twenty4/README.md

TWENTY4 - a fun stream cipher

THIS IS JUST FOR LEARINING CRYPTO, DO NOT EVER USE THIS FOR ANYTHING

This is the implementation of the fun stream cipher TWENTY4 by T.v. Dein, 09/2015. Published under the public domain, Creative Commons Zero License. It works bytewise, with keys between 1-256 bits in 17 rounds, uses S-Boxes and key output-feedback mode. The cipher also works with CBC or ECB mode (sample CBC implementation included).

The name TWENTY4 is a reverence to article 20 paragraph 4 of the german constitution which reads:

All Germans shall have the right to resist any person seeking to abolish this constitutional order, if no other remedy is available.

Also, the cipher uses the contents of the german constitution as the source for its S-Boxes.

S-Box generation

TWENTY4 uses the german constitution (called "basic law" in germany) as the source for S-Boxes. The EPUB version (included in sbox/ subdir) is encrypted using AES-256-CBC with the passphrase "grundgesetz\n". The resulting byte stream is used as the source for S-Boxes.

The following version of the german consitution is used:

Basic Law for the Federal Republic of Germany in the revised version published in the Federal Law Gazette Part III, classification number 100-1, as last amended by the Act of 23 December 2014 (Federal Law Gazette I p. 2438).

Linux Shell commands to generate the S-Boxes:

curl -o BJNR000010949.epub http://www.gesetze-im-internet.de/gg/BJNR000010949.epub echo grundgesetz > BJNR000010949.pass cat BJNR000010949.epub | openssl aes-256-cbc -kfile BJNR000010949.pass | ./gen-static-sbox

'gen-static-sbox' compiled from gen-static-sbox.c in this directory, which has SHA256 checksum: 29bfd8bd6dbca696d4d8b7ca997497e091875d6bf939e9702b1edf669d0742b0.

However, it just prints out bytes which it reads from STDIN, collecting them into an 256 byte array, ignoring possible duplicates, and prints it out as hex.

Both S-Boxes are bijective and have the following properties (calculated using analyze.c):

Char distribution: 100.000000% Char redundancy: 0.000000% Char entropy: 8.000000 bits/char Compression rate: 0.000000%

TWENTY4 uses two S-Box arrays, one for key expansion and one for encryption.

Key expansion

The input key will be expanded into a 17 byte array. Maximum key size is 17 bytes (136 bit).

IV = KU[0] for ROUND in 0..16 if KU[ROUND] K[ROUND] = IV xor KU[ROUND] else K[ROUND] = IV yor KBOX[ROUND * 8]; endif K[ROUND] = KBOX[K[ROUND]] IV = K[ROUND] endfor

for KROUND in 0..31 for ROUND in 0..17 K[ROUND] = IV xor (rotateleft-3(K[ROUND]) xor KBOX[rcon(IV)]) IV = K[ROUND] endfor endfor

where:

KU: input key K[17]: initial round key array ROUND: encryption round 1-17 KROUND: key expansion round 1-32 KBOX[256]: pre computed S-Box for key expansion

Encryption

for INBYTE in OUTBYTE = INBYTE for ROUND in 0..17 OUTBYTE = OUTBYTE xor K[ROUND] OUTBYTE = OUTBYTE xor SBOX[OUTBYTE] OUTBYTE = rotateleft-ROUND%8(OUTBYTE) OUTBYTE = rotateright-4(K[ROUND]) endfor rotatekey(K, OUTBYTE) OUTBYTE => endfor

func rotatekey(K, B) [rotate K[17] array elementy 1 to the right] for N in 0..16: K[N] = KBOX[K[N] xor B] endfor endfunc

where:

K[17]: expanded key ROUND: encryption round 1-17 INBYTE: one input byte OUTBYTE: encrypted result for output SBOX[256]: pre computed S-Box for encryption

Analysis so far

While this stuff only exists for me to play around with crypto, I tried to test the cipher a little bit. Here are my results using a couple of statistical measurements:

I encrypted the GPLv3 contents using the key "1". To compare, I encrypted the same file with AES-256-CBC using the same passphrase.

Check using analyze.c

My own measurement, see analyze.c:

      File size: 35147 bytes

Char distribution: 100.000000% Char redundancy: 0.000000% Char entropy: 7.995333 bits/char Compression rate: 0.000000% (35147 => 35168 bytes)

For comparision, AES result:

     File size: 35168 bytes

Char distribution: 100.000000% Char redundancy: 0.000000% Char entropy: 7.994892 bits/char Compression rate: 0.000000% (35168 => 35189 bytes)

Check using ent

(ent from http://www.fourmilab.ch/random/):

Entropy = 7.995333 bits per byte.

Optimum compression would reduce the size of this 35147 byte file by 0 percent.

Chi square distribution for 35147 samples is 229.98, and randomly would exceed this value 86.79 percent of the times.

Arithmetic mean value of data bytes is 127.6631 (127.5 = random). Monte Carlo value for Pi is 3.172955438 (error 1.00 percent). Serial correlation coefficient is -0.004405 (totally uncorrelated = 0.0).

For comparision, AES result:

Entropy = 7.994892 bits per byte.

Optimum compression would reduce the size of this 35168 byte file by 0 percent.

Chi square distribution for 35168 samples is 250.98, and randomly would exceed this value 55.94 percent of the times.

Arithmetic mean value of data bytes is 127.8717 (127.5 = random). Monte Carlo value for Pi is 3.151680601 (error 0.32 percent). Serial correlation coefficient is 0.002014 (totally uncorrelated = 0.0).

Check using dieharder

I fed the contents of my primary disk into TWENTY4 and its output into diehard:

dd if=/dev/sda4 of=/dev/stdout | ./stream 1 e | dieharder -a -g 200 #=============================================================================#

dieharder version 3.31.1 Copyright 2003 Robert G. Brown

#=============================================================================# rng_name |rands/second| Seed | stdin_input_raw| 1.86e+05 |2067533949| #=============================================================================# test_name |ntup| tsamples |psamples| p-value |Assessment #=============================================================================# diehard_birthdays| 0| 100| 100|0.11286983| PASSED
diehard_operm5| 0| 1000000| 100|0.14228207| PASSED
diehard_rank_32x32| 0| 40000| 100|0.08372938| PASSED
diehard_rank_6x8| 0| 100000| 100|0.47630577| PASSED
diehard_bitstream| 0| 2097152| 100|0.68878582| PASSED
diehard_opso| 0| 2097152| 100|0.36965490| PASSED
diehard_oqso| 0| 2097152| 100|0.85360068| PASSED
diehard_dna| 0| 2097152| 100|0.41389081| PASSED
diehard_count_1s_str| 0| 256000| 100|0.64198483| PASSED
diehard_count_1s_byt| 0| 256000| 100|0.48126427| PASSED
diehard_parking_lot| 0| 12000| 100|0.61281762| PASSED
diehard_2dsphere| 2| 8000| 100|0.98794548| PASSED
diehard_3dsphere| 3| 4000| 100|0.86553337| PASSED
diehard_squeeze| 0| 100000| 100|0.47837267| PASSED
diehard_sums| 0| 100| 100|0.26661852| PASSED
diehard_runs| 0| 100000| 100|0.78455791| PASSED
diehard_runs| 0| 100000| 100|0.56428921| PASSED
diehard_craps| 0| 200000| 100|0.81900152| PASSED
diehard_craps| 0| 200000| 100|0.54592338| PASSED
ctrl-c

(FIXME: I aborted here, I'll repeat that one later)

So, all those checks don't look that bad, but of course this doesn't say much about TWENTY4. However, not THAT bad for the first cipher :)