Due to the existence of indeterminate equation integer solutions and the difficulty of large numbers factorization, a publicly verified secret sharing scheme was proposed based on Shamir(t, n) threshold scheme. With the difficulty of big integer factorization, the scheme established a secret share for the sharers and calculated special solution combination of equation through the existence of indeterminate equation integer solutions. Share secret was recovered common calculation of sharers' secret share and special solution combination elements. In addition, the scheme realized the effective validation of the secret share, between the participants, as well as participants and the distributors. Security analysis shows that the scheme is safe, and has certain practical value.