Disclosed herein is a system and method for storage and recovery of a private key in a cryptographic system by providing a parameterization of the private key that uses less storage space than the full CRT parameter set {p, q, d_p, d_q, v} and that provides better computational efficiency than the minimal parameter set {p, q}. Also disclosed is a system and method for storage and recovery of a private key in a cryptographic system by providing a parameterization of the private key that uses less storage space than the full non-CRT parameter set {n, d} and that provides better computational efficiency than the minimal parameter set {p, q}. Furthermore, disclosed herein is a means for computing the parameters d_p, d_q, and d in a manner such that the computational sequence is independent of the values of the prime factors p and q, thereby reducing vulnerability to attacks that exploit such dependence.