sharing-Based Secure Multiparty Computation

This text serves as a general guide to secure multiparty computation based on secret-sharing, focusing more on practical aspects of the techniques and constructions rather than their theoretical grounds. It is intended to serve as an introductory reference text for readers interested in the area, assuming essentially no background in these topics. This work in progress currently includes an introduction to several core concepts in secure multiparty computation, an overview of simulation-based security, and detailed constructions for honest and two-thirds honest majority MPC, and also dishonest majority in the preprocessing model

A Study on Multisecret-Sharing Schemes Based on Linear Codes

Secret sharing has been a subject of study since 1979. In the secret sharing schemes there are some participants and a dealer. The dealer chooses a secret. The main principle is to distribute a secret amongst a group of participants. Each of whom is called a share of the secret. The secret can be retrieved by participants. Clearly the participants combine their shares to reach the secret. One of the secret sharing schemes is  threshold secret sharing scheme. A  threshold secret sharing scheme is a method of distribution of information among  participants such that  can recover the secret but  cannot. The coding theory has been an important role in the constructing of the secret sharing schemes. Since the code of a symmetric  design is a linear code, this study is about the multisecret-sharing schemes based on the dual code  of  code  of a symmetric  design. We construct a multisecret-sharing scheme Blakley’s construction of secret sharing schemes using the binary codes of the symmetric design. Our scheme is a threshold secret sharing scheme. The access structure of the scheme has been described and shows its connection to the dual code. Furthermore, the number of minimal access elements has been formulated under certain conditions. We explain the security of this scheme

Secret sharing schemes for ports of matroids of rank 3

summary:A secret sharing scheme is ideal if the size of each share is equal to the size of the secret. Brickell and Davenport showed that the access structure of an ideal secret sharing scheme is determined by a matroid. Namely, the minimal authorized subsets of an ideal secret sharing scheme are in correspondence with the circuits of a matroid containing a fixed point. In this case, we say that the access structure is a matroid port. It is known that, for an access structure, being a matroid port is not a sufficient condition to admit an ideal secret sharing scheme. In this work we present a linear secret sharing scheme construction for ports of matroids of rank 3 in which the size of each share is at most $n$ times the size of the secret. Using the previously known secret sharing constructions, the size of each share was $O(n^2/\log n)$ the size of the secret. Our construction is extended to ports of matroids of any rank $k\geq 2$, obtaining secret sharing schemes in which the size of each share is at most $n^{k-2}$ times the size of the secret. This work is complemented by presenting lower bounds: There exist matroid ports that require $(\mathbb{F}_q,\ell)$-linear secret schemes with total information ratio $\Omega(2^{n/2}/\ell n^{3/4}\sqrt{\log q})$

Compression image sharing using DCT- Wavelet transform and coding by Blackely method

The increased use of computer and internet had been related to the wide use of multimedia information. The requirement forprotecting this information has risen dramatically. To prevent the confidential information from being tampered with, one needs toapply some cryptographic techniques. Most of cryptographic strategies have one similar weak point that is the information is centralized.To overcome this drawback the secret sharing was introduced. It’s a technique to distribute a secret among a group of members, suchthat every member owns a share of the secret; but only a particular combination of shares could reveal the secret. Individual sharesreveal nothing about the secret. The major challenge faces image secret sharing is the shadow size; that's the complete size of the lowestneeded of shares for revealing is greater than the original secret file. So the core of this work is to use different transform codingstrategies in order to get as much as possible the smallest share size. In this paper Compressive Sharing System for Images UsingTransform Coding and Blackely Method based on transform coding illustration are introduced. The introduced compressive secretsharing scheme using an appropriate transform (Discrete cosine transform and Wavelet) are applied to de-correlate the image samples,then feeding the output (i.e., compressed image data) to the diffusion scheme which is applied to remove any statistical redundancy orbits of important attribute that will exist within the compressed stream and in the last the (k, n) threshold secret sharing scheme, where nis the number of generated shares and k is the minimum needed shares for revealing. For making a certain high security level, eachproduced share is passed through stream ciphering depends on an individual encryption key belongs to the shareholder

SePEnTra: A secure and privacy-preserving energy trading mechanisms in transactive energy market

In this paper, we design and present a novel model called SePEnTra to ensure the security and privacy of energy data while sharing with other entities during energy trading to determine optimal price signals. Furthermore, the market operator can use this data to detect malicious activities of users in the later stage without violating privacy (e.g., deviation of actual energy generation/consumption from forecast beyond a threshold). We use two cryptographic primitives, additive secret sharing and Pedersen commitment, in SePEnTra. The performance of our model is evaluated theoretically and numerically. We compare the performance of SePEnTra with the same Transactive energy market (TEM) framework without security mechanisms. The result shows that even though using advanced cryptographic primitives in a large market framework, SePEnTra has very low computational complexity and communication overhead. Moreover, it is storage efficient for all parties

On the information ratio of non-perfect secret sharing schemes

The final publication is available at Springer via http://dx.doi.org/10.1007/s00453-016-0217-9A secret sharing scheme is non-perfect if some subsets of players that cannot recover the secret value have partial information about it. The information ratio of a secret sharing scheme is the ratio between the maximum length of the shares and the length of the secret. This work is dedicated to the search of bounds on the information ratio of non-perfect secret sharing schemes and the construction of efficient linear non-perfect secret sharing schemes. To this end, we extend the known connections between matroids, polymatroids and perfect secret sharing schemes to the non-perfect case. In order to study non-perfect secret sharing schemes in all generality, we describe their structure through their access function, a real function that measures the amount of information on the secret value that is obtained by each subset of players. We prove that there exists a secret sharing scheme for every access function. Uniform access functions, that is, access functions whose values depend only on the number of players, generalize the threshold access structures. The optimal information ratio of the uniform access functions with rational values has been determined by Yoshida, Fujiwara and Fossorier. By using the tools that are described in our work, we provide a much simpler proof of that result and we extend it to access functions with real values.Peer ReviewedPostprint (author's final draft

Compartmented Secret Sharing Based on the Chinese Remainder Theorem

A secret sharing scheme starts with a secret and then derives from it certain shares (or shadows) which are distributed to users. The secret may be recovered only by certain predetermined groups. In case of compartmented secret sharing, the set of users is partitioned into compartments and the secret can be recovered only if the number of participants from any compartment is greater than a fixed compartment threshold and the total number of participants is greater than a global threshold. In this paper we present a new compartmented secret sharing scheme by extending the Brickell\u27s construction to the case that the global threshold is strictly greater than the sum of the compartment thresholds and we indicate how to use the threshold secret sharing schemes based on the Chinese remainder theorem in order to decrease the size of shares

TSKY: a dependable middleware solution for data privacy using public storage clouds

Dissertação para obtenção do Grau de Mestre em Engenharia InformáticaThis dissertation aims to take advantage of the virtues offered by data storage cloud based systems on the Internet, proposing a solution that avoids security issues by combining different providers’ solutions in a vision of a cloud-of-clouds storage and computing. The solution, TSKY System (or Trusted Sky), is implemented as a middleware system, featuring a set of components designed to establish and to enhance conditions for security, privacy, reliability and availability of data, with these conditions being secured and verifiable by the end-user, independently of each provider. These components, implement cryptographic tools, including threshold and homomorphic cryptographic schemes, combined with encryption, replication, and dynamic indexing mecha-nisms. The solution allows data management and distribution functions over data kept in different storage clouds, not necessarily trusted, improving and ensuring resilience and security guarantees against Byzantine faults and at-tacks. The generic approach of the TSKY system model and its implemented services are evaluated in the context of a Trusted Email Repository System (TSKY-TMS System). The TSKY-TMS system is a prototype that uses the base TSKY middleware services to store mailboxes and email Messages in a cloud-of-clouds