GBD threshold cryptography with an application to RSA key recovery

We present protocols for threshold decryption and threshold key generation in the GBD public-key cryptosystem in the "honest-butcurious" setting. These allow GBD computations to be performed in a distributed manner during both key generation and decryption, without revealing the private key to any party. GBD threshold decryption is similar to El-Gamal threshold decryption. GBD threshold key generation is based on adaptations of protocols for RSA key generation by Boneh and Franklin, and Catalano et al, and includes a new protocol for efficiently computing the inverse of a shared secret modulo another shared secret. We also show an application of GBD threshold cryptography to RSA key recovery, and point out two open problems in this application.