Bacon Cipher

The cipher was first encountered in Bacon's work: “On the Advancement of Sciences” (1605) and is described in more detail in the essay “On the Dignity and Advancement of Sciences” (1623) ^[1] . In his writings, F. Bacon formulated three requirements that must be met by any “good” code ^[1] . It should be:

1. Uncomplicated and uncomplicated in work.
2. Reliable and not decryptable.
3. If possible, do not cause any suspicion.

The cipher with the third property is "secret" - that is, no one realizes its existence. F. Bacon worked on the creation of just such ciphers. As a result, he came up with the following encryption method ^[2] :

• A secret message is taken.
• The encoding method is selected (that is, the law by which each letter of the alphabet will be assigned a specific set of characters) and the message is encrypted.
• The method of hiding the message is selected (that is, the rule by which other letters or words of the alphabet are mapped to the characters of the encrypted message) and the final text is obtained.

To implement the basic principle of steganography (that is, hiding the fact of the existence of a secret message) ^{[6], the} final text should have some specific meaning, and not look like an arbitrary set of characters. Creating such a “meaningful” text is the most time-consuming task when encoding with Bacon cipher .

To encode messages, Francis Bacon suggested replacing each letter of the text with a group of five characters “A” or “B” (since a sequence of five binary characters can encode 2 ⁵ = 32 characters, which is enough to encrypt 26 letters of the English alphabet) ^[2] . There are several ways to do this:

Alphabetical Method

At the time of Francis Bacon, the English alphabet consisted of 24 letters: the letters " I " and " J ", as well as " U " and " V " were indistinguishable in pairs and were used one instead of the other ^[2] .

Bacon cipher version using the modern English alphabet:

Loop sequences

In addition to compiling the cipher alphabet, there is a more complex method of matching letters with sequences of 5 characters “A” and “B” ^[7] .

Let there be a chain of 32 characters, such that there are no repeating blocks of 5 elements in it. For example:

aaaaabbbbbabbbaabbababbaaababaab

.

It can be considered as cyclic connecting the beginning with the end. For clarity, this chain is depicted as a ring of characters. Opposite each character is a letter of the English alphabet. For characters without letters, numbers from 1 to 6 are added. Now this chain will be used as a key for encoding the letters of the English alphabet ^[7] .

Each letter will be encoded in a chain of 5 characters starting with this letter (clockwise or counterclockwise). For example, for the letter "R" we get the chain: babab , for "K" - abbba , etc.

There are many ways to hide a secret message in plain text. Here are some of them:

Method 1

It was proposed by Francis Bacon himself. Let the text use two different typographic fonts: one for encoding the character “A”, the other for “B” ^[2] . In the simplest case, you can print italic letters instead of “A” and straight lines instead of “B”. For example, last name:

B aco n

BAAAB

will match the letter "S".

An example of the use of this method is an excerpt from a letter (lat.) [1] (Rus.) (56 BC) Cicero , cited by Bacon in his works ^[8] .

In accordance with the two typographic fonts used in the passage, all letters of the text of the letter are replaced by the characters “A” and “B”. The result is encrypted text:

Everything is lost. Mindar is killed. The food supplies of the soldiers are exhausted. We cannot get provisions and therefore cannot stay here longer.

Method 2

Plain phrase:

here comes the long winter

The text is divided into 5 letters, spaces are removed:

Votin Astupt or until winter

The capital letters in the text are assigned the symbol "B", and the small ones - "A" ^[7] . It turns out a message of the form:

AAAAB AAAAA AAABA ABBAB ABBAA

When using the first variant of coding the alphabet, a secret message is obtained:

bacon

Method 3

Now the rule is as follows: the letters of the alphabet “A” to “M” correspond to “A”, and the letters “N” to “Z” correspond to the character “B” ^[7] . The secret message is encrypted like this:

I set the chair right.

A BAB BAA AAAAB BAAAB

The sequence of characters is divided into parts of 5 pieces:

ABABB AAAAA ABBAA AB

The last 2 characters are discarded, then according to the first variant of coding the alphabet, a secret message is received:

man

This encryption method is more complex than the second, and the encrypted message is not so obvious.

Method 4

Now consider the following rule: the letters “A” in odd places in the alphabet (a, c, e ...) will be mapped, and “B” will be mapped to even positions (b, d, f ...) ^[7] .

With this method of hiding text, the word:

knife

Ababa

will encode the letter "K".

• Weak cryptographic strength - the difficult part of decryption is to determine how to hide the message. Once defined, the message is easily sorted alphabetically.
• The length of the transmitted text is five times the length of the secret message ^[7] .
• At the same time, the advantage and disadvantage of the Bacon cipher is that several messages can be hidden in the same ciphertext ^[7] . For example, consider the following message:

GkwRt ceUya porrE

The key is the cyclic sequence of characters given above:

aaaaabbbbbabbbaabbababbaaababaab

That is, the letter “A” is encoded as aaaaa , “B” is aaaab , “C” is aaabb , etc.

Now the letters in odd places in the alphabet (a, c, e ...) denote the character "A", and the letters in even places (b, d, f ...) - "B" (Method 4), we get a sequence of binary characters, which as a result of decryption using the selected key is converted into a secret message ^[7] :

aaabb aaaaa babba

CAT

If the letter from the first half of the alphabet means the symbol “A”, and from the second “B” (Method 3), an expression is obtained that, when decrypted with the same key as in the previous case, gives the word “DOG”:

aabbb aabba bbbba

Dog

And if uppercase letters mean “A” and lowercase letters “B” (Method 2), the result is a secret message “PIG”:

abbab bbabb bbbba

Pig

This example shows that you can get different messages from the same text in different ways.

According to some researchers (called the Baconists or Baconists), the author of William Shakespeare's plays is Sir Francis Bacon . The most famous representatives of the " Baconian theory " are: Ignatius Donnelly , Elizabeth Wells Gallup .

To prove their claims, they cite, for example, the following fact:

• On the tombstone of the grave of William Shakespeare, you can see a two-font seal ^[3] , that is, the same code that F. Bacon worked on:

Good Frend for Iesus SAKE forbeare

To diGG þE Dust Enclo-Ased He.RE.

Blese be THE Man þat spares TEs Stones

And curst be He þat moves my Bones.

There are a number of research papers devoted to the search for encrypted messages in the works of W. Shakespeare (including using the Bacon cipher). Among them are the following:

The Great Cryptogram (1888)

The book The Great Cryptogram was written by Ignatius Donnelly, a well-known political figure and writer in the United States in the USA, and published in 1888. He argued that the works of W. Shakespeare are “a huge steganogram,” and through their “cryptanalysis” one can find evidence that the author of the plays is Francis Bacon . I. Donnelly also claimed that F. Bacon was unable to publicly admit his authorship for several reasons: high social status, reputation as a philosopher, politician and lawyer, etc. ^[5] But Donnelly had no doubt that with the help of steganography, Bacon captured his authorship in plays ^[4] .

I. Donnelly tried to find the “root” numbers, using which he wanted to discover the key to secret messages in the plays of W. Shakespeare. Based on indirect conclusions not explained in any way on the pages of his book, I. Donnelly chose 505, 506, 513, 516, 523 as the “main” numbers. Performing various mathematical operations with these numbers (subtracting constants, multiplying by factors, subtracting the number of words written in italics on this page, etc.) he received a number supposedly indicating the number of words from the ciphertext. At the same time, the author did not specify why precisely such mathematical operations must be performed to obtain ciphertext ^[4] . In such a confusing way, I. Donnelly extracted the following phrases from Shakespeare's works:

"Shakespeare has not written a single word in these plays."

"I, F. Bacon - Author of these plays."

etc.

The Great Cryptogram was harshly criticized and, despite the author’s reputable authority, failed to sell. Minnesota resident Joseph Pyle wrote his own book, The Tiny Cryptogram, parodying not only the name, but also the methods of “cryptanalysis” of the book by I. Donnelly ^[4] . Using them, Pyle “decrypted” the following secret message in Hamlet :

"Donnelly, writer, politician and quack, will reveal the secret of this play."

Another refutation of the works of I. Donnelly was written by another US citizen - Rev. A. Nicholson ^[4] . He used one of Donnelly’s “root” numbers and even worked on the same pages as the author of The Great Cryptogram. As a result, Nicholson received the following:

"Mr. William Shakespeare wrote this play and worked at the curtain."

Donnelly himself never ceased to believe in his "cryptographic" discoveries and continued to work on opening the ciphers. In 1899, he published the book “Ciphers in plays and tombstones,” but it was not successful with readers.

“The two-letter cipher of Sir Francis Bacon, discovered in his writings and decrypted by Ms. Elizabeth Gallup” (1899)

High school writer and principal Elizabeth Wells Gallup , who graduated from the Sorbonne and Margburg universities, was the first Bacon to choose William Shakespeare to use the two-letter cipher invented by Bacon himself to search for “secret messages”. Gallup searched the plays for texts written in various typographic fonts and arranged them alphabetically in the Bacon code. For example, the prologue to the play “ Troilus and Cressida ” was almost entirely typed in italics ^[4] . As a result of her work, E. Gallup received the following encrypted messages:

“Queen Elizabeth is my real mother, and I am the rightful heir to the throne ...

... Find the encrypted tale contained in my books. She talks about great secrets, each of which, if it were transmitted openly, would cost me my life. F. Bacon. "

According to the "secret" messages found by E. Gallup, Bacon hid the manuscripts of the plays in his London castle. In 1907, she went in search of manuscripts, but they did not lead to a positive result ^[4] .

A Study of Shakespearean Ciphers (1957)

Famous American cryptographers William Friedman and his wife Elizabeth Friedman set themselves the task of finding out if anyone had discovered a “real cipher” in Shakespeare’s works, the disclosure of which would challenge Shakespeare’s authorship. Under the words "real code" Friedman understood ^[4] :

• Initial clear text makes sense
• The result of decryption is one of a kind (should not represent one of several options for decryption)

In their book (1957), Friedmans examined the studies of many such Baconists: Orville Ward Owen , Walter Conrad Arensberg , Edwin Durning-Lawrence and others. Logical arguments confirming the Baconian version were not found by the Friedmans. And on the contrary, a lot of baconist evidence was called into question ^[4] .

• Cipher
• Decryption
• Steganography
• Bacon, Francis
• Shakespearean issue

1. Boyle R.,. Bacon Cipher // Brockhaus and Efron Encyclopedic Dictionary : in 86 volumes (82 volumes and 4 additional). - SPb. , 1890-1907.
2. Gardner M. Bacon Cipher (rus.) // Popular Science Physics and Mathematics Journal "Quantum": Journal. - 1992. - No. 8 . - S. 21-26 . - ISSN 0130-2221 .
3. Babash A.V., Shankin G.P. Next to Cryptography (Russian) // ICSI, Department of Cryptography, lectures on the History of Cryptography: Portal. - ICSI, Department of Cryptography.
4. David Kahn Pathological Cryptanalysis // Code Crackers = The Codebreakers - The Story of Secret Writing. - Centerpolygraph, 2000. - 480 p. - (Secret folder). - 10,000 copies. - ISBN 5-227-00678-4 .
5. Donnelly, Ignatius. Part II, Chapter VII - The Reasons for Concealment // The great cryptogram: Francis Bacon's cipher in the so-called Shakespeare plays . - Chicago: New York, London, RS, Peale & company, 1888 .-- P. 246-259. - 1002 p. - ISBN 9780403004195 .