Improved DES algorithm based on irrational numbers

DES (data encryption standard) is a cryptographic standard. However, the applications of it are limited because of the small key space. Based on irrational numbers, an improved scheme that enhances the randomness of sub-key is proposed, in which the permutation is controlled by irrational number which is considered as false chaos. Moreover, the permutation controlled by data can be performed at high speed in generic CPU. It is shown that this scheme can expand the key space without costing any more time to run.