Multi-secret sharing scheme based on XOR operations in combination with AES-GCM
Haoyi Sun, Shuihai Zhang, Chunli Lv · 2023
Blakley and Shamir independently proposed the basic idea of (k, n)-threshold secret sharing schemes in 1979. To this day, most secret sharing schemes, represented by Shamir's scheme, often require arithmetic operations in the Galois field. Such schemes are difficult to meet the needs of low cost, low power consumption and high performance in practical applications. Therefore, we propose an efficient secret sharing scheme based on XOR operations and improve it according to the requirements of multiple secret sharing. Our scheme is similar to Kurihara's scheme, but our scheme is relatively more concise and easier to understand. In addition, our scheme also eliminates the security implications of the reduction of random vectors when multiple secrets are shared by incorporating AES-GCM. In combination with the AES-GCM, we can verify the integrity of the secret. From experimental simulations, our solution is feasible and efficient, with our simulated PC program taking only 50 seconds to distribute a 1G byte file.