Fast Algorithm Research And Implementation Of Elliptic Curve Public Key Cryptosystem

The elliptic curve public key cryptography is studied widely in the field of cryptology in recent years. The scalar multiplication in ECC is important to the rapid realization of ECC.Based on the geometric feature of Montgomery algorithm, a geometric multi-scalar multiplication mode was proposed, the analysis and realization of the rectangular multi-scalar multiplication and triangle multi-scalar multiplication show that the rectangular multi-scalar multiplication is simple, all-purpose and easy to realize.Further the triangle multi-scalar multiplication is proposed as an improvement, which enhanced the efficiency by 12.5%. Then some analysis and improvement on relevant multi-scalar multiplication was made to get general and expanded multi-scalar multiplication algorithm which was given epagoge and program verification. And then based on the subsection and parallel method, the improved algorithm was used to compute scalar multiplication, the analysis and realization shows that efficiency can be increased by about 37%. Finally, the subsection and parallel scalar multiplication algorithm was applied in ECC, the whole ECC was programmed in VC6.0. The research of this paper possesses good performance on the the signature verification and elliptic curve scalar multiplication.