Hardware implementations of cryptography face increasingly more stringent demands for lower cost and greater computational power. In order to meet those demands, more efficient approaches to implementations are needed. This paper presents detailed studies of MixColumn and InvMixColumn operations used in Advanced Encryption Standard that aim at their hardware implementations in constrained environments. Our studies are supported by mathematical analysis of both transformations and lead to efficient serial and parallel decompositions. Furthermore, deeper resource sharing is demonstrated at word-, byte- and bit-level. All derived architectures are evaluated using popular low-cost field-programmable gate arrays. Application of proposed methods resulted in reduction of reconfigurable logic area of the complete cipher by up to 20%.

The new design methodology for secret-key block ciphers, based on introducing an optimum number of pipeline stages inside of a cipher round is presented and evaluated. This methodology is applied to five well-known modern ciphers, Triple DES, Rijndael, RC6, Serpent, and Twofish, with the goal to first obtain the architecture with the optimum throughput to area ratio, and then the architecture with the highest possible throughput. All ciphers are modeled in VHDL, and implemented using Xilinx Virtex FPGA devices. It is demonstrated that all investigated ciphers can operate with similar maximum clock frequencies, in the range from 95 to 131 MHz, limited only by the delay of a single CLB layer and delays of interconnects. Rijndael, RC6, Twofish, and Serpent achieve throughputs in the range from 12.1 Gbit/s to 16.8 Gbit/s; and Triple DES achieves the throughput of 7.5 Gbit/s. Because of the optimum speed to cost ratio, the proposed architecture seems to be very well suited for practical implementations of secret-key block ciphers using both FPGAs and custom ASICs. We also show that using this architecture for comparing hardware performance of secret-key block ciphers, such as AES candidates, operating in non-feedback cipher modes, leads to the more prudent and fairer analysis than comparisons based on other types of pipelined architectures.