This article presents a performance comparison of two known public key cryptography techniques namely RSA (Rivest–Shamir–Adleman) and El-Gamal algorithms to encrypt/decrypt the speech signals during transferring over open networks. Specifically, this work is divided into two stages. The first stage is enciphering-deciphering the input speech file by employing the RSA method. The second stage is enciphering-deciphering the same input speech file by employing the El-Gamal method. Then, a comparative analysis is performed to test the performance of both cryptosystems using diverse experimental and statistical analyses for the ciphering and deciphering procedures like some known speech quality measures: histogram, spectrogram, correlation, differential, speed performance and noise effect analyses. The analyses outcomes reveal that the RSA and El-Gamal approaches are efficient and adequate for providing high degree of security, confidentiality and reliability. Additionally, the outcomes indicate that the RSA speech cryptosystem outperforms its counterpart the El-Gamal speech cryptosystem in most of ciphering/deciphering speech performance metrics.