Power signature attack resistant cryptography

A method of computing a multiple k of a point P on an elliptic curve defined over a field in a processor which generates distinct power signatures for adding and doubling operations, said method comprising the steps of:

• a) representing the number k as binary vector of bits ki;
• b) forming an ordered pair of points P1 and P2, wherein the points P1 and P2 differ at most by P;
• and
• c) selecting each of said bits ki in sequence;
• and for each of said bits ki;
• i) upon ki being a zero, computing a new set of points P1′, P2′ by first doubling the first point P1 to generate said point P1′ and thereby producing a first power signature, and subsequently adding the points P1 and P2 to generate the point P2′ and thereby producing a second power signature distinct from said first power signature;
• or
• ii) upon ki being a one, computing a new set of points P1′, P2′ by first doubling the second point P2 to generate the point P2′ and thereby producing said first power signature;
• and subsequently adding the points P1 and P2 to produce the point P1′, and thereby producing said second power signature;
• whereby said doubles or adds arc always performed in the same order for each of said bits ki, thereby producing a consistent power signature waveform and minimizing a timing attack on said method.