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Public-key cryptosystems using very large distance algebraic codes have been studied previously. Private-key cryptosystems using simpler codes have also been subject of some study recently. This paper proposes a new approach to the private-key cryptosystems which allows use of very simple codes such as distance 3 and 4 Hamming codes.This new approach gives not only very efficient encoding/decoding and very high information rates but also appears to be secure even under chosenplaintext attacks.