Showing papers on "Homomorphic encryption published in 1999"
02 May 1999
TL;DR: A new trapdoor mechanism is proposed and three encryption schemes are derived : a trapdoor permutation and two homomorphic probabilistic encryption schemes computationally comparable to RSA, which are provably secure under appropriate assumptions in the standard model.
Abstract: This paper investigates a novel computational problem, namely the Composite Residuosity Class Problem, and its applications to public-key cryptography. We propose a new trapdoor mechanism and derive from this technique three encryption schemes : a trapdoor permutation and two homomorphic probabilistic encryption schemes computationally comparable to RSA. Our cryptosystems, based on usual modular arithmetics, are provably secure under appropriate assumptions in the standard model.
7,008 citations
IBM1
TL;DR: A novel and efficient protocol for bargaining between two parties and secure and efficient auctions in the absence of a fully trusted auction service is described, which combines homomorphic encryption with the φ-hiding assumption and which may be of independent interest.
Abstract: We describe a novel and efficient protocol for the following problem: A wants to buy some good from B if the price is less than a. B would like to sell, but only for more than b, and neither of them wants to reveal the secret bounds. Will the deal take place? Our solution uses an oblivious third party T who learns no information about a or b, not even whether a > b. The protocol needs only a single round of interaction, ensures fairness, and is not based on general circuit evaluation techniques. It uses a novel construction, which combines homomorphic encryption with the p-hiding assumption and which may be of independent interest. Applications include bargaining between two parties and secure and efficient auctions in the absence of a fully trusted auction service.
299 citations
TL;DR: A necessary condition for the existence of perfect two-operation homomorphic sharing schemes over finite rings without identities is given in this article, where the set of keys is a Boolean algebra or a finite field.
Abstract: Two-operation homomorphic sharing schemes were introduced by Frankel and Desmedt. They have proved that if the set of keys is a Boolean algebra or a finite field, then there does not exist a two-operation homomorphic sharing scheme. In this paper it is proved that there do not exist perfect two-operation homomorphic sharing schemes over finite rings with identities. A necessary condition for the existence of perfect two-operation sharing schemes over finite rings without identities is given.