Cryptographic Properties and Application of a Generalized Unbalanced Feistel Network Structure

In this paper, we study GF-NLFSR, a Generalized Unbalanced Feistel Network (GUFN) which can be considered as an extension of the outer function

FO

of the KASUMI block cipher. We prove upper bounds for the differential and linear hull probabilities for any

n

 + 1 rounds of an

n

-cell GF-NLFSR. Besides analyzing security against differential and linear cryptanalysis, we provide a frequency distribution for upper bounds on the true differential and linear hull probabilities. We also demonstrate a (2

n

 − 1)-round impossible differential distinguisher and a (3

n

 − 1)-round integral attack distinguisher on the

n

-cell GF-NLFSR. As an application, we design a new block cipher Four-Cell based on a 4-cell GF-NLFSR. We prove the security of Four-Cell against differential, linear, and boomerang attack. Based on the 7-round impossible differential and 11-round integral attack distinguisher, we set the number of rounds of Four-Cell to be 25 for protection against these attacks. Furthermore, Four-Cell can be shown to be secure against other attacks such as higher order differential attack, cube attack, interpolation attack, XSL attack and slide attack.