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In the context of the rapid development of quantum computing technology, in order to meet the security requirements of cryptographic applications, this paper proposed an ElGamal public key cryptosystem based on Polar codes. The paper adopted Polar codes as the public code in the ElGamal public key cryptosystem based on error-correcting codes, used SC decoding algorithm to decode, and analyzed the decoding failure probability and security of the scheme. The results show that the algorithm has a high transmission rate, the selected parameters meet the requirements of information set decoding complexity and decoding failure probability, and the algorithm meets IND-CPA security. [ABSTRACT FROM AUTHOR]