We introduce a new family of symmetric block ciphers based on group bases. The main advantage of our approach is its full scalability. It enables us to construct, for instance, a trivial 8-bit Caesar cipher as well as a strong 256-bit cipher with 512-bit key, both from the same specification. We discuss the practical aspects of the design, especially the choice of carrier groups, generation of random group bases and an efficient factorization algorithm. We also describe how the cryptographic properties of the system are optimized, and analyze the influence of parameters on its security. Finally we present some experimental results regarding the speed and security of concrete ciphers from the family.