## 2 Preliminary Knowledge  
### ECEIS Method  
With the fast development of the public key system, [PERSON] [25] and [PERSON] [26] independently proposed a cryptosystem based on elliptic curves in 1985. Subsequently, [PERSON] et al. [27] discussed the elliptic curve cryptosystems and their implementation, which leads to the Menezes-Vanstone cryptosystem. Compared with other public key encryption systems like RSA, ECC presented better performance in terms of efficiency and security due to the significantly shorter keys. Despite these good attributes being shown, however, in [28], under certain conditions, the Menezes-Vanstone cryptosystem is insecure, which means it could not be considered a probabilistic encryption algorithm. On the basis of the Diffie-Hellman augmented encryption scheme (DHAES) presented in [29] in 1998, ECIES was presented in [30], which contained the vital attributes of the DHAES with the usage of elliptic curves in an integrated scheme: (1) public key operations, (2) symmetric encryption algorithms, (3) MAC codes, and (4) hash computations.  
[PERSON] et al. discussed a variety of the ECIES, and introduced the functions of the basic ECIES:  
* Key agreement (KA): Function used for the generation of a shared secret by two parties.
* Key derivation (KDF): Mechanism that produces a set of keys from keying material and some optional parameters.
* Hash (HASH): Digest function.
* Encryption (ENC): Symmetric encryption algorithm.
* Message authentication code (MAC): Information used to authenticate a message [31]. The whole encryption procedure was narrated below:  
1. Before starting the process, a pair of temporary keys must be generated by the sender. We assume that the private key in this key pair will be named as u, and the name for the public key will be U.
2. By using the sender's temporary private key and the recipient's public key (we define it as V here and the private key is v) together, a shared secret value is obtained through the key agreement function, KA.
3. The shared secret value (and optionally with other parameters) will be taken as the input data for the KDF (key derivation function). After the process of the KDF, the encryption key, noted as \(k_{ENC}\), and the MAC key, noted as \(k_{MAC}\), are both obtained in the format of the concatenation.
4. By using the ENC symmetric algorithm and the encryption key \(k_{ENC}\), the plain message will be encrypted as a cipher message (Here we denoted as c).
5. With the fabrication through the MAC function, a tag will be produced by the input of the MAC key and the encrypted message c.
6. Finally, the sender will concatenate these three parts together: (1) the temporary public key U; (2) the encrypted message c; and (3) the tag. The final message which will be sent to the recipient is in the following format: U\(\mid\)\(\mid\)c\(\mid\) tag [32]. For the recipient, by using the reversed procedure, the plain message will be obtained. The specific flow charts for encryption and decryption of the ECIES are shown in Figures 1 and 2.  
In this paper, an open-source python application provided by ecies.org is applied to the encryption of the sensitive data related with the initial parameters of the hyperchaotic system.