Improved Indifferentiability Analysis Of SIMON-like Key-alternation Feistel Ciphers

After the indifferentiability between a Feistel construction and a random permutation is proven,researchers start to study how to mix a key into such a Feistel construction which is provably secure.In a Feistel construction with n-to-n-bit random functions which are public and independent,an identical key is mixed into a half of the whole state,which is exactly a basic structure of SIMON family.More specifically,the state is updated by:(Xi,xi-1)?(xi-1(?)Fi(xi)(?)k,xi).In the paper,an idea adopted from John Steinberger et al.is applied to the simulator which is exploited by Guo and Lin for their proof.It is successfully shown that 18 rounds are sufficient to realize the indifferentiability from ideal ciphers with 2n-bit blocks and n-bit keys,which is a reduction from 21 rounds to 18 rounds to achieve indifferentiability from an ideal cipher.