Cloud computing is one of the most rapidly evolving technologies today; it provides numerous advantages that increase its affordability and dependability for use in the company. This paper goes over the concepts of cloud computing, such as its characteristics, deployment model, and service model, discusses the various benefits of cloud computing, and highlights the most pressing issues and security concerns in cloud storage. As a consequence, that leads to a review of distinctive cryptography algorithms that meet the security requirements (CIA: confidentiality, integrity, and availability) that are used to secure communications in cloud computing situations. It also displays many algorithms depending on the previous studies, such as Blowfish, RSA, DES, AES, MD5, Feistel, SP, HIGHT, LED, Cybpher, PRESENT, RC6, Diamond2, mCrypton, SLIM, Klein, PUFFIN-2, SEA, CLEFIA, LBlock, TWINE, 2, ANU, ANU-II, NLBSIT, Piccolo, BORON, RECTANGLE, LICI, QTL, LOGIC, TRIVIUM, Fruit-v2, Fruit-80, A4, the Enocoro family, and Grain family, to make a comparison among them using many measurements. It found that modern and lightweight algorithms are more suitable for use in this field. Furthermore, the purpose of this paper is to make some suggestions for improving the safety and security of cloud computing technologies.