Abstract. A simple one-way function along with its proposed application in symmetric cryptography is described. The function is computable with three elementary operations on permutations per byte. Inverting the function, using the most efficient method known to the author, is estimated to require an average computational effort of about 2260 operations. The proposed stream cipher based on the function was designed to be efficient in software implementations and, in particular, to eliminate the known weaknesses of the alleged RC4 keystream generator while retaining most of its speed and simplicity.