A new construction of threshold cryptosystems based on RSA

There have been many ways to construct a threshold cryptosystem. Most often they are constructed by combining original public encryption schemes with some methods such as Shamir's secret sharing. In this paper a new threshold cryptosystem based on RSA is presented, which is constructed by several RSA instances with chosen moduli and private keys. In fact, by computing the common private keys of some individual RSA instances and modifying the moduli, we combine those RSA instances and get a new threshold cryptosystem (hereinafter called combined RSA for simplification). First, it is proved that this system has similar security properties to the CRT-based (Chinese remainder theorem) threshold RSA while being convenient to implement, i.e., it only needs modular multiplication once to encrypt or decrypt respectively. Although the new system has the same security strength as the CRT-based RSA theoretically, it will provide fewer opportunities for adversaries in practical applications as there is only one step for encryption or decryption. Second, for complexity, as plain RSA is efficient, the combined RSA is also practical in computation. Therefore, if a plain RSA user wants to develop threshold decryption or threshold signature more conveniently and more securely, the combined RSA would be suitable. Finally, an application of the combined RSA is provided in this paper to realize distributed data access control with collusion-resistance.