Cryptography is used by all of us and in its never-ending development many cryptosystems have been designed and implemented in ways which have rendered them unsolvable (or at least not solved up until now).

Generally the unsolved ciphers we describe here result from unorthodox implementations of classical cryptosystems or cryptosystems that are revealed without any context within which to solve them. Ultimately they may also be unsolved due to their complexity and the resources that would be required for a solution which are diverted to more pressing cryptographic problems.

Zodiac Cipher

The zodiac cipher takes its name from the zodiac killer, a serial murderer in California who used a cipher to write letters of his plans and revealing his identity. The first instance of this cipher was a 408-character cipher in three parts each enclosed with a letter to a California newspaper. The zodiac killer demanded that they be published on the front page. They were all eventually published. Subsequent communications included further ciphers with varying numbers of characters used for enciphering.

The first set of messages has been deciphered and while there are claims that the later ciphers have also been cracked this has not been confirmed by cryptanalysts or the police. The complexity of the cipher comes from its suspected use of single symbols to represent multiple letters and frequent inaccuracies in spelling and enciphering. The imprecise nature of the messages and cipher is deduced from the deciphered message and the plaintext letters that the zodiac killer sent wherein the killer made many spelling and grammatical errors. This has made decryption harder because when there are often severe spelling mistakes the plaintext itself can be disconcertingly unclear and with hundreds of symbols to map to a 26-letter English alphabet ambiguity can ensue.

The most promising attacks have used forms of letter frequency analysis and ‘smart brute force’ whereby part of the message is mapped to many possible presumed plaintexts that are inferred from the context of the message and the repeating pattern of symbols. For example, given the murderous nature of the messenger the ciphertext VEFF may be considered to decrypt to KILL and hence L maps to F. This can then be used to extend decryption assuming a Caesar-style cipher was used with consistency.

Voynich Manuscript

The Voynich Manuscript is a 15^th century manuscript written using an unknown writing system. It is named after Wilfird Voynich the polish book dealer who purchased the manuscript in 1912. It is thought that the manuscript is a pharmacopoeia detailing the practices and knowledge of medieval or early modern medicine.

The manuscript contains images and some extraneous text written in Latin that has helped to determine the document’s purpose and origin. It is thought to have originated in Europe given by the Latin spelling thought to show ancient French or Italian hallmarks.

The ‘code’ in this manuscript comes from the writing being in some unknown and seemingly indecipherable language. This is not necessarily explicit encryption but in its way translation to an unknown language is a code made more complex by its own grammar.

Attempts at deciphering the document have used transcription alphabets that aim to map the unknown language to modern known languages. More cipher led approaches have posited that the text is a cipher that decrypts to a now dead European language. This would explain why letter frequency analysis of the text and grammatical analysis have achieved little progress. The grouping of letters in the document is suggestive of a verbose cipher wherein single plaintext letters are enciphered into groups of letters. It could also be that the manuscript is not only enciphered by also obscured through steganography so that the plaintext (or even the original ciphertext) follows some pattern in the manuscript such as every fourth character or the last letter of each word.

Fenn Treasure

Art dealer and author Forrest Fenn has supposedly hidden a treasured piece of art in the Rocky Mountains and released a poem containing nine clues as to its location. He will return for the treasure once it has reached $10 million in value. The puzzle began when he hid the treasure in 2010.

He has stated that no one has yet given him the clues in the right order. He has however confirmed that previous searches have been within 60m or 200 feet of the treasure.

The poem containing the clues to the location of the treasure is as below.

As I have gone alone in there, And with my treasures bold, I can keep my secret where, And hint of riches new and old.

Begin it where warm waters halt, And take it in the canyon down, Not far, but too far to walk. Put in below the home of Brown.

From there it’s no place for the meek, The end is ever drawing nigh; There’ll be no paddle up your creek, Just heavy loads and water high.

If you’ve been wise and found the blaze, Look quickly down, your quest to cease, But tarry scant with marvel gaze, Just take the chest and go in peace.

So why is it that I must go, And leave my trove for all to seek? The answers I already know, I’ve done it tired, and now I’m weak.

So hear me all and listen good, Your effort will be worth the cold. If you are brave and in the wood, I give you title to the gold.

Such is the lure of the wealth that could be attained by solving the puzzle and the wilderness nature of its location two people have died in search of the treasure.

Kyrptos

Kryptos is a sculpture by American artist Jim Sanborn which can be found in the grounds of the CIA campus in Virginia. It contains 4 encrypted messages passages carved out of copper plate. Three of the four ciphertexts have been resolved for the original plaintext however one remains unsolved. The creator has stated that solving all four ciphers will reveal a riddle within a riddle which is the ultimate challenge.

The sculpture was created in 1990 and since its placement at the CIA its creator has given two clues to aid towards its solution. Sanborn has stated that the first three passages contain clues to solving the fourth. Further to this he has states that the 64^th to 74^th letters in passage four (NYPVTTMZFPK) correspond to the plaintext BERLINCLOCK.

Of the solved ciphers two have been revealed to be Vigenère ciphers. Passages 1 and 2 were encrypted using Vigenère ciphers using keywords Kryptos, Palimpsest and Kryptos, Abscissa respectively. The third passaged proved to have been encrypted using a method known as transposition wherein the plaintext appears as a spatial pattern in the ciphertext through permutation or inclusion of erroneous text (e.g. every prime number letter index).

Beale Cipher

The Beale ciphers (a.k.a. the Beale papers) are a set of three ciphertexts which allegedly state the location of buried treasure worth tens of millions of dollars. The original ciphertexts were publishes in 1885 by Thomas J. Beale. The second of the three ciphers has been solved but despite many decades of work the other two remain unsolved. The extent of the trials and failures have led many to question if the puzzle is indeed legitimate and this argument has been supported by several qualified cryptanalysis after detailed analysis.

Decryption of the second ciphertext requires a copy of the United States Declaration of Independence. Decryption requires that one find the word corresponding to the number in the encrypted passage. Then one must take the first letter of that word in the Declaration of Independence. For example 22 would correspond to the first letter of the 22^nd word of the Declaration of Independence.

The second plaintext reads as follows:

I have deposited in the county of Bedford, about four miles from Buford’s, in an excavation or vault, six feet below the surface of the ground, the following articles, belonging jointly to the parties whose names are given in number three, herewith:

The first deposit consisted of ten hundred and fourteen pounds of gold, and thirty-eight hundred and twelve pounds of silver, deposited Nov. eighteen nineteen. The second was made Dec. eighteen twenty-one, and consisted of nineteen hundred and seven pounds of gold, and twelve hundred and eighty-eight of silver; also jewels, obtained in St. Louis in exchange to save transportation, and valued at thirteen thousand dollars.

The above is securely packed in iron pots, with iron covers. The vault is roughly lined with stone, and the vessels rest on solid stone, and are covered with others. Paper number one describes the exact locality of the vault, so that no difficulty will be had in finding it.

Beale’s encryption was done with a slightly different version of the United States Declaration of Independence but the differences are slight enough such that one can correct any errors in deciphering.

While some maintain that the two unsolved ciphers are hoaxes analysis using supercomputers suggests that the numbers are not simply random. However, the story of the treasure and the passage of the ciphertexts from hand to hand before publication are based solely on heresay and circumstantial evidence. The validity of the puzzle remains a contentious issue.

Rongorongo

The Rongorongo glyphs refers to the system of glyphs used by the inhabitants of Easter Island thought to be one of few examples of the independent invention of writing, a key step in human progress. The glyphs are thought to each represent a word or concept. Most of the ‘ciphertext’ is engraved on wooden tablets. Since their discovery in the 19^th century many attempts to decrypting the ‘code’ have been made but none have been successful.

Ricky McCormick Murder Notes

The body of Rick McCormick was found in 1999 after his murder with two enciphered notes in his pockets. The notes are thought to have been written by McCormick to aid in leading to his attackers. The notes were not public knowledge until twelve years after the murder and the reaction of McCormick’s parents was to dismiss the messages since “the only thing he could do was write his name”. The FBI, the Racketeering Records Unit and the American Cryptogram Association have all attempted and failed to decrypt the messages. This remains one of the top unsolved cases for the FBI’s cryptanalysis and racketeering records unit.

Summary

Cryptanalysis has progressed greatly throughout the 20^th and 21^st centuries but some problems remain beyond the mathematical, mechanical and computing skills we have developed. There are many unsolved ciphers, and we have highlighted a few of the more famous examples. If you’re looking for more examples, a useful resource is Wikipedia’s list of unresolved ciphers.