We present an efficient improvement of the strong RSA signature scheme [1], which is very similar to Fischlin signature [2]. Both two signatures are based on strong RSA assumption. In the original scheme, the signer has to choose a prime with prescribed length in signing phase. Except that, three generators of QR_n should be chosen in the setup phase. Our scheme removes or relaxes these restrictions. It only needs to choose two generators of QR_n and an odd. Our scheme saves about 1/2 computational cost of the original scheme. Moreover, we propose a blind signature scheme and a partially blind signature scheme based on the basic scheme. To the best of our knowledge, it?s the first time to propose such a blind signature scheme and a partially blind signature scheme based on strong RSA assumption.