scalar multiplication
3.In this paper, it applies the technique of Artificial Neural Network to classify the EM signals from the scalar multiplication in ECC, and gets the secret parameter in scalar multiplication successfully.
4.Finally, a totally new multiplication algorithms in finite field GF(2~n), which is designed according to the sliding-window algorithms used in scalar multiplication in ECC.
5.In this new protocol, the authentication code of the its initiator depend on the shared long term key, but the authentication code of the its responder relies on session key, and the session key is a hashed value of concatenation of the long-term shared key, the scalar multiplication of the long-term private key and ephemeral public key, and the scalar multiplication of the private key and long-term public key, which ensure that the protocol resists key-compromise impersonation.
6.The main place of innovation of this paper is to grasp the advantage of different algorithms, from different angles and levels improve modular exponentiation algorithm and scalar multiplication algorithm, and achieve new algorithm which can provide reference to the implementation of RSA and ECC,meantime the new algorithm have greater practical value.
7.When a message is encrypted in (H)ECC, there will be a large amount of message expansion. Due to this fact, (H)ECC is often applied in Diffie-Hellman key agreement protocols and digital signature schemes, though ECC encrypting cards have appeared but only devised for some special kind of small data area. In the application of hyperelliptic curve cryptosystems, the key operation is divisor scalar multiplication.
