How to share a function securely
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Perfect Homomorphic Zero-Knowledge Threshold Schemes over any Finite Abelian Group
SIAM Journal on Discrete Mathematics
Communications of the ACM
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Shared Generation of Authenticators and Signatures (Extended Abstract)
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Wallet Databases with Observers
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Sharing Decryption in the Context of Voting or Lotteries
FC '00 Proceedings of the 4th International Conference on Financial Cryptography
Some Recent Research Aspects of Threshold Cryptography
ISW '97 Proceedings of the First International Workshop on Information Security
Adaptive Security in the Threshold Setting: From Cryptosystems to Signature Schemes
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Threshold cryptography based on Asmuth-Bloom secret sharing
Information Sciences: an International Journal
A novel efficient (t,n) threshold proxy signature scheme
Information Sciences: an International Journal
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Practical threshold signatures
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
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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.