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.