Patent ID: 8775813

Claim:
A computing device implemented method for implementing a digital signature operation in place of a signing equation specified by a digital signature protocol, based on an underlying group, applied to a message, the method being performed by a correspondent computing device having a processing unit and memory storing a long-term private key, said protocol specifying a digital signature having a first signature component and a second signature component, said second signature component defined to be calculated by direct multiplication of said long term private key with another value, the method comprising: (a) the processing unit obtaining an ephemeral private key and deriving said first signature component using said ephemeral private key; and (b) the processing unit generating the second signature component by performing operations comprising: (i) calculating a first value, said calculating based on said message and including a multiplication with an inverse of said other value; (ii) obtaining said long-term private key from the memory and performing a single additive operation, said additive operation being one of an addition and a subtraction, on said long-term private key to combine said long-term private key with said first value to obtain a masked value; (iii) deriving a second value based on said other value; and, (iv) multiplying said masked value with said second value to obtain said second signature component, wherein a value of said second signature component is equivalent to a value calculated by direct multiplication of said long term private key with said other value.