
{"publication_number": "US-7991154-B2", "abstract": "a method of scalar multiplication for use in elliptic curve - based cryptosystems is provided . scalars are represented using a generic multibase form combined with the non - adjacency property , which greatly reduces the nonzero density in the representation . the method allows for flexibly selecting an unrestricted number of bases and their weight in the representation according to the particular characteristics of a setting , in such a way that computing costs are minimized . a simple , memory - friendly conversion process from binary to multibase representation and an inexpensive methodology to protect the multibase scalar multiplication against simple - side channel attacks are also provided .", "application_number": "US-15245008-A", "description": "embodiments are described below , by way of example only , with reference to fig1 - 5 . a system and method are provided for accelerating scalar multiplication by representing the scalar value with a short multibase representation , which is obtained by means of a conversion methodology that does not require additional memory resources . a direct calculation of a scalar multiplication of the form kp would involve adding p to itself ( i . e ., p + p + . . . + p ) ( k \u2212 1 ) times . this procedure is highly time consuming for typical sizes of k . a straightforward improvement would be representing the scalar value using a binary representation with elements { 0 , 1 