• https://gitlab.com/imtheforce/pat
• https://bitbucket.org/fourthorigin/pat
• https://github.com/NoviceLive/pat

I learned from pwntools that there is another kind of sequences, named De Bruijn sequence, which is powerful and has excessive potentials.

Check it if you are interested.

Its pattern looks like the following as produced by cyclic provided by pwntools.

$ cyclic 400
aaaabaaacaaadaaaeaaafaaagaaahaaaiaaajaaakaaalaaamaaanaaaoaaapaaaqaaaraaasaaataaauaaavaaawaaaxaaayaaazaabbaabcaabdaabeaabfaabgaabhaabiaabjaabkaablaabmaabnaaboaabpaabqaabraabsaabtaabuaabvaabwaabxaabyaabzaacbaaccaacdaaceaacfaacgaachaaciaacjaackaaclaacmaacnaacoaacpaacqaacraacsaactaacuaacvaacwaacxaacyaaczaadbaadcaaddaadeaadfaadgaadhaadiaadjaadkaadlaadmaadnaadoaadpaadqaadraadsaadtaaduaadvaadwaadxaadyaad

$ cyclic -l yaad
396

pip install pat works, elevate privilege if necessary.

Python composable command line utility.

Simple cross-platform colored terminal text in Python.

Python module for cross-platform clipboard functions.

A high level API for Python internationalization.

This is not used for the time being.

./pat.py --help
Usage: pat.py [OPTIONS] ARGUMENT [SETS]...

  Customizable Lazy Exploit Pattern Utility.

Options:
  -V, --version          Show the version and exit.
  -b, --big-endian       Use big-endian.
  -O, --optimal INTEGER  Use the optimal profile in this position.
  -o, --output FILENAME  Write to this file.
  -c, --clipboard        Output to the clipboard.
  -v, --verbose          Be verbose.
  -q, --quiet            Be quiet.
  -h, --help             Show this message and exit.

• Create a pattern of length 100 using the default profile.

  ./pat.py 100
  Aa0Aa1Aa2Aa3Aa4Aa5Aa6Aa7Aa8Aa9Ab0Ab1Ab2Ab3Ab4Ab5Ab6Ab7Ab8Ab9Ac0Ac1Ac2Ac3Ac4Ac5Ac6Ac7Ac8Ac9Ad0Ad1Ad2A

• Locate the pattern Cz9 in the default profile.

  ./pat.py Cz9
  2337

• Locate the pattern in hex, 0x5a6232, using the default profile.

  For big-endian systems.

  ./pat.py 0x5a6232 -b
  19536

• Create a pattern of length 200 in optimal 3-position profile.

  ./pat.py 200 -O3
  AVqAVrAVsAVtAVuAVvAVwAVxAVyAVzAV0AV1AV2AV3AV4AV5AV6AV7AV8AV9AWqAWrAWsAWtAWuAWvAWwAWxAWyAWzAW0AW1AW2AW3AW4AW5AW6AW7AW8AW9AXqAXrAXsAXtAXuAXvAXwAXxAXyAXzAX0AX1AX2AX3AX4AX5AX6AX7AX8AX9AYqAYrAYsAYtAYuAYvAY

• Search for pattern vAY in optimal 3-position profile.

  ./pat.py vAY -O3
  197

See pydoc pat.Pat.

Simply speaking, it is a string of continuous numbers in some special positional numeral systems, where symbols in each position are mutually unique, often with a big radix.

It can be created by taking the needed count of characters from the Cartesian product of chosen character sets.

• Three-position: The most popular choice

  • Maximum Length

    26 ² * 10 * 3 B = 20280 B = 19 KiB.

  ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789

Suppose that we have a limited set of characters, e.g. alphanumeric ones, in which there are 62 characters available.

According to the inequality of arithmetic and geometric means, fixed radix systems will achieve the best length.

• Maximum Length

  21 ² * 20 * 3 B = 26460 B = 25 KiB

ABCDEFGHIJKLMNOPQRSTU VWXYZabcdefghijklmnop qrstuvwxyz0123456789

• Maximum Length

  16 ² * 15 ² * 4 B = 230400 B = 225 KiB

ABCDEFGHIJKLMNOP QRSTUVWXYZabcdef ghijklmnopqrstu vwxyz0123456789

• Maximum Length

  8 ⁶ * 7 ² * 8 B = 102760448 B = 98 MiB

ABCDEFGH IJKLMNOP QRSTUVWX YZabcdef ghijklmn opqrstuv wxyz012 3456789