Study of Safe Elliptic Curve Cryptography over Gaussian Integer

抄録

Gaussian integer has a potential to enhance the safety of elliptic curve cryptography (ECC) on system under the condition fixing bit length of integral and floating point types, in viewpoint of the order of a finite field. However, there seems to have been no algorithm which makes Gaussian integer ECC safer under the condition. We present the algorithm to enhance the safety of ECC under the condition. Then, we confirm our Gaussian integer ECC is safer in viewpoint of the order of finite field than rational integer ECC or Gaussian integer ECC of naive methods under the condition.