The paper proposes a general method for construction cryp- toschemes based on dificulty of simultaneous solving factoring (FP) and discrete logarithm modulo prime problem (DLpP). The proposed approach is applicable for construction digital signa- tures (usual, blind, collective), public key encryption algorithms, public key distribution protocols, and cryptoschemes of other types. Moreover, the proposed approach provides reducing the signature size and increasing the rate of the cryptoschemes, while comparing with the known designs of the digital signature protocols based on the FP and DLpP.