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A very preliminary presentation of this paper was done at the rump session of CRYPTO '86 and kindly played by Gus Simmons (Sandia). The full paper will be complete description of some cycling experiments applied to DES using only very fast software for the computations. Using only software permitted many measures and tests.The used version of DES has a speed of about 2 Mbits/sec for a given key and a speed of about 600 kbits/sec for a change of key and an encryption (this version is not fully optimized due to some problems with the cache of the computer). For these experiments we used the idle time of an IBM 3090 and a total of 234 encryptions were performed. Many techniques were used in order to avoid duplicate computations and big files.