  In this paper, we give the mutually unbiased bases on the p^2 -dimensional
quantum system where p is an odd prime number, and construct the corresponding
unitary transformation based on the properties of these mutually unbiased
bases. Then, we construct a (N,N) threshold secret sharing scheme using unitary
transformation between these mutually unbiased bases, and analyze the scheme's
security by several ways, for example, intercept-and-resend attack,
entangle-and-measure attack, Trojan horse attack, and so on. Using our method,
we construct a single-particle quantum protocol involving only one qudit, and
the method shows much more scalability than other schemes.
