## 6 Security Analysis  
The most crucial security concern of the signature techniques is the potential retrieval of the private key or the forgery of the signature process, which we will discuss below. HMPS represents a complex approach to ensuring both message integrity and confidentiality by combining elements of ElGamal-based encryption with symmetric architecture. The ciphertext is formed by the expression \(c=a\times s+m\), where \(m\) is the plaintext message, and \(s\) is a symmetric encryption key known only to the communicating parties. This intricate combination of digital signatures and encrypted message handling introduces a multi-layered security scheme resistant to attacks from both external and internal adversaries. A comprehensive analysis of the proposed HMPS requires examining its security guarantees against different types of attackers. This begins by considering an external attacker who has no privileged access to the system. Such an adversary's primary objectives would likely include forging a valid signature, \(\sigma\), and decrypting the ciphertext, \(c\), to recover the message, \(m\), or the key, \(s\), or both. First, the security of the signature generation process relies heavily on the computational infeasibility of solving the discrete logarithm problem. For a more secure protocol, the modulus, \(p\), can be kept secret, so the attacker cannot obtain it. The signature, \(\sigma\)  
Figure 2: Illustrative use case for the proposed protocol: (1) the accident occurs; (2) the blue vehicle detects the accident; (3) the blue vehicle sends a message to an LEC; (4–5) the LEC sends a message to an NTCC via satellite; (6–7) the NTCC sends a message to other vehicles via satellite. computed by \(a\); then, \(b\) binds the message, \(m\), to the signer, ensuring both the authenticity and integrity of the message. Without knowledge of the private key, \(k\), an attacker cannot generate a valid signature for any message, thus preventing forgery. Moreover, the inclusion of a hash function in the signature computation ensures that the signature is uniquely tied to the specific content of the message. A cryptographically secure hash function possesses properties such as pre-image resistance, second pre-image resistance, and collision resistance. Pre-image resistance ensures that, given a hash output, it is computationally infeasible to determine the original input. Second pre-image resistance makes it difficult to find a different input that produces the same hash output. Collision resistance further ensures that it is unlikely to find two different messages producing the same hash value. These properties collectively ensure that, even if an attacker attempts to manipulate the message content, they cannot produce a valid signature for a modified message. The confidentiality of the message, \(m\), is protected by the ciphertext \(c\). Here, \(s\) serves as a symmetric encryption key, adding an additional layer of security. Since the values of \(a\), \(s\), and \(m\) are all unknown to an external attacker, Equation (6) does not readily reveal \(m\) without solving for multiple unknowns simultaneously. The security of the symmetric key, \(s\), is paramount; ensuring that it is securely generated and shared between the communicating parties without interception is critical for maintaining the confidentiality of the message. Analyzing the level of security against brute force attacks, it is evident that the protocol leverages both the strength of the ElGamal system and the unpredictability introduced by the symmetric key encryption. The discrete logarithm problem for recovering \(k\) is computationally infeasible for sufficiently large values of \(p\), or keeping \(p\) secret for more security. This property, coupled with the complexity of guessing \(a\) or deducing \(s\) from the ciphertext, makes a direct brute force approach impractical for an external attacker.