## 5 Security Properties  
A mature blockchain system should fulfill three security attributes established [58; 59]. The security properties guarantee blockchain accuracy, consensus, and validity with a high probability, whereas redaction designs must not impact them. They are classified as follows:  
* **Chain Quality:** It refers to the ratio of the blocks controlled by an adversary in a chunk of an honest party's chain that cannot exceed a certain fraction \(X\) where it represents the total amount of adversary-dominated resources.
* **Common Prefix:** Formally common prefix property represents two honest node chains S1 and S2, whereas the shortest chain is a common prefix for the longest chain at different time segments T1 and T2. The common prefix \(\text{K}\in\mathbb{Z}\) indicates the number of blocks required to be removed from a timely older chain. If \(\text{S1}\leq\text{S2}\) where \(\text{T1}\leq\text{T2}\), it means removing k blocks at the end of S1 and becoming a common prefix to S2.
* **Chain Growth:** The growth of an honest chain must be compatible with the number of blocks produced regardless of adversarial employed methodology.  
The security properties guarantee blockchain accuracy, consensus, and validity with a high probability. Specifically, accuracy maintains the \"healthy\" degree of a redactable  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multicolumn{2}{c}{**Public**} & \multicolumn{2}{c}{**Private**} & \multirow{2}{*}{**Consortium**} \\  & \multicolumn{2}{c}{**(Permissionless)**} & & **(Permissioned)** & \\ \hline \multirow{2}{*}{**Network**} & \multirow{2}{*}{Decentralized} & \multicolumn{2}{c}{Decentralized} & Hybrid Among Public and \\  & & & Partially & Private \\ \hline \multirow{2}{*}{**Access**} & \multirow{2}{*}{Any participant} & \multicolumn{2}{c}{Predefined} & Multiple Predefined \\  & & & Participant & & Participants \\ \hline \multirow{5}{*}{**Concept**} & 1. & Read and write & \multirow{5}{*}{1.} & Conditional & \multirow{5}{*}{1.} & Permission \\  & & transactions. & & read and write & & read/write by multi \\  & 2. & Vote to add & & operations. & controlling nodes. \\  & & & transactions. & 2. & Conditional & \\  & 3. & Validate & & verification. & & among participated \\  & & transactions and consequently & 3. & Public read & entities. \\  & & they are secured. & & & allowed. & \\ \hline \multirow{2}{*}{**Consensus**} & \multirow{2}{*}{PoW/PoS} & \multirow{2}{*}{Multi party} & \multirow{2}{*}{Multi party} & \multirow{2}{*}{Multi party} \\ \hline
**Approval Time** & 10 Minutes & 100 ms & & 100 ms \\ \hline
**Scalability** & Slow & Fast, Light & Fast, Light \\ \hline
**Security,** & Lack of privacy and & \multirow{2}{*}{High Privacy} & \multirow{2}{*}{High Privacy} & \multirow{2}{*}{High Privacy} \\
**Privacy** & & anonymity. & & \\ \hline
**Cost** & Costive. & Costive. & Costive. \\ \hline
**Energy** & High Consumption & Low Consumption & Low Consumption \\ \hline
**Efficiency** & Non-Efficient & Efficient & Efficient \\ \hline
**Immutability** & Non-tempered & Can Be Tampered & Can Be Tampered \\ \hline
**Centralization** & No & Yes & Partially \\ \hline
**Use Cases** & Cryptocurrency & Supply Chain & Banking, Insurance \\ \hline
**Application** & Bitcoin & Ethereum & Edexa \\ \hline \hline \end{tabular}
\end{table}
Table 1: Blockchain types.  
blockchain, while consensus necessitates all honest nodes to concur on a particular sequence. Meanwhile, validity specifies that most blocks emanate from honest nodes [59]. A redaction technique is required to not impact the aforementioned blockchain security properties.