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 three novel function sharing schemes for RSA, ElGamal and Paillier cryptosystems. To the best of our knowledge, these are the first provably secure threshold cryptosystems realized using the Asmuth–Bloom secret sharing. Proposed schemes are comparable in performance to earlier proposals in threshold cryptography.