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

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, 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 new validity check in the verification phase to overcome this drawback. Our new schemes are based on XTR public key system, and can realize GF(p6) security by computations in GF(p2) without explicit constructions of GF(p6), where p is a prime. Compared with the VMSS schemes using RSA and linear feedback shift register (LFSR) public key cryptosystems, we 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 two schemes are dynamic and threshold changeable, which means that it is efficient to implement our schemes when participants, secrets or the threshold needs to be changed.