Patent ID: 7657029

Claim:
A method comprising: receiving, by a processor of a computing system, input parameters that are used by the computing system and the processor to generate an exponent for a cryptographic process, wherein said generating said exponent comprises; generating an addition chain based on the input parameters by: (a) initiating a chain; (b) flipping a biased coin; (c) performing a doubling step or a star step on the chain based on the biased coin flip; (d) when said star step is performed, choosing a random element and adding the random element to a set of random elements; (e) determining whether the size of the set of random elements is outside a bounded interval; and repeating steps (b)-(d) a number of times based on a length of the chain, wherein when the size of the set of random elements is outside the bounded interval, determining that generation of the chain is complete; deriving said exponent from the generated addition chain; and storing the exponent.