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A method for constructing endomorphic stream-ciphers over the alphabet of an arbitrary finite order q, based on quasigroups, is described. The presented ciphers, due to their simplicity, can be easily implemented, giving in consequence a very fast speed of enciphering and deciphering. The ciphers are also much more secure than the stream-cipher over GF(2), because, if q > 2, the method allows one to form many invertible transformations which may be used to encipher and decipher; the number of these transformations increases very rapidly with respect to q.