The current speech content authentication process directly constructs the extracted biometrics into a binary hashing sequence and stores them in the cloud for hashing matching, so the authentication process is vulnerable to similarity attacks, which may lead to the disclosure of biometrics and hash sequences. In order to solve the above problem, this paper proposes an algorithm that is speech BioHashing security authentication algorithm based on CNN hyperchaotic map. Firstly, the user terminal conducts on linear prediction coefficients (LPC) analysis for the pre-processed speech signal, then extracts the improved Mel frequency cepstral coefficients (MFCC) features to obtains the new feature parameter, and calculates the Euclidean distance of the parameter as the biometric vector. Then, the biometrics and the orthogonal set matrix which is constructed by the improved random Fourier measurement matrix are inner product to form biosafety templates, and the templates are further quantified into BioHashing sequences. Finally, the BioHashing sequences are encrypted by CNN hyperchaotic map encryption algorithm and upload them to the cloud server. The experimental results show that the biosafety template not only provides the safe template for the biometric, but also the encryption algorithm of CNN hyperchaotic map guarantees the safety of the BioHashing sequence. At the same time, the algorithm has better robustness and discrimination, and tamper detection and location can better detect and locate mute attacks and substitution attacks.