Computationally asymmetric cryptographic systems

A method of electronically signing data, the method comprising:

• determining a hash value of the data to be signed using a cryptographic hash function and a time-lock puzzle algorithm for computing an intermediate value computable by a first method or a second method with each of the first and second methods employing at least one common first parameter and with the second method additionally employing at least one second parameter whereby the second method is computationally faster than said first method;
• computing the result of the hash value using the first method to compute the intermediate value L;
• and
• encrypting the result to sign said data.

A method of verifying electronically signed data, the method comprising:

• determining a hash value of at least a portion of the data to be verified using a cryptographic hash function and a time-lock puzzle algorithm for computing an intermediate value computable by a first method or a second method with each of the first and second methods employing at least one common first parameter and with the second method additionally employing at least one second parameter whereby the second method is computationally faster than said first method;
• computing the result of the hash value using the second method to compute the intermediate value L;
• and
• encrypting data dependent on said result for comparing with a signature of said data to verify said signed data.

A method providing a computationally asymmetric electronic signature, the method comprising:

• receiving message data for signing;
• computing an intermediate value of data derived from said message data, wherein said intermediate value is calculated using a cryptographic hash function and a time-lock puzzle algorithm for computing an intermediate value computable by a first method or a second method with each of the first and second methods employing at least one common first parameter and with the second method additionally employing at least one second parameter whereby the second method is computationally faster than said first method and wherein said first method is employed to compute the intermediate value;
• determining a symmetric cryptographic signature of data derived from said intermediate value;
• and
• providing said intermediate value in association with said symmetric cryptographic signature to provide a computationally asymmetric signature for said message data.