Techniques for compressing binary input data streams and files by reducing entropy of the input data prior to compression. Entropy reduction is achieved by first getting a stream of single-digit decimal pseudo random numbers and calculating the frequency of occurrence of each decimal number in the even and odd positions of the pseudo random number stream. Subsets of the frequencies of occurrence of the decimal digits are selected to best match the frequency of occurrence of “0” and “1” in the odd and even positions of the binary input data stream. The decimal digits of the subsets of frequencies of occurrence are selectively set to “0” or “1” thereby creating a binary pseudo random number (i.e. mapping) stream, which is XORed with the binary input stream and compressed. Decompression uses the same pseudo random number stream using the mapping stream and the seed number used during compression.