We propose a framework for designing randomized stream ciphers with enhanced security. The key attribute of this framework is using of nonlinear bijective mappings or keyless hash functions for random coding. We investigate the computational security of the proposed ciphers against chosen-plaintext-chosen-initialization-vector attacks and show that it is based on the hardness of solving some systems of random nonlinear Boolean equations. We also provide guidelines for choosing components to design randomizers for specified ciphers.