# Why 3 round Feistel cipher are not common

Luby and Rackoff showed that 3 rounds are sufficient to make the Feistel networks a pseudorandom permutation.

Question: why are 3 round Feistel Ciphers not common?

My thoughts about the round functions of Luby and Rackoff construction are

1. They are hard to find one
2. They are hard to analyze
3. They are complex to fit small devices.
4. 3 rounds of Luby and Rackofd constructions are slower than 16 rounds non-Luby and Rackoff constructions. Assuming that they have the same security.
• how do they not fit on small devices ? the same circuitry can be used on encryption and decryption Oct 13 '18 at 13:03
• @hardyrama Well, this is maybe a bit older issue where we have very limited devices. If the $F$ function in Feistel is complex i.e. requires more space to satisfy Luby and Rackoff requirements, then a simple $F'$ that requires small space can fit the device. Of course, will have a bigger key scheduling algorithm. Oct 13 '18 at 15:00
• @PaulUszak These are my thoughts, I will try to find reasons or counter examples. If the speed of the a Luby and Rackoff round function is $>16/3$ where a unit 1 is non-LR's speed then this is the case. Oct 13 '18 at 15:11