This paper introduces the classification of the navigation signal authentication technology, introduces the two methods of navigation message authentication (NMA), ECDSA and TESLA, which are commonly used, and compares and analyzes these two methods. This paper analyze the research background and mainstream design ideas of the navigation message authentication method of the Galileo navigation system from Europe and the GPS navigation system from the United States. With the continuous development of the world satellite navigation system, civil navigation security will be more and more concerned by the countries have the navigation system and the researchers.