With the advent of IoT and Cloud computing service technology, the size of user data to be managed and file data to be transmitted has been significantly increased. To protect users' personal information, it is necessary to encrypt it in secure and efficient way. Since servers handling a number of clients or IoT devices have to encrypt a large amount of data without compromising service capabilities in real-time, Graphic Processing Units (GPUs) have been considered as a proper candidate for a crypto accelerator for processing a huge amount of data in this situation. In this paper, we present highly efficient implementations of block ciphers on NVIDIA GPUs (especially, Maxwell, Pascal, and Turing architectures) for environments using massively large data in IoT and Cloud computing applications. As block cipher algorithms, we choose AES, a representative standard block cipher algorithm; LEA, which was recently added in ISO/IEC 29192-2:2019 standard; and CHAM, a recently developed lightweight block cipher algorithm. To maximize the parallelism in the encryption process, we utilize Counter (CTR) mode of operation and customize it by using GPU's characteristics. We applied several optimization techniques with respect to the characteristics of GPU architecture such as kernel parallelism, memory optimization, and CUDA stream. Furthermore, we optimized each target cipher by considering the algorithmic characteristics of each cipher by implementing the core part of each cipher with handcrafted inline PTX (Parallel Thread eXecution) codes, which are virtual assembly codes in CUDA platforms. With the application of our optimization techniques, in our implementation on RTX 2070 GPU, AES and LEA show up to 310 Gbps and 2.47 Tbps of throughput, respectively, which are 10.7% and 67% improved compared with the 279.86 Gbps and 1.47 Tbps of the previous best result. In the case of CHAM, this is the first optimized implementation on GPUs and it achieves 3.03 Tbps of throughput on RTX 2070 GPU. [ABSTRACT FROM AUTHOR]