Calculation of cryptographic characteristics for a cipher based on a generalized Feistel network

Cipher Specification

$F:Z_2^n \times Z_2^n\to Z_2^n$ - bijective in the second variable function. $\omega_i \in Z_2^n\ (Z_{2^n})$ - words.

Round transformition $R^F[l,s]:Z_2^{mn} \to Z_2^{mn} $:

$R^F [l,s] (\omega_1,...,\omega_m)=(\omega_1,...,\omega_{s-1},F(\omega_l,\omega_s),\omega_{s+1},...,\omega_m) $

The composition $R^F[l_1,s_1]R^F[l_2,s_2]...R^F[l_h,s_h]$ implements substitution on the $nm$-bit block: $\Phi^F_N : Z_2^{nm}\to Z_2^{nm}$

Subtitution parameters: $n, m, h$, where $h$ - number of rounds (or height). Network (sequence of pairs ($l$, $s$)) - also public parameter. The secret parameter is $F$ (tipical size $n$ - byte, so $n=8 $).

Example Network for 7 Rounds: $m=4,\ h=7$, and network $N=(1,2),(2,4),(4,3),(3,1),(1,2),(2,1),(1,4) $

Experiment

1. This work considers networks only $(s_0, s_1), (s_1, s_2),..., (s_{i\ mod(m)}, s_{i+1\ mod(m)}),... = (1,2),(2,3),(3,4),... $
2. An equally probable choice of $F$ with the return from the set of all matrices whose rows are permutations (the cardinality of such a set is $(2^{n}!)^{2^{n}} \sim 2^{n2^{2n}}$).
3. Calculate MDP, AI, NL.

Build

cd ~
git clone https://github.com/jmpleo/netcip-crypt-char.git
cd ~/netcip-crypt-char

Research Build

1. You need cmake to build this porject.

   cd ~/netcip-crypt-char/netcip-research

   and run

   ./build.sh <N> <M> <H>

   or

   cmake . -D__N=<N> -D__M=<M> -D__H=<H>
   cmake --build build

2. Build range configuration

   Linux:

   ./brut-build.sh

3. Run Computing

   For example, NL-computing:

   cd ~/netcip-crypt-char/netcip-research/stat
   ../bin/netcip-nl-<N>-<M>-<H>
   # saving in ./netstat-nl-<N>-<M>-<H>.csv

Application Build

cd ~/netcip-crypt-char/netcip-application
cmake -B build
cd build
make

after this tests and speedtest binaries created - run it:

~/netcip-crypt-char/netcip-application/bin/netcip-test
~/netcip-crypt-char/netcip-application/bin/netcip-speedtest

Founded

Cherednik, I. V. On the use of binary operations for the construction of a multiply transitive class of block transformations / I. V. Cherednik // Discrete Mathematics and Applications. 2021. 31: 2. P. 91–111.) (Scopus, WoS) // https://www.mathnet.ru/rus/dm1597