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Cryptographic cores are the key components to enforce information security properties related to confidentiality and integrity. Since the security of a cryptographic core implementation and the security of the cryptographic algorithm itself from the mathematical perspective are two different problems, cryptographic cores may contain hidden security vulnerabilities such as design flaws and side channels. Security analysis methods based on functional verification rely heavily on the quality of test vectors and usually have low test coverage, which is difficult to meet the security verification requirements of security-critical components like cryptographic cores. This work proposes a cryptographic core security verification and vulnerability detection method from the perspective of information flow security. The proposed method can accurately measure all logical information flows in cryptographic core designs to formally verify security properties such as confidentiality and integrity. It can detect potential security vulnerabilities in cryptographic implementations by capturing harmful information flows. Experimental results show that our information flow security verification method is effective in detecting sensitive information leakage caused by the design vulnerabilities and side channels in cryptographic cores.