Cryptography

Creativity embodied in Alchemical Processes encoded by the forms of Zodiacal Signs.

The alchemical magnum opus was sometimes expressed as a series of chemical operations. In cases where these numbered twelve, each could be assigned one of the Zodiac signs as a form of cryptography. The following example can be found in Pernety’s 1758 “Mytho-Hermetic Dictionary”:

Calcination (Aries)
Congelation (Taurus)
Fixation (Gemini)
Dissolution (Cancer)
Digestion (Leo)
Distillation (Virgo)
Sublimation (Libra)
Separation (Scorpio)
Incineration (Sagittarius)
Fermentation (Capricorn)
Multiplication (Aquarius)
Projection (Pisces)

The Polybius Square is an uncomplicated cipher developed by the Greek scholar Polybius. Consisting of a 5x5 grid, each of the 25 letters of the Greek alphabet occupied a single square. With 26 letters, the English alphabet must be altered in order to fit a Polybius square. This is usually done by combining two letters, typically “I” and “J”, or by including the digits 0-9 on a 6x6 grid with 36 squares:

 Each plaintext letter is represented by the two numbers corresponding to its location on the grid. In the above 6x6 grid, the letter “K” could be written as “25” (across, then down), or “52” (down, then across). The phrase “gay baby jail” could be encrypted as “2111511211125124112326”. 

Alternately, Polybius squares can be constructed with a keyword. Each letter may only be used once. Example: using the key “SWAMP QUEEN”, you would end up with a Polybius square that looks something like this:

Polybius squares are also easy to decrypt. They may be recognized by frequent repetitions of the same digits, none of them higher than 6. 

24 23 52 23 25 34 44 24 24 23 34 41 52 23 54 44 22 22 15
24 23 52 23 25 34 44 24 24 23 43 23 51 54 44 22 34

Journal 3 Code

Hello Gravity Falls fandom! If you have the journal, like me, and you’re eager to solve the cryptograms, like me, you may have noticed that much of the code in the journal is not in either of the two known gravity falls symbol ciphers. Instead, it appears to be in a completely new cipher. The key to this cipher can be found opposite the Trust No One page:

Each number next to the symbol corresponds with a letter of the alphabet. 

So if you want to use this key to decode the secrets awaiting you in this book, just flip it open to that page or use the key I set up, and get codebreakin’!

It is possible to define a consistent addition of points on certain kinds of curves (elliptic curves). This arithmetic plays an important role in modern mathematics. For instance, Wiles’ proof of Fermat’s last theorem is a consequence of the modularity theorem (once known as the Taniyama-Shimura-Weil conjecture), which gives a strong connection between elliptic curves and modular forms. Elliptic curves over finite fields also have cryptographic applications, or can be used for integer factorization.

Cicada 3301.

Cicada 3301 is perhaps the most mysterious seemingly Internet-based organization in the history of online mysteries. Since 2012, the group has posted numerous puzzles online under that name and has made no reference as to what it does or even where it is from. No one knows who runs it, assuming it really is an organization, or even the name of a single member. Cicada 3301 is able to keep its reputation with so little information strictly because of the interesting scavenger hunt of sorts it has released for three years running.

It all started on January 5, 2012 when a 4chan user posted a steganography clue on the “random” board. The image stated that Cicada 3301 was looking for “intelligent” people. In fact, the word used was “recruiting.” For what, no one has said and Cicada 3301 is certainly keeping it a secret. The image hid a clue that takes some level of specialized knowledge to find. It involved a Caesar cipher, which is pretty standard crypto, but the rest took at least some technical knowledge.

From there, and in future puzzles, clues varied greatly in skill-set necessary for solving and even location. Some of the clues were in physical locations, making it necessary for people who could not reach the clues to use posts on the Internet to get further in the hunt. Moreover, some of the references in the clues are pop culture, literature and other non-tech topics.

Some have touted the Cicada 3301 puzzles as unsolvable. This is not true. Several have solved the hunt and have allegedly received emails from the organization. Still, no one has come forward and stated what they were recruited to do, if anything. Judging by the puzzles, it is possible that Cicada 3301 is simply a cyber group like Anonymous. Of course, there is also the possibility that it is really MI6, the CIA or a similar organization. Information security, cryptography and a number of other skills necessary to crack the puzzles offered by Cicada would be helpful to virtually any large organization, which makes it hard to discover who is behind it. In fact, this would not be the first time an organization used such tactics to recruit new members. We have to assume that Cicada succeeded on that front, as it stated that it found the people it needed after the first puzzle. It began all over again on January 5, 2013 and again on January 5, 2014, so it must be an ongoing recruitment effort.

At this juncture, it is impossible to tell when these recruitment efforts from Cicada 3301 will stop, but that is not stopping people from looking forward to the next year’s puzzles. It may not be a very public honor, but it must be satisfying to know you have reached the end of one of the most famous puzzles in Internet history.

3

Are we looking at the key to Alexander Hamilton’s secret correspondence? Perhaps. This grille cipher was found among Hamilton’s papers after his death, but the question of if or how the late general ever used it remains unanswered. In the letter, Nathaniel Pendleton, who served as Hamilton’s second in the infamous duel, is asking Evan Jones, whose name appeared on the envelope containing the grille, if he might be able to remember anything about the object’s intended use. 

Grille cipher. The Nathaniel Pendleton Papers, MS 483. New-York Historical Society.

Nathaniel Pendleton. Letter to Evan Jones. November 5, 1808. The Nathaniel Pendleton Papers, MS 483. New-York Historical Society.

3

Scribbles or secrets? (1602)

Few annotations, but lots of evidence of use in a copy of Samuel Archivolti’s Arugath Ha-bosem (Venice: Giovanni di Gara, 1602), an Hebrew grammar that includes a chapter on steganography and cryptography. It would be interesting to know what all the little marks and math problems scrawled in this book might mean, and who might have made them. The two images below the the open book picture are details of the front pastedown. One shows that a small sliver of paper has been carefully excised.

I ♥ mathematics

Thanks for all the positive feedback and new ideas! This is why I love the Tumblr math community. Based on your suggestions and remarks, some other designs:

  • A heart-filled matrix for linear algebra:

  • Cryptography gets a bitstream encoding a heart:

  • Complex analysis with a heart-shaped contour integral:

  • A logical Boolean circuit:

  • Another cardioid for geometry:

Still to do: number theory, algebra, combinatorics, perhaps trigonometry?