Authenticated Encryption Schemes with Linkage Between Message Blocks

Nyberg and Rueppel proposed a digital signature scheme, which is the first signature scheme based on the discrete logarithm problem and provides message recovery. One of the main advantages of that digital signature scheme over the ElGamal-type digital signature scheme is that it can be combined with ElGamal encryption in a natural manner. We call this combination the authenticated encryption scheme. The major property of digital signature with message recovery is that the verification equation recovers the message itself. Hash function, thus, cannot apply to the message as in the regular signture schemes; otherwise, the message cannot be recovered. For this reason, we need some extra methods to link up the message blocks if there are more than one message blocks needing to be transmitted. In this paper, we propose an efficient authenticated encryption scheme with message linkage based on the discrete logarithm problem. The computation and communication costs in our scheme are lower than those of the straightforward method.