# Negotiation-Free Encryption for Securing Vehicular Unicasting Communication
## 5 Feasibility and Safety Analysis
### Security Analysis  
**Lemma 1**.: _The Cloud stores a large amount of vehicles' state information, and it is characterized by accuracy, timeliness, confidentiality, integrity, etc._  
Proof of Lemma 1.: The Negotiation-free encryption algorithm depends on the state information of the vehicle. Therefore, there is a high requirement for the accuracy, timeliness, confidentiality and integrity of the state information. Thanks to the rapid development of V2X and sensor technology, the state of the vehicle can be accurately measured and stored in the cloud, which ensures the accuracy of the data. When the vehicle-end requests the data in the cloud, it will follow a mechanism through which vehicles can check their own history state and can also request the real-time state of other vehicles. However, one cannot query the historical state of other vehicles. Thus, one can use different permissions of the vehicle state to ensure the confidentiality of the information transmission. In the Negotiation-free encryption algorithm, the establishment process of the session key can be shortened or even canceled. To a large extent, this ensures the timeliness of message transmission. These states can be viewed as collections of infinite attributes, such as the density of the vehicle around vehicles, the signal strength, etc. Therefore, the vehicle can be viewed as a mobile object in which its state can be measured, and the entropy of the state value is very large. The integrity of information transmission can be ensured by using signatures to identify the source of the public key to prevent attacks from middlemen.  
**Lemma 2**.: _For the passive attacker, there is no security problem._  
Proof of Lemma 2.: No matter whether the cloud uses its own private key or a shared public key to decrypt the message sent by the vehicle that uses the public key to encrypt the query request, it fully complies with the existing public key encryption protocol. For passive attackers, there will be no security issues at all.  
**Lemma 3**.: _For the active Man-in-the-Middle Attack, it is very difficult to decrypt the ciphertext in vehicle-to-vehicle communications when an attacker intercepts the message._  
Proof of Lemma 3.: This encryption algorithm proposed by us naturally prevents the active Man-in-the-Middle Attack. When vehicle A send a message to vehicle B, the timestamp and vehicle B's real-time state value are used to encrypt the message. If an attacker intercepts the message and modifies the timestamp, the ciphertext information will not be decrypted, since the correct state value cannot be obtained.  
**Lemma 4**.: _Even if the attacker intercepts the ciphertext and obtains the timestamp, he is still unable to decrypt the ciphertext._  
Proof of Lemma 4.: The ciphertext between vehicles is encrypted based on the historical state of the receiver. At this time, for any users, only the receiver can query the value of its own history state from the cloud. This means that others cannot obtain the prerequisites to decrypt the ciphertext, and thus the problem is solved.  
**Lemma 5**.: _The attacker uses the exhaustive method to attack the ciphertext through brute force, but the algorithm is still in a safe state._  
Proof of Lemma 5.: If attackers use brute force to decrypt the ciphertext, they have to traverse all the possible status values until they find the right one. However, the Negotiation-free encryption has a great feature in that the entropy value of the key space is very large. These states can be considered as a collection of infinite properties around the vehicle, such as the vehicle density, signal strength, etc. The state can be measured while the entropy value of the state is large. That is, the value range is large and cannot be completed at all for a limited time.