Pat 0.3.0

Pat

Installation

pip install pat works, elevate privilege if necessary.

Mathematical Background

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.

Profiles

Default Profile

• Three-position: The most popular choice

  • Maximum Length: 20280 B = 19 KiB.

  ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789

Optimal Profiles

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.

Three-position

• Maximum Length: 26460 B = 25 KiB

ABCDEFGHIJKLMNOPQRSTU VWXYZabcdefghijklmnop qrstuvwxyz0123456789

Four-position

• Maximum Length: 230400 B = 225 KiB

ABCDEFGHIJKLMNOP QRSTUVWXYZabcdef ghijklmnopqrstu vwxyz0123456789

Eight-position

• Maximum Length: 102760448 B = 98 MiB

ABCDEFGH IJKLMNOP QRSTUVWX YZabcdef ghijklmn opqrstuv wxyz012 3456789

Usage

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

Options:
  -V, --version  Show the version and exit.
  -h, --help     Show this message and exit.

Examples

• 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.

  ./pat.py 0x5a6232
  19536

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

  ./pat.py 200 ABCDEFGHIJKLMNOPQRSTU VWXYZabcdefghijklmnop qrstuvwxyz0123456789
  AVqAVrAVsAVtAVuAVvAVwAVxAVyAVzAV0AV1AV2AV3AV4AV5AV6AV7AV8AV9AWqAWrAWsAWtAWuAWvAWwAWxAWyAWzAW0AW1AW2AW3AW4AW5AW6AW7AW8AW9AXqAXrAXsAXtAXuAXvAXwAXxAXyAXzAX0AX1AX2AX3AX4AX5AX6AX7AX8AX9AYqAYrAYsAYtAYuAYvAY

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

  ./pat.py vAY ABCDEFGHIJKLMNOPQRSTU VWXYZabcdefghijklmnop qrstuvwxyz0123456789
  197