Taking into account the need for personal communications impervious to eavesdroppers, and commercial communications resistant to industrial espionage, the author shows how to build very strong and flexible, yet easily implemented symmetric-key block cipher, using an algebraic system, which can be a little "defective", and which is named a generalized finite field. The cipher presented works in CBC mode, may practically have any block length, any key length, and can be used for encrypting messages of any kind and of any size.