Abstract: Based on the security of RSA (Rivest-Shamir-Adleman) cryptosystem and Hash function, a threshold multi-secret sharing scheme with different weights was proposed. In the scheme, each participant can share many secrets with other participants by holding only one secret shadow. Each participants secret shadow is selected and saved by himself and even the secret dealer does not know anything about it. In the recovery phase, participant only needs to submit a pseudo-shadow instead of his secret shadow. The scheme does not require a secure channel between each participant and the dealer, and can guarantee secure delivery and verify authenticity of information. Analyses show that the scheme is more secure and feasible than the existing ones.

Key words: secret sharing, threshold scheme, Rivest-Shamir-Adleman (RSA) cryptosystem, Hash function

摘要： 考虑参与者权重不同，基于RSA密码体制和Hash函数的安全性，设计了一种参与者有权重的多重秘密共享方案。方案中，参与者只需维护一个秘密份额，可实现对多个秘密的共享。秘密份额由参与者确定和保管，秘密分发者也不知晓，秘密共享过程中，只需出示伪秘密份额。方案不需要安全信道，算法能够保证信息安全传送，以及验证参与者是否进行了欺骗。分析表明，方案具有更高的安全性和可行性。

关键词: 秘密共享, 门限方案, RSA密码体制, Hash函数