ACCELERATING SCALAR MULTIPLICATION ON ELLIPTIC CURVE CRYPTOSYSTEMS OVER PRIME FIELDS

摘要

A method and apparatus for accelerating scalar multiplication in an ellipticcurve cryptosystem (ECC) over prime fields is provided. Multiplicationoperationswithin an ECC point operation are identified and modified utilizing anequivalentpoint representation that inserts multiples of two. Algebraic substitutions ofthemultiplication operations with squaring operations and other cheaper fieldoperationsare performed. Scalar multiplication can also be protected against simple side-channelattacks balancing the number of multiplication operations and squaringoperations and providing novel atomic structures to implement the ECCoperation.In addition, a new coordinate system is defined to enable more effectiveoperation ofECC to multiprocessor environments.