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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 participating parties using a secret sharing scheme (SSS). Several function sharing schemes have been proposed in the literature, with most of them using Shamir secret sharing as the underlying SSS. In this paper, we investigate how threshold cryptography can be conducted with any linear secret sharing scheme and present a function sharing scheme for the RSA cryptosystem. The challenge is that constructing the secret in a linear SSS requires the solution of a linear system, which normally involves computing inverses, while computing an inverse modulo ᵠ(N) cannot be tolerated in a threshold RSA system in any way. 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. At the end of the paper, we show how this scheme can be extended to other public key cryptosystems and give an example on the Paillier cryptosystem. [ABSTRACT FROM AUTHOR]

We consider the problem of scheduling an application on a computing system consisting of heterogeneous processors and one or more file repositories. The application consists of a large number of file-sharing, otherwise independent tasks. The files initially reside on the repositories. The interconnection network is heterogeneous. We focus on two disjoint problem cases. In the first case, there is only one file repository which is called as the master processor. In the second case, there are two or more repositories, each holding a distinct set of files. The problem is to assign the tasks to the processors, to schedule the file transfers from the repositories, and to order the executions of tasks on each processor in such a way that the turnaround time is minimized. This chapter surveys several solution techniques; but the stress is on our two recent works [22,23]. At the first glance, iterative-improvement-based heuristics do not seem to be suitable for the aforementioned scheduling problems. This is because their immediate application suggests iteratively improving a complete schedule, and hence building and exploring a complex neighborhood around the current schedule. Such complex neighborhood structures usually render the heuristics time-consuming and make them stuck to a part of the search space. However, in both of the our recent works, we show that these issues can be solved by using a three-phase approach: initial task assignment, refinement, and execution ordering. The main thrust of these two works is that iterative-improve-based heuristics can efficiently deliver effective solutions, implying that iterative-improve-based heuristics can provide highly competitive solutions to the similar scheduling problems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate how to achieve verifiable secret sharing (VSS) schemes by using the Chinese Remainder Theorem (CRT). We first show that two schemes proposed earlier are not secure by an attack where the dealer is able to distribute inconsistent shares to the users. Then we propose a new VSS scheme based on the CRT and prove its security. Using the proposed VSS scheme, we develop a joint random secret sharing (JRSS) protocol, which, to the best of our knowledge, is the first JRSS protocol based on the CRT. [ABSTRACT FROM AUTHOR]

Recently, Chinese Remainder Theorem (CRT) based function sharing schemes are proposed in the literature. In this paper, we investigate how a CRT-based threshold scheme can be enhanced with the robustness property. To the best of our knowledge, these are the first robust threshold cryptosystems based on a CRT-based secret sharing. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

One of the fundamental problems of public key cryptography is protecting the private key. Private keys are too long to be remembered by the user, and storing them in the device which performs the private key operation is insecure as long as the device is subject to capture. In this paper, we propose server-assisted protocols for the ElGamal signature scheme which make the system capture resilient in the sense that the security of the system is not compromised even if the signature device is captured. The protocols also have a key disabling feature which allows a user to disable the device's private key in case both the device and the password of the user are compromised simultaneously. [ABSTRACT FROM AUTHOR]