Stability‐guaranteed dynamic ElGamal cryptosystem for encrypted control systems

Designing Optimal Key Lengths and Control Laws for Encrypted Control Systems based on Sample Identifying Complexity and Deciphering Time

“…This is true in a traditional setup of public-key encryption, referred to as static-key encryption in this paper, where the keys used for encrypting all samples are identical [34]. On the other hand, when the keys of individual samples are completely different, in other words, dynamic-key encryption is used [33], the deciphering-time clearly depends on the number of samples. We show an explicit representation of τ (T, k) for each encryption scheme, and show an advantage of the dynamic case in terms of the security in Definition 5.…”

“…Statickey encryption is traditional public-key encryption of which the key pair is identical throughout the communication. In contrast, a key pair in dynamic-key encryption [33] is updated at a short time interval, e.g., a sampling period. Although dynamic-key encryption would improve the security level of encrypted control systems, its security has not yet been proved.…”

“…Although dynamic-key encryption would improve the security level of encrypted control systems, its security has not yet been proved. We extend the dynamic-key encryption scheme in [33] and provide a security proof of the extended scheme.…”

“…However, this approach is not suitable for realtime controls due to the high computational costs. As an alternative approach, we employ the dynamic-key encryption [33] that is an augmented concept of public-key encryption. The overview is as follows: First, give a key pair by Gen at the initial time.…”

“…Additionally, the dynamic-key encryption refreshes only the second element of ciphertext, and so, the first element remains the same value. In the following, we extend the dynamic-key encryption in [33] to update all components of ciphertext and provide the security proof of the scheme.…”