Threshold cryptography based on asmuth-bloom secret sharing

In this paper, we investigate how threshold cryptography can be conducted with the Asmuth-Bloom secret sharing scheme and present two novel function sharing schemes, one for the RSA signature and the other for the ElGamal decryption functions, based on the Asmuth-Bloom scheme. To the best of our knowledge, these are the first threshold cryptosystems realized using the Asmuth-Bloom secret sharing. The proposed schemes compare favorably to the earlier function sharing schemes in performance as well as in certain theoretical aspects. © Springer-Verlag Berlin Heidelberg 2006

Threshold cryptography based on Asmuth–Bloom secret sharing

Cataloged from PDF version of article.In this paper, we investigate how threshold cryptography can be conducted with the Asmuth-Bloom secret sharing scheme and present three novel function sharing schemes for RSA, ElGamal and Paillier cryptosysterns. To the best of our knowledge, these are the first provably secure threshold cryptosystems realized using the Asmuth-Bloom secret sharing. Proposed schemes are comparable in performance to earlier proposals in threshold cryptography. (c) 2007 Elsevier Inc. All rights reserved

Multilevel Threshold Secret and Function Sharing based on the Chinese Remainder Theorem

A recent work of Harn and Fuyou presents the first multilevel (disjunctive) threshold secret sharing scheme based on the Chinese Remainder Theorem. In this work, we first show that the proposed method is not secure and also fails to work with a certain natural setting of the threshold values on compartments. We then propose a secure scheme that works for all threshold settings. In this scheme, we employ a refined version of Asmuth-Bloom secret sharing with a special and generic Asmuth-Bloom sequence called the {\it anchor sequence}. Based on this idea, we also propose the first multilevel conjunctive threshold secret sharing scheme based on the Chinese Remainder Theorem. Lastly, we discuss how the proposed schemes can be used for multilevel threshold function sharing by employing it in a threshold RSA cryptosystem as an example

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

Comparison of Secret Splitting, Secret Sharing and Recursive Threshold Visual Cryptography for Security of Handwritten Images

The secret sharing is a method to protect confidentiality and integrity of the secret messages by distributing the message shares into several recipients. The secret message could not be revealed unless the recipients exchange and collect shares to reconstruct the actual message. Even though the attacker obtain shares shadow during the share exchange, it would be impossible for the attacker to understand the correct share. There are few algorithms have been developed for secret sharing, e.g. secret splitting, Asmuth-Bloom secret sharing protocol, visual cryptography, etc. There is an unanswered question in this research about which method provides best level of security and efficiency in securing message. In this paper, we evaluate the performance of three methods, i.e. secret splitting, secret sharing, and recursive threshold visual cryptography for handwritten image security in terms of execution time and mean squared error (MSE) simulation. Simulation results show the secret splitting algorithm produces the shortest time of execution. On the other hand, the MSE simulation result that the three methods can reconstruct the original image very well

A secure data outsourcing scheme based on Asmuth – Bloom secret sharing

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Data outsourcing is an emerging paradigm for data management in which a database is provided as a service by third-party service providers. One of the major benefits of offering database as a service is to provide organisations, which are unable to purchase expensive hardware and software to host their databases, with efficient data storage accessible online at a cheap rate. Despite that, several issues of data confidentiality, integrity, availability and efficient indexing of users’ queries at the server side have to be addressed in the data outsourcing paradigm. Service providers have to guarantee that their clients’ data are secured against internal (insider) and external attacks. This paper briefly analyses the existing indexing schemes in data outsourcing and highlights their advantages and disadvantages. Then, this paper proposes a secure data outsourcing scheme based on Asmuth–Bloom secret sharing which tries to address the issues in data outsourcing such as data confidentiality, availability and order preservation for efficient indexing

The Chinese Remainder Theorem

The oldest remainder problems in the world date back to 3rd century China. The Chinese Remainder Theorem was used as the basis in calendar computations, construction, commerce and astronomy problems. Today, the theorem has advanced uses in many branches of mathematics and extensive applications in computing, coding and cryptography. The Chinese Remainder Theorem is an excellent example of how mathematics that emerged in the 3rd century AC has developed and remains relevant in today’s world. This paper will explore the historical development of the Chinese Remainder Theorem along with central properties of linear congruences. In addition to providing a historical overview of the Chinese Remainder Theorem, this paper will examine several modern applications of the Chinese Remainder Theorem

A Randomized Kernel-Based Secret Image Sharing Scheme

This paper proposes a ($k,n$)-threshold secret image sharing scheme that offers flexibility in terms of meeting contrasting demands such as information security and storage efficiency with the help of a randomized kernel (binary matrix) operation. A secret image is split into $n$ shares such that any $k$ or more shares ($k\leq n$) can be used to reconstruct the image. Each share has a size less than or at most equal to the size of the secret image. Security and share sizes are solely determined by the kernel of the scheme. The kernel operation is optimized in terms of the security and computational requirements. The storage overhead of the kernel can further be made independent of its size by efficiently storing it as a sparse matrix. Moreover, the scheme is free from any kind of single point of failure (SPOF).Comment: Accepted in IEEE International Workshop on Information Forensics and Security (WIFS) 201