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We present a combinatorial algorithm for transformation of long input binary strings to short codewords called the passwords. Having received the password and another long binary string, the decoder has to decide whether it can be considered as a corrupted version of the input string or not. In the presented examples, the length of strings is 10 Kbytes, the code rate has the order of magnitude 10-4, the decision about the closeness of strings has to be made if the Hamming distance is less than 4096, and the decoding error probabilities that can be attained by the algorithm have the order of magnitude 2-17. The algorithm is derived on the basis of random coding arguments and the proposed probabilistic data reduction scheme, which show that an efficient authentication can be organized with the use of passwords having much smaller length than the length of the original data.