A design technique based on the composite power residue codes has been proposed for building new constructions of nonlinear substitution S-boxes of length N = 256 and volume |S| = 8.6248×10^13. The synthesized constructions possess good cryptographic properties, appreciably amplify and extend the class of Nyberg constructions of the Rijndael cipher and also ensure the possibility of their application as a long-term key.
