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We present two universally composable and practical protocols by which a dealer can, verifiably and non-interactively, secret-share an integer among a set of players. Moreover, at small extra cost and using a distributed verifier proof, it can be shown in zero-knowledge that three shared integers a, b, c satisfy ab = c. This implies by known reductions… (More)
We introduce the notion of Linear Integer Secret-Sharing (LISS) schemes, and show constructions of such schemes for any access structure. We show that any LISS scheme can be used to build a secure distributed protocol for exponentiation in any group. This implies, for instance, distributed RSA protocols for arbitrary access structures and with arbitrary… (More)
We show how to effectively convert a secret-shared bit b over a prime field to another field. If initially given a random replicated secret share this conversion can be done by the cost of revealing one secret shared value. By using a pseudo-random function it is possible to convert arbitrary many bit values from one initial random replicated share.… (More)
In this work, we introduce the Linear Integer Secret Sharing (LISS) scheme, which is a secret sharing scheme done directly over the integers. I.e., the generation of shares is done by an integer linear combination of the secret and some random integer values. The reconstruction of the secret is done directly by a linear integer combination of the shares of… (More)
In  Damgard and Thorbek proposed the linear integer secret sharing (LISS) scheme. In this note we show that the LISS scheme can be made proactive.
This paper is written in connection with an exam project in the course Mathematical Aspects of Cryptology, spring 2006. It covers the quantum prime factoring algorithm which was first presented by Shor . First, we give the reduction from prime factoring to order finding. Secondly, we present an efficient quantum algorithm for the order finding problem.