Key Safe Algorithms for Blockchain Technologies

In the fast-changing world of blockchain tech, keeping cryptographic algorithms secure and efficient is crucial, especially for managing keys in groups. This paper compares three cryptographic algorithms—Shamir's Secret Sharing Scheme, Blakley's Scheme, and the Asmuth-Bloom Scheme—to see how well they work in managing group keys in blockchain systems. We look at how fast they are and how well they resist attacks to understand their strengths and weaknesses in blockchain. Key management is really important for keeping things secure with cryptography, especially in systems like distributed ledgers. We study how long it takes to use Shamir's Secret Sharing, Blakley's Scheme, and the Asmuth-Bloom Scheme in blockchain, showing how efficient and scalable they are, which matters a lot in big distributed systems. We also look at how secure these cryptographic schemes are against different types of attacks, like trying lots of passwords, intercepting messages, working together to attack, and finding vulnerabilities in the system. By focusing on both efficiency and security, we try to get a clear picture of which cryptographic scheme is best for blockchain, especially when managing group keys securely and dynamically. In our research, we found that in terms of speed, Shamir's Secret Sharing Scheme outperforms the Asmuth-Bloom Scheme and Blakley's Scheme, with Shamir being the fastest, followed by Asmuth and then Blakley. However, regarding security, all three schemes demonstrate robustness against various attack vectors. We also discovered that Shamir Secret Sharing Scheme’s efficiency could be further enhanced by implementing Newton's interpolation technique for value interpolation.