## 2 Encryption Principle  
### Elliptic Curve Cryptography  
In the past few years, blockchain technology has gained significant attention due to its association with digital currencies. The unique features of blockchain technology, such as decentralization, nontampering, nonforgeability, and traceability, have been thoroughly researched [18]. By applying blockchain technology to the secure storage of spatiotemporal big data, the limitations of traditional centralized models can be overcome, and the security of spatiotemporal big data can be ensured. The Internet of Things and the Internet have led to the generation of an enormous amount of spatiotemporal big data worldwide. Therefore, it has become an urgent task to ensure the storage security of spatiotemporal big data.  
Elliptic curve cryptography (ECC) was first discovered in 1985 by [PERSON] et al. The security of the ECC cryptosystem is based on the intractability of the elliptic curve discrete logarithm problem. ECC has several advantages compared with other public key cryptosystems, such as RSA, DSA, and DH. ECC can use smaller elliptic curve groups while maintaining the same security level, resulting in smaller key sizes, reduced storage and transmission requirements, and faster operations. These advantages of ECC not only solve implementation difficulties that arise from increasing the key length of other public key cryptosystems to enhance the security of the cryptosystem, but also enable fast encryption and decryption, digital signatures, key exchange, identity authentication, and other applications [19]. The specific applications of ECC can be seen in the following aspects:  
1. Applications within ECDSA: The elliptic digital signature algorithm first produces a message digest through a hash function, followed by signature computation using the elliptic curve. Private keys are utilized for signing, while public keys serve verification purposes [20].
2. Deployment in wireless networks: Certificates encompass the public key and signature of both the certificate issuer and the certificate holder, with the signature relying on ECC [21].
3. Implementation on web servers: This approach curtails the data and time transmitted between the system and application program, thus enhancing practicality; it conserves time and bandwidth, while addressing compatibility issues more effectively through algorithm negotiation [22].
4. Utilization in IC cards: In the absence of a dedicated processor, ECC swiftly and securely executes digital signatures on IC cards, a feat difficult to achieve in RSA systems. Additionally, ECC minimizes the program code, key length, and certificate size, substantially reducing IC card costs [23].  
Addressing the issue of secure storage for blockchain spatiotemporal big data, this paper introduces a secure storage scheme founded on elliptic curve encryption.  
For finite fields \(Fp\), the addition operation on elliptic curves is defined as follows. Suppose a point \(P=(x1,y1)\) and \(Q=(x2,y2)\) on \(E\).  
Null:  
\[O+P=P,\;O+O=O\;(\text{point at infinity}) \tag{3}\]  
Click to add:  
\[P+Q=\begin{cases}O&x_{1}=x_{2}\;\text{and}\;y_{1}=-y_{2}\\ \left(x_{3},\;y_{3}\right)&\text{others}\end{cases} \tag{4}\]  
\[in,k=\begin{cases}\left(3x_{1}+a\right)/2y_{1}(mod\;p)&P=Q\\ \left(y_{2}-y_{1}\right)/\left(x_{2}-x_{1}\right)\;(mod\;p)&P\
eq Q\end{cases} \tag{5}\]  
\[x_{3}=k^{2}-x_{1}-x_{2}\;(mod\;p) \tag{6}\]  
\[y_{3}=k(x_{1}-x_{3})-y_{1}\;\;(mod\;p) \tag{7}\]  
Doubling:  
\[if\;P=Q,\;then\;P+Q=2P \tag{8}\]  
Dot multiplication:  
\[kP=P+P+\dots+P \tag{9}\]