  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.
