Efcient Scalar Multiplications In Elliptic Curve Cryptosystem

As a promising branch of modern cryptography, elliptic curve cryptosystem (ECC),with advantages of short key and high security, is especially suitable for informationsecurity applications in resource-constraint devices such as smart cards, mobile plat-form and wireless network nodes. This thesis focuses on efficient or fast algorithmsof scalar multiplications in ECC. With regard to single-scalar multiplication, we firststudy existing coordinates, low weight representations and fast point operations, thenimprove the m-DBL operation formulae to achieve faster arithmetic. After that, wepropose our new evaluation scheme that takes advantage of m-DBL, and combine itwith the Frac-wMOF form with the ?exibility to utilize memory. Our scheme offersfaster computation than the mixed coordinates method for a broad range of I/M ra-tios. In comparison to the general left-to-right scheme, our scheme saves 7.71% ofcost in general cases. With regard to dual-scalar multiplication, we propose modifiedltrJSF form by adding one round of recoding to ltrJSF at the cost of a larger digit set.By taking advantage of it, we propose our m-DBL and modified ltrJSF based dual-scalar multiplication algorithm including new evaluation scheme using m-DBLDAand 18-points precompuation strategy. Both the theoretical analysis and simulationresult prove that our algorithm speeds up the dual-scalar multiplication by 2.7%-6.1%on average, compared to original algorithm.