Research On Parallel Schedule Of Scalar Multiplication Of Elliptic Curve Cryptography

Scalar multiplication is the key operation of Elliptic Curve Cryptography (ECC), and the efficiently implementated of scalar multiplication is the main research of ECC and the popular method is parallel schedule. In this thesis, the parallel schedule of scalar multiplication is researched. the main work is given below:The Montgomery scalar multiplication algorithm is researched in this thesis, the parallel of Montgomery scalar multiplication scheduled the finite field modular arithmetic is analyzed and the parallel algorithms with 2-parallel and 4-parallel finite field modular arithmetic are presentd.The NAF scalar multiplication algorithm is researched, the parallel NAF scalar multiplication algorithms are present based on the research of parallelity in the scheduling point adding (ECADD) and point doubling (ECDBL) of NAF scalar multiplication, for removing the relativity between ECADD and ECDBL by use several temporary variables, and the finite field modular arithmetic could be scheduled paralleled by NAF scalar multiplication.The Comb scalar multiplication algorithm is researched in this thesis, the parallel Comb scalar multiplication algorithms are present based on the research of parallelity of Comb scalar multiplication with one precomputation table and two precomputation tables, in which the relativity between ECADD and ECDBL is removed by use of several temporary variables. And the ECADD and ECDBL could be scheduled paralleled, and the finite field modular arithmetic could be scheduled paralleled in Comb scalar multiplication.The performance of the three parallel scalar multiplication algorithms are analyzed and evaluated, and the circuit architecture is designed for simulation and verification in this thesis, by experiment, the parallel schedule method is efficient to reduce the the time of computation in scalar multiplication.