In recent years, cryptographic chips have developed rapidly. However, they are also facing a significant threat from non-invasive attacks. Although both international and domestic standards provide testing methods for non-invasive attacks, these standards are formulated for public algorithms and are not applicable to private algorithms, which still present considerable security risks. This study proposes a detection framework for private-algorithm cryptographic chips, which includes three components: timing analysis tests, simple power/electromagnetic analysis tests, and differential power/electromagnetic analysis tests. For the timing analysis test, a method based on average denoising is adopted, which significantly improves the accuracy of execution time measurements. Methods based on visual observation and cross-correlation analysis are presented for simple power/electromagnetic analysis tests. Finally, for differential power analysis, TVLA-1 and TVLA-2 are employed to detect leakages from various sources and evaluate the vulnerabilities of private-algorithm cryptographic chips to differential power attacks. The proposed framework serves as an effective supplement to traditional non-invasive attack detection, significantly expanding its application range. To verify the effectiveness of the framework, black-box experiments are conducted on several cryptographic chips. The results demonstrate that the framework can effectively assess the resilience of private-algorithm cryptographic chips against non-invasive attacks.