Although threshold key-recovery systems for the discrete log based cryptosystems such as the ElGamal scheme have been proposed by Feldman and Pedersen , no (practical) threshold key-recovery system for the factoring based cryptosystems such as the RSA scheme has been proposed. This paper proposes the first (practical) threshold key-recovery systems for the factoring based cryptosystems including the RSA and Rabin schemes. Almost all of the proposed systems are unconditionally secure, since the systems utilize unconditionally secure bit-commitment protocols and unconditionally secure VSS.

This paper proposes practical escrow cash schemes with particular emphasis on countermeasures against social crimes such as money laundering and extortion. The proposed cash schemes restrict "unconditional" privacy in order to prevent these social crimes while preserving off-line-ness, divisibility and transferability, properties listed in [25] as criteria for ideal cash schemes.