| Summary: | 碩士 === 東吳大學 === 資訊科學系 === 92 === In 1985, Miller and Koblitz independently proposed a new public key cryptosystem, called elliptic curve cryptosystem (ECC), whose security is based on the elliptic curve discrete logarithm problem (ECDLP). The key length of ECC is shorter than that of other public key cryptosystems in the same security strength, for instance, the key length of ECC with 160 bits and the key length of RSA or Diffie-Hellman with 1024 bits have the same security strength. Since the elliptic curve operations are more complex then RSA or Diffie-Hellman, we propose a fast computational algorithm that uses joint window non-adjacent form for the simultaneous scalar multiplication on an elliptic curve, where k, l are scalars, and P, Q are the points on elliptic curve. The joint window non-adjacent form will be reduced the joint Hamming weight by above 5%, and the better efficiency can be gained by using the direct formula of doubling operations.
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