New (k,l,m)-verifiable multi-secret sharing schemes based on XTR public key system

TL;DR

This paper introduces two new verifiable multi-secret sharing schemes based on the XTR public key system, offering enhanced security, simplicity, and flexibility over existing schemes using RSA, LFSR, or ECC.

Contribution

The paper proposes novel VMSS schemes utilizing XTR cryptography with added validity checks, improving security, efficiency, and adaptability compared to prior methods.

Findings

Achieve GF(p^6) security via GF(p^2) computations without explicit GF(p^6) construction.

Shorter parameters for same security level compared to RSA and LFSR-based schemes.

Schemes are simpler, dynamic, and threshold changeable, facilitating practical implementation.

Abstract

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.