Can we parallelize the Feistel Networks? 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 ?


Hoang, Viet Tung, and Phillip Rogaway. "On generalized Feistel
networks." Advances in Cryptology–CRYPTO 2010. Springer Berlin
Heidelberg, 2010. 613-630.
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.