Multiple-input multiple-output (MIMO) communication systems have recently been considered as one of the most significant technology breakthroughs for modern wireless communications, due to the higher spectral efficiency and improved link reliability. The sphere decoding algorithm (SDA) has been widely used for maximum likelihood (ML) detection in MIMO systems. It is of great interest to develop low-complexity and high-speed VLSI architectures for the MIMO sphere decoders. The first part of this dissertation is focused on the low-complexity and high-speed sphere decoder design for the MIMO systems. It includes the algorithms simplification, and transformations, hardware optimization and architecture development. Specifically, we propose the layered reordered K-Best sphere decoding algorithm and dynamic K-best sphere decoding algorithm, which can significantly improve the detection performance or reduce the hardware complexity. We also present the efficient K-Best sorting architecture, which greatly simplifies the sorting operation of the K-Best SDA. In addition, we introduce the early-pruning K-Best SD scheme, which eliminates the unlikely candidate at early decoding stages, thus saves computational complexity and power consumptions. For the conventional sphere decoder design, we develop the parallel and pipeline interleaved sphere decoder architecture, which considerably increases the decoding throughput with negligible extra complexity. Finally, we design the efficient radius and list updating units for the list sphere decoder, which increases the speed of obtaining the new radius and reduces the complexity for generating the new candidate list. The wireless communication technologies are widely used for the benefits of portability and flexibility. However, the wireless security is extremely important to protect the private and sensitive information since the communication medium, the airwave, is shared and open to the public. Cryptography is the most standard and efficient way for information protection. The second part of this thesis is thus dedicated to the high-speed and efficient architecture design for the cryptography systems including ECC and Tate pairing. We propose an efficient fast architecture for the ECC in Lopez-Dahab projective coordinates. Compared with the conventional point operation implementations, the point addition and doubling operations can be significantly accelerated with reasonable hardware overhead by applying parallel processing and hardware reusing. Moreover, we develop a complexity reduction scheme and an overlapped processing architecture for the Tate pairing in characteristic three. The proposed architecture can achieve over 2 times speedup compared with conventional sequential implementations for the Duursma-Lee and Kwon-BGOS algorithms.