Verifiable Multi-secret Sharing Schemes from Homogeneous Linear Recursion

The research on secure and efficient implementation method of secret sharing has been a hotspot in the field of information security and cryptography. Based on homogeneous linear recursion, we construct two new verifiable multi-secret sharing schemes. In our schemes, all participants themselves select their shares, so the calculation amount of dealer is reduced and secure channel between the dealer and any participant is avoided. Compared with other similar schemes, our schemes have more advantage, such as low calculation amount and no secure channel. In addition, security analysis also shows that our schemes can resist ordinary attacks.