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A new ELGamal-type public key cryptosystem using ergodic matrix is proposed in this paper, which is based on isomorphism over finite field. The security of this scheme is equal to the intractability of polynomial discrete logarithm problem over finite field in the standard mode. At the same time, an optimization is described after the performance is analyzed in details. Since the ciphertext expand rate of new scheme is approximately 1, the proposed scheme can encrypt more information one time. Moreover, compared with the original ELGamal scheme, its security has been not reduced.
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