New (k,l,m)-verifiable multi-secret sharing schemes based on XTR public key system
This work provides an incremental improvement in the security and efficiency of verifiable multi-secret sharing schemes for cryptographic system designers and users, particularly in scenarios requiring dynamic and threshold-changeable secret sharing.
This paper proposes two new verifiable multi-secret sharing (VMSS) schemes based on the XTR public key system. These schemes address vulnerabilities in previous methods by Dehkordi and Mashhadi (2008), specifically by adding validity checks to detect malicious dealer behavior. The new schemes achieve GF(p^6) security with computations in GF(p^2), offering the same security as RSA and LFSR-based VMSS schemes with shorter parameters.
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.