The paper review the public-key cryptosystems based on the error correcting codes such as Goppa code, BCH code, RS code, rank distance code, algebraic geometric code as well as LDPC code, and made the comparative analyses of the merits and drawbacks of them. The cryptosystem based on Goppa code has high security, but can be achieved poor. The cryptosystems based on other error correcting codes have higher performance than Goppa code. But there are still some disadvantages to solve. At last, the paper produce an assumption of the Niederreiter cascade combination cryptosystem based on double public-keys under complex circumstances, which has higher performance and security than the traditional cryptosystems.
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