Difference between revisions of "Crimo Cipher"

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* Calculate compression rate compared to random shuffles, as a way to estimate non-randomness in the cipher.
 
* Calculate compression rate compared to random shuffles, as a way to estimate non-randomness in the cipher.
 
* Calculate symmetry of ngram counts (for example, the pairs of bigrams {01,10}, and {67,76} have roughly similar counts).
 
* Calculate symmetry of ngram counts (for example, the pairs of bigrams {01,10}, and {67,76} have roughly similar counts).
 +
* Test for longer repeating ngram patterns allowing for a fixed number of permitted errors / skips / nulls.
  
 
= Other Links =
 
= Other Links =

Latest revision as of 06:20, 18 July 2022

Background

Case information: https://en.wikipedia.org/wiki/Highland_Park_parade_shooting

Robert Eugene Crimo III perpetrated a mass shooting event on July 4th, 2022 in Highland Park, Illinois. He is an aspiring rapper, calling himself "Awake the Rapper", who posted music videos and violent content on social media.

He allegedly published an encrypted manifesto on Amazon. According to this Fandom page (formerly Wikia):

"Arcturus, or more formally known as 'Project Arcturus' is an archaic manifesto/book conceived by Robert Crimo (Awake). It was published on the 19th of February in the year 2021. It is 28 pages long and is composed entirely of an undeciphered sequence of numbers. There is a coinciding video to Arcturus on YouTube, which is composed of footage from the music videos to On My Mind, out.of.this.world, and Toy Soldier. The numbers 23, 47, and 115 seem to be of significance in decoding Arcturus, however, Arcturus remains an unsolved mystery." (Image)

Some people reported that the book's description on Amazon contained Morse code translating to "Hello Friend", which was the name of one of his music videos. In the video, a small building is shown while the camera pans slowly back while haunting music is played. Crimo's symbol appears to be mounted at the top right corner of the building. The scene then switches to a car with the number "47" painted on its side and a red zig zag pattern painted on the front. The haunting music is from the game Call of Duty Black Ops Cold War, a piece titled Comrade by Jack Wall. (2:08 in this video)

One of Crimo's videos, titled Building A F$@_ing Cabin In The CITY, shows the date Feb 2021 printed on an unfinished wall of the cabin. The same cabin appears in his Hello Friend video. The manifesto was also apparently published on Feb 2021.


Connections / Similarities

Alessa tumblr

Some people found this tumblr page which features Awake's symbol in the profile picture. The post contains a mysterious message and a series of symbols (moons, stars, etc.) that resembles an encoded message. The current version of the page shows that the profile picture has changed. The archive shows references to Awake the Rapper. It's unclear if the references were made before or after Crimo was arrested.

Arcturus Project

The Arcturus project, a seemingly unrelated site, describes a radio signal received from the star Arcturus in 1997. The signal is described as a binary sequence, and the site appeals to readers to help decode the mysterious signal. However, the task is a fiction constructed to challenge people to complete the decryption, which is a binary representation of an image containing a further message.

The Arcturus Code

A book titled The Arcturus Code, by Randy Kovicak, is a story about a boy who discovers a mysterious code beaming from the star Arcturus.

Equestria At War: Arcturus cipher

In a game called Equestria at War, an "Arcturus Cipher" appears. Evidently it is an ASCII Shift Cipher +41.


Online discussions

Images

  • Images of entire book
  • PDF format:
  • Word search book that was listed on Amazon by the same seller as the Arcturus book. There is speculation it could be a possible key. The book's author is listed as Samuel Bromley.


Transcriptions


Observations

  • The book contains 27 pages of numbers.
  • Only the first 9 pages are unique. The next 9 and last 9 pages are repeats of the first 9 pages.
  • Each page has 38 rows, and 86 characters per row, for a total of 3268 characters per page.
  • In some of his online posts, Crimo emphasizes the number 333. The book is 27 pages long which is a perfect cube: 3x3x3.
  • Each 9 page group has a total of 29412 characters (88236 for all 27 pages).
  • The book's description on Amazon included the phrase "Hello Friend" encoded in Morse code. (Image)
  • One additional book was listed under the same seller on Amazon. The title was Classic Large Print Word Search Book For Adults (Image). Being listed together with Arcturus led to speculation it may be a hint or key. PDF of the book is linked above.
    • The puzzles vary in size, such as 16x16, 18x18, and 23x23.
  • JFGariepy's "exhaustive offset analysis"


Unigrams

  • Index of Coincidence: 0.104
  • Frequency count
    • 9, 1, and 2 have relatively low frequencies.
    • 6, 7, and 3 have relatively high frequencies.
  • Frequency count, window size 1000 (interactive plot)
  • There is a backtick character in the bottom right corner of the 2nd, 11th, and 20th pages of numbers. The affect rows still have a length of 86.
  • The cipher seems to have a bias against 9s (i.e., there are far fewer 9s than other digits).
  • There is evidence of multiple alphabets but with a wide span.

Ngrams

Heat Maps


Cycles

  • The cipher appears to demonstrate some cycling behavior.


Sliding Window tests

Does the cipher have consistent statistics throughout? If not, maybe that is evidence of a different scheme being used in different sections. The following plots use a window size of 1000 applied to different parts of the first 9 pages of Crimo's cipher. The plots marked "no overlap" move the window 1000 positions forward with each step. The ones marked "overlap" move the window 1 position with each step.

Index of Coincidence

Homophone cycles (length 2)

Keyboard number distance tests

Keyboard test

Did Crimo simply "mash the keyboard" to generate a seemingly random sequence of digits? What if the distance between successive number reflects short distances between number keys on his keyboard? I made three measurements:

  • Average distance between successive digits, based on 1D layout of number keys (horizontal row on standard keyboard).
    • Observed to be 29 sigma above average compared to shuffles.
  • Average distance between successive digits, based on 2D layout of number keys on a standard number pad on extended keyboards.
    • Observed to be 13 sigma above average compared to shuffles.
  • Average distance between successive digits, based on simple absolute difference of the digits.
    • Observed to be 6 sigma below average compared to shuffles.

Table of shuffle test results

Ideas for experiments to perform / TODO

  • Pollux was ruled out. But what if he used a custom Morse alphabet?
    • Experiment: Ignore the standard Morse alphabet. Determine all dot/dash/space mappings that produce:
      • A sequence consisting of no more than ~26 distinct Morse-like patterns (units).
      • With valid use of spaces in between the patterns (i.e., only one or two spaces should appear between Morse units)
    • There are differences between American and International Morse.
    • Test for larger Morse-like alphabets (for example: dot, dash, star, moon; resembling this cipher-like message). Determine assignments of sets of digits that partition groups of n custom symbols into an alphabet-sized set.
  • What if he used Pollux but didn't use spaces? The Morse sequence would have many ambiguous interpretations.
    • Experiment: Polyalphabetic Pollux? I.e., symbol groups may have overlapping assignments: Dash: 0 1 4 3 6, Dot: 3 8 7 4, Space: 4 5 2 9 6.
  • Run similar experiments to rule out Morbit.
  • Make heatmaps of ngram frequencies
  • Crimo was heavily influenced by the Call of Duty video game. Are there any ciphers in the game? Could he have been influenced by them?
  • In this video Crimo appears to be watching a video of the Gravity Falls theme song. Gravity Falls is a show that features ciphers. Look for any relevant encipherment schemes.
  • Do a more detailed periodic ngram analysis.
  • Try to obtain the document that was originally linked here, titled Awake Short Auto-Biography Paper.
  • Calculate average difference between successive numbers
    • Compare to "keyboard distance"
    • Compare to number keypad distances
    • Test for hand dominance (i.e., each half of a row of number keys might cluster together in the cipher)
  • Calculate compression rate compared to random shuffles, as a way to estimate non-randomness in the cipher.
  • Calculate symmetry of ngram counts (for example, the pairs of bigrams {01,10}, and {67,76} have roughly similar counts).
  • Test for longer repeating ngram patterns allowing for a fixed number of permitted errors / skips / nulls.

Other Links

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