This paper presents two signature schemes which are specially designed so as to reduce the online computational work for a signer. In many schemes of signature, the signer's major online computational cost is the operation of modular multiplication which consists of an integer multiplication and a reduction. The proposed schemes are arranged to remove the operation of integer multiplication from online signing procedure. The benefit is to reduce the amount of online computations. Theoretically, while sizes of public key and secret key, signature size, and security level remain unchanged, the cost of online computations can be reduced about 14%, comparing with that of Schnorr signature scheme.