| Summary: | 碩士 === 逢甲大學 === 資訊工程學系 === 103 === Abstract—In recent years, Elliptic Curve Cryptography (ECC) to be attracted the attention of researcher and product developer. There are two reasons, first is having powerful mathematical structure; attackers need to know background of elliptic curve arithmetic will be easy attack. Second, for using less bit of key to reach the same safety with RSA encryption algorithm, therefore, to keep enough safety, when bit of key increase gradually, relative to RSA encryption algorithm, process time of ECC will reduce, with this characteristic, when we keep same safety in resource-constrained device, ECC will be suitable to use in the environment.
This paper is based on implementation of ECC to design two safety protocols; one is Diffie–Hellman key exchange (D-H). This target of protocol is to give both communications can exchange a key in safety to provide following using encryption and decryption. The second one is digital signature algorithm (DSA) .Its purpose is to prevent non-repudiation. However digital signature can be divided into two parts, signature and verification. These two protocols are based on point arithmetic, includes point addition and point doubling. And these two point arithmetic are both from finite field arithmetic, this paper is based on GF(
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