Secret sharing was proposed primarily in 1979 to solve the problem of key distribution. In recent decades, researchers have proposed many improvement schemes. Among all these schemes, the verifiable multi-secret sharing (VMSS) schemes are studied sufficiently, which share multiple secrets simultaneously and perceive malicious dealer as well as participants. By pointing out that the schemes presented by Dehkordi and Mashhadi in 2008 cannot detect some vicious behaviors of the dealer, we propose two new VMSS schemes by adding validity check in the verification phase to overcome this drawback. Our new schemes are based on XTR public key system, and can realize $GF(p^{6})$ security by computations in $GF(p^{2})$ without explicit constructions of $GF(p^{6})$, where $p$ is a prime. Compared with the VMSS schemes using RSA and linear feedback shift register (LFSR) public key cryptosystems, our schemes can achieve the same security level with shorter parameters by using trace function. What's more, our schemes are much simpler to operate than those schemes based on Elliptic Curve Cryptography (ECC). In addition, our schemes are dynamic and threshold changeable, which means that it is efficient to implement our schemes according to the actual situation when participants, secrets or the threshold needs to be changed.

中文翻译：

---

基于XTR公钥系统的新型(k,l,m)-可验证多秘密共享方案

秘密共享主要是在 1979 年提出来解决密钥分发问题的。近几十年来，研究人员提出了许多改进方案。在所有这些方案中，可验证的多秘密共享（VMSS）方案得到了充分的研究，该方案​​同时共享多个秘密并感知恶意经销商和参与者。通过指出 Dehkordi 和 Mashhadi 在 2008 年提出的方案无法检测到经销商的一些恶意行为，我们提出了两种新的 VMSS 方案，通过在验证阶段添加有效性检查来克服这一缺陷。我们的新方案基于 XTR 公钥系统，可以通过 $GF(p^{2})$ 中的计算实现 $GF(p^{6})$ 的安全性，而无需显式构造 $GF(p^{6} )$，其中 $p$ 是素数。与使用 RSA 和线性反馈移位寄存器 (LFSR) 公钥密码系统的 VMSS 方案相比，我们的方案可以通过使用跟踪功能以更短的参数实现相同的安全级别。更重要的是，我们的方案比基于椭圆曲线加密 (ECC) 的方案更易于操作。此外，我们的方案是动态的，阈值可变的，这意味着当参与者、秘密或阈值需要改变时，根据实际情况来实施我们的方案是有效的。