Is DES a Pure Cipher? (Results of More Cycling Experiments on DES)

Abst rac t During summer 1985, we performed eight cycling experiments on the Data Encryption Standard (DES) to see if DES has certain algebraic weaknesses. Using special-purpose hardware, we applied the cycling ciosure test described in our Eurocrypt 85 paper to determine whether DES is a pure cipher. We also carried out a stronger version of this test,. ( A cipher is pure if, fgr a n y keys i , j , k , there exists some key 1 such that T,T’-’Tk = z, where T, denotes encryption under key w.) In addition, we followed the orbit of a randomly chosen DES transformation for 236 steps, as well as the orbit of the composition of two of the “weak key’ transformations. Except for the weak key experiment, our results are consistent with the hypothesis that DES acts like a set of randomly chosen permutations. In particular, our results show with overwhelming confidence that DES is not pure. The weak key experiment produced a short cycle of about 233 steps, the consequence of hitting a fixed point for each weak key.