Cryptography private key storage and recovery method and apparatus

A cryptosystem private key recovery device comprising in combination:

• a processor;
• a nonvolatile memory space operatively coupled to said processor;
• and
• a set of private key parameters stored in said nonvolatile memory space utilizing less storage space than the full parameter set {p, q, dp, dq, v} and providing better computational efficiency than the minimal parameter set {p, q},
• wherein said private key recovery device is configured to recover a private key from said set of stored private key parameters utilizing equation kp (p−1) mod e=1, wherein kp is a private key parameter, p is a prime factor of a public modulus, and e is a given public exponent.

A cryptosystem private key recovery device, comprising in combination:

• a processor;
• a nonvolatile memory space operatively coupled to said processor;
• and
• a set of private key parameters stored in said nonvolatile memory space and utilizing less storage space than the full parameter set {n, d} and providing better computational efficiency than the minimal parameter set {p, q},
• wherein said set of private key parameters comprises a parameter k, said parameter k is derived from k(p−1)(q−1) mod e=1, p and q are given prime factors of a public modulus, and e is a given public exponent.

A method for recovering a private key, comprising in combination:

• storing private key parameters in a memory space;
• utilizing less storage space for said private key parameters than the full parameter set {p, q, dp, dq, v};
• and
• providing better computational efficiency than the minimal parameter set {p, q},
• wherein said set of private key parameters comprises a parameter kp, said parameter kp is derived from kp(p−1) mod e=1, p is a prime factor of a public modulus, and e is a given public exponent.

A method for recovering a private key, comprising in combination:

• storing private key parameters in a memory space;
• utilizing less storage space for said private key parameters than the full parameter set {n, d};
• and
• providing better computational efficiency than the minimal parameter set {p, q},
• wherein said set of private key parameters comprises a parameter k, said parameter k is derived from k(p−1)(q−1) mod e=1, p and q are given prime factors of a public modulus, and e is a given public exponent.