Secure Data Distribution and Reconstruction using Rainbow Antimagic Graph Coloring in Secret-Share Schemes

Conceitos Básicos

Rainbow Antimagic Connection Number (RACN) can be leveraged within secret-share schemes to facilitate secure transmission and reconstruction of sensitive information across multi-participant groups.

Resumo

The paper presents a method for enhancing data security through the application of Rainbow Antimagic Graph Coloring within secret-share distribution and reconstruction schemes.
Key highlights:

Secret-sharing schemes allow critical information to be divided and distributed across multiple participants, reducing the risk of a single point of failure.
The Rainbow Antimagic Connection Number (RACN) principle is used to split the secret into k pieces and distribute them among n participants, ensuring that the secret can only be accessed by authorized pairs of participants.
The reconstruction process involves a series of sequential phases to gather the minimum threshold of k shares required to reconstruct the original secret.
After successful reconstruction, a communication strategy is devised to securely disseminate the retrieved information to all relevant participants through multiple rounds of communication.
The number of participants, threshold values, and distribution method significantly impact the minimum stages required for successful secret reconstruction.
Theorems are provided to determine the RACN for various graph operations on path graphs, yielding insights into the minimum number of shares, participants, and reconstruction phases needed.
The scheme addresses challenges like data security, privacy, and flexibility, making it a robust approach for safeguarding sensitive information in multi-participant environments.

Estatísticas

The paper presents the following key data points:

For a graph with n = 2p participants, the number of shares to be distributed are:

D(2)
rac(Pp) = k = p + 1 for p ≡ 0 (mod 2), and k = p + 3 for p ≡ 1 (mod 2)
Spl(2)
rac(Pp) = k = p + 1

For a graph with n = 2p + 1 participants, the number of shares to be distributed is:

µrac(Pp) = k = 2p

The minimum number of participants m required from an n-participant group is:

m(D(2)
rac(Pp)) = 1/2(2p + 5 + (-1)^(p-1))
m(Spl(2)
rac(Pp)) = p + 2 for p ≥ 2, p ≠ 3, and p + 1 for p = 3
m(µrac(Pp)) = 2p + 1

The number of reconstruction phases is:

RP(D(2)
rac(Pp)) = 1 when p is even, and 2 when p is odd
RP(Spl(2)
rac(Pp)) = 1 for p ≥ 2, p ≠ 3, and 2 for p = 3
RP(µrac(Pp)) = 1

Citações

"Secret-sharing scheme has evolved as a most successful cryptographic technique that allows a secret to be divided or distributed among a group of participants in such a way that only a subset of those participants can reconstruct the original secret."
"The implementation of Rainbow Antimagic coloring within these schemes not only safeguards the data but also ensures an advanced level of information security among multi-participant groups."
"Leveraging the principles of RACN, we introduce a method for the secure transmission of secret shares. This approach ensures that secret information can be successfully reconstructed when transmitted along a rainbow path."

Principais Insights Extraídos De

Enhancing Data Security through Rainbow Antimagic Graph Coloring for Secret-Share Distribution and Reconstruction

by Raul M. Falc... às arxiv.org 04-29-2024

https://arxiv.org/pdf/2404.16843.pdf

Perguntas Mais Profundas

How can the scheme address the loss or corruption of a secret code, and what measures are in place to ensure successful recovery of the original secret despite such occurrences?

In the event of loss or corruption of a secret code in the scheme, several measures can be implemented to ensure the successful recovery of the original secret. One approach is to incorporate redundancy in the secret-sharing process by generating additional shares beyond the required threshold. By having extra shares distributed among participants, the loss or corruption of a single share would not impede the reconstruction of the secret. This redundancy ensures that even if some shares are compromised, the original secret can still be reconstructed.
Furthermore, error detection and correction techniques can be employed to identify and rectify any discrepancies or errors in the shared secret codes. By implementing error-correcting codes or checksums, participants can verify the integrity of their shares and detect any inconsistencies that may arise due to loss or corruption. Through error correction mechanisms, the scheme can automatically recover the original secret by recalculating or reconstructing the missing or erroneous parts of the secret.
Additionally, regular audits and monitoring of the shared secret codes can help detect any anomalies or discrepancies early on. By conducting periodic checks on the integrity and availability of the secret shares, any issues related to loss or corruption can be identified promptly, allowing for timely intervention and recovery measures to be implemented.

How does the absence of closed circuits impact the scheme and secret communication, and what strategies can be employed to mitigate the challenges posed by such scenarios?

The absence of closed circuits in the scheme can significantly impact secret communication and the reconstruction process. Closed circuits play a crucial role in facilitating secure and efficient communication among participants by establishing direct paths for transmitting the reconstructed secret. Without closed circuits, the communication process may become fragmented, leading to delays, inefficiencies, and potential security vulnerabilities.
To mitigate the challenges posed by the absence of closed circuits, alternative communication strategies can be employed. One approach is to implement multi-hop communication protocols, where participants relay the reconstructed secret through intermediate nodes to reach all intended recipients. By leveraging a multi-hop communication framework, the secret can be securely transmitted across the network, even in the absence of direct closed circuits.
Furthermore, the use of encryption and secure communication channels can enhance the confidentiality and integrity of secret communication in the absence of closed circuits. Encrypting the reconstructed secret and transmitting it through secure channels can safeguard the information from unauthorized access or interception, mitigating the risks associated with open communication paths.
Implementing redundancy in communication paths and establishing backup routes can also help mitigate the impact of closed circuit absence. By creating redundant communication channels and alternative paths for transmitting the secret, the scheme can ensure reliable and resilient communication, even in challenging network conditions.

How can the number of communication rounds needed post-secret recovery be further minimized to enhance the efficiency and responsiveness of the overall system?

To minimize the number of communication rounds needed post-secret recovery and enhance the efficiency of the system, several strategies can be implemented:

Optimizing Communication Paths: By identifying and utilizing the most direct and efficient communication paths between participants, the number of rounds can be reduced. Employing algorithms that prioritize shortest paths or minimize the number of intermediate nodes can streamline communication and minimize the rounds needed.

Parallel Communication: Implementing parallel communication channels can enable multiple participants to receive the reconstructed secret simultaneously, reducing the overall time required for dissemination. By transmitting the secret to multiple recipients in parallel, the system can expedite the communication process and minimize the number of rounds needed.

Dynamic Threshold Adjustment: Introducing dynamic threshold adjustment mechanisms can optimize the number of participants required for secret reconstruction based on network conditions or security requirements. By dynamically adjusting the threshold value, the system can adapt to varying scenarios and minimize the rounds needed for successful secret recovery.

Efficient Routing Algorithms: Utilizing efficient routing algorithms, such as Dijkstra's algorithm or A* search, can help identify the most optimal communication paths and minimize the number of rounds required for secret dissemination. By leveraging intelligent routing strategies, the system can expedite communication and reduce the overall time needed post-secret recovery.

Real-time Monitoring and Feedback: Implementing real-time monitoring and feedback mechanisms can enable participants to provide instant confirmation of secret receipt, allowing for rapid progression to the next stage without unnecessary delays. By incorporating feedback loops, the system can ensure swift and efficient communication rounds post-secret recovery.

By integrating these strategies and leveraging advanced communication technologies, the number of communication rounds needed post-secret recovery can be minimized, enhancing the efficiency and responsiveness of the overall system.