A fault injection attack is a sort of side-channel attack in the domain of cryptography. The concept is to derive the secret key by analyzing the correct and incorrect ciphertext and is more efficient and powerful than traditional cryptanalysis. This article introduces three common algorithms, Advanced Encryption Standard (AES), RSA, and Elliptic Curve Cryptography (ECC). Then provides an in-depth discussion and analysis of how they can be accelerated in practice and how they may be subjected to fault injection attacks.