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Classic Feistel Networks and various types of FN's are sequential in nature. [1]has a good overview of different types. But is there a way we can do Feistel Networks in parallel and achieve good security bounds ?
The standard way to make best advantage of parallelism is to use a parallelizable mode of operation. For instance, counter mode (CTR mode) is highly parallelizable. Parallelism at the level of the mode of operation is typically more effective and easier to implement than parallelism inside the block cipher.
The Feistel network approach to block ciphers is inherently sequential, so not a good candidate for parallelization. If you wanted to do fine-grained parallelism inside the block cipher, you'd probably design your block cipher differently (e.g., a la Serpent and bitslice ciphers) -- but doing parallelism at the level of the mode of operation is typically even more effective.
MISTY 2 structure provide possibility of parallelism. Two rounds can be evaluated in parallel. New Block Encryption Algorithm Misty.
This advantage is taken also when designing larger s-boxes from smaller ones.
The main advantage of the MISTY network is that it can offer a reduced latency because the first two S-Boxes can be evaluated in parallel. Construction of Lightweight S-Boxes using Feistel and MISTY structures
