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The article proposes a method for constructing public-key block cipher schemes based on the difficulty of the discrete logarithm problem on elliptic curves. The schemas are construc according to the proposed method and can simultaneously perform security functions and authenticate the origin and integrity of the encrypted message. In addition, a shared secret key is established between the sender/encryptor and the receiver/decryptor for each encrypted message based on public key cryptography which also improves the security of these cipher schemes.