Multiple Time Servers Timed-Release Encryption Based on Shamir Secret Sharing

Timed-release encryption (TRE) is a cryptographic primitive that can realize the data be decrypted and accessed only at a specified time in the future preset by the data sender. Currently, most TRE schemes adopt noninteractive single time server mode. However, once the single time server is attacked or corrupted, it is prone to directly threaten the TRE security application. Although there are some TRE schemes that "distribute" the single time server into multiple ones, there is a problem that they cannot resist single-point failure. For this reason, a multi-time server TRE scheme based on Shamir secret sharing and its variant scheme are proposed. In our proposed schemes, the ciphertext can be decrypted when the number of time trapdoors obtained by the data receiver exceeds or equals to the threshold. It can not only guarantee the security of data sender's identity privacy information, but also greatly improve the reliability of TRE. Security analysis shows that our schemes have data confidentiality, verifiability, anti-advance decryption and multi-time trapdoor robust decryption. Efficiency analysis shows that when choosing a reasonable threshold, the computational efficiency of our schemes is slightly improved compared with the existing multiple time servers TRE schemes.