To learn the order of my fingering, I must begin with rudiments of art. --Shakespeare
As he was in many other things of a scientific nature, Francis Bacon was interested in cryptology. In the 1640 English translation of The Advancement of Learning , (Gilbert Wats) Book VI, he says:
Wherefore let us come to CYPHARS. Their kinds are many as, Cyphars simple; Cyphars intermixt wifh Nulloes , or non-significant Characters; Cyphers of double Letters under one Character; Wheele-Cyphars; Kay-Cyphars; Cyphars of words; Others ; But the virtues of them whereby they are to be preferr'd are Three; That they be ready, and not laborious to write; That they be sure, and lie not open to Deciphering; And lastly, if it be possible, that they may be managed without suspition . For if Letters Missive fall into their hands, that have some command and authority over those that write; or over those to whom they were written; though the Cypher it selfe bee sure and impossible to be decypher'd , yet the matter is liable to examination and question; unless the Cypher be such, as may be voide of all suspition, or may elude all examination. As for the shifting off examination, there is ready prepared a new and profitable invention to this purpose; which, seeing it is easily procured, to what end should we report it, as Deficient . The invention is this: That you have two sorts of Alphabets , one of true letters , the other of Non-significants ; and that you likewise fould up two Letters ; one which may carrie the secret, another such as is probable the Writer might send yet without perill. Now if the Messenger be strictly examined concerning the Cypher , let him present the Alphabet of Non-significants for true Letters , but the Alphabet of true Letters for Non-significants : by this Art the examiner falling upon the exterior Letter , and finding it probable, shall suspect nothing of the interior Letter . But that jealousies may be taken away, we will annexe an other invention, which, in truth, we devised in our youth, when we were at Paris : and is a thing that yet seemeth to us not worthy to be lost. It containeth the highest degree of Cypher , which is to signifie omnia per omnia , yet so as the writing infolding , may beare a quintuple proportion to the writing infolded ; no other condition or restriction whatsoever is required. It shall be performed thus: First let all the Letters of the Alphabet , by transposition, be resolved into two Letters onely; for the transposition of two Letters by five placeings will be sufficient for 32. Differences, much more for 24. which is the number of the Alphabet . The example of such an Alphabet is on this wise.
An Example of a Bi-literarie Alphabet.
[A (Aaaaa) ... Z (babbb)]
The excerpt above is exactly copied [scanned], including the periods and their placement. It may be worth noticing that three of the periods are missing, while one is misplaced. The following is a table of the Binary Scale, upon which the calculating ability of modern computers is based:
Charles S. Ingram (who wrote under the name of Jacobite) seems to have been the first to notice the similarity between the Binary Scale and Bacon's Bi-literarie alphabet;he called attention to it in the English periodical Baconiana (No. 160, March 1960, p. 12). The invention of the Binary Scale traditionally has been credited to Leibniz who devised a calculating machine in 1671 and found the binary useful for his purposes, though there is evidence that it was known in an earlier century. The binary scale has been extended and continues as the ASCII "code" which is now used in most computers and telecommunication systems.
Therefore, Bacon in an earlier Latin edition of the Advancement of Learning (De Augmentis Scientarium published in 1623) and Leibniz in 1671 produced the same tables; in Bacon's cipher version "0" = "a" and "1" = "b", and this is imitated in Leibniz' arithmetical notation. And John Napier, who invented logarithms, had previously illustrated the use of the binary scale in his Rabdologiae published in 1617.
This is hardly a trivial coincidence. It should be recognized that Francis Bacon had more than a passing interest in basic mathematics, in addition to his known and often published "call for papers" in experimental, observational and empirical scientific research. And, as will be seen, Bacon and John Napier were in communication.
To continue with Francis Bacon's exposition of the Biliteral (or Bi-literarie Alphabet, as he called it) cipher:
"Neither is it a small matter these Cypher-Characters have, and may performe: For by this Art a way is opened, whereby a man may expresse and signifie the intentions of his minde, at any distance of place, by objects which may be presented to the eye, and accommodated to the eare: provided those objects be capable of a twofold difference onely; as by Bells, by Trumpets, by Lights and Torches, by the report of Muskets, and any instruments of like nature. But to pursue our enterprise, when you addresse your selfe to write, resolve your inward-infolded Letter into this Bi-literarie Alphabet . Say the interiour Letter be. . ."
Here Bacon gives an example of his method, using two dissimilar styles of letters in order to convey a message. The compositor of the book used italic characters having fairly obvious differences, but not by typesetting them; he engraved the letters in 5 letter groups. It should also be noted that, although Bacon illustrated his scheme by thus varying the form of the letters in his books, he spoke always of "writing" and never of printing. The system suffered from the fact that the ciphertext had to be five times longer than the plaintext message, but the method had the advantage of almost perfect safety. If no one noticed the varying style of the hand-written characters, the cipher was quite secure. Bacon's description of his Bi-literarie cipher was a single example of a general stratagem that has become known as steganography; the term includes the many ways by which the very existence of a cipher is concealed (as in the following passage). Francis Bacon continues:
The knowledge of Cyphering , hath drawne on with it a knowledge relative unto it, which is the knowledge of Discyphering , or of Discreting Cyphers , and the Capitulations of secrecy past between the Parties. Certainly it is an Art which requires great paines and a good witt and is (as the other was) consecrate to the Counsels of Princes: yet notwith standing by diligent prevision it may be made unprofitable, though, as things are, it be of great use. For if good and faithfull Cyphers were invented & practised, many of them would delude and forestall all the Cunning of the Decypherer , which yet are very apt and easie to be read or written: but the rawnesse and unskilfulnesse of Secretaries, and Clarks in the Courts of Princes, is such that many times the greatest matters are Committed to futile and weake Cyphers. But it may be. . ."
And here, without pausing for breath or a new paragraph, he breaks off into a discussion of "Arts." He never returns to the subject of "Cyphars," or "Cyphers," or even of "Cyphras" as he spells it in the original Latin version of De Augmentis Scientarium , 1623. To quote a few lines:
"Ad Ciphras igitur veniendum. Earum Genera haud pauca sunt. Ciphrae simplices; Ciphrae Non significantibus Characteribus intermix tae, Ciphra duplices Literas uno Charactere complexae; Ciphrae Rotae, Ciphrae Clauis, Ciphrae verborum , aliae. . .Quod si quis Ciphra severe interrogetur. . ."
The ciphers discussed in this book are mainly elementary, but a glossary of cipher terms may be helpful:
Acrostic Any cipher system which generally depends upon the occasional and regular appearance of ciphertext letters within an apparently unsuspicious plaintext. An example of the cryptographer's use of this method is the selection of the initial letters of each line of a poem so as to spell a word or name. The letters may first be superenciphered to make the solution more difficult.
Anagram An intelligible word or phrase produced by rearranging the letters of the original according to no particular pattern. This is not useful for communication, and thus is not an ordinarily acceptable cipher method.
Caesar Cipher A simple substitution cipher which is accomplished by replacing each ciphertext letter with some other, preceding or following, letter of the alphabet in a regular manner. Thus to encipher the word DOG, using the next letter of the alphabet, we may write "eph". Using the next letter after that, the result is "fqi", and so on.
Cipher Alphabet The modern, normal alphabet may be scrambled to produce a very large number of variations, 26 factorial or about 4000 billion billion billion ways. Doing so complicates, for example, the cryptanalysis of a Caesar substitution cipher; sometimes the alphabet is disarranged by using an easily remembered keyword. Further complication may be added by changing to a new alphabet each time a letter is enciphered. For a monoalphabetic cipher, if the text is long enough, a solution may sometimes be found by tabulating the frequency of the use of each letter and comparing that to the ordinary frequency of letters in English words.
Cipher In the uses of cryptography (not mathematics), the cipher is defined as a method of transforming a text to conceal its meaning (1) by systematically replacing the letters of the plaintext by substitutes in the same sequence, either singly or in pairs or in other polygraphs (as by writing 1 for A, 2 for B, etc., or F for A, S for B, etc., or QL for AB, etc.) or (2) by systematically rearranging the plaintext letters into another sequence (as by writing them normally in a rectangle and then copying them off from the columns taken in an arbitrary succession)--called respectively (1) substitution cipher and (2) transposition cipher (from Webster's Third New International Dictionary, Unabridged). [This definition is most elementary, and there are a multitude of other cipher systems.]
Ciphertext A series of unintelligible letters which results from passing a plaintext (a message) through a cipher system.
Cleartext A message sent without encipherment, referred to as "in clear," "en clair," "in plain language," or sometimes "open text."
Code To be distinguished from cipher, though sometimes loosely used as a synonym, as in "decode." A simple code might be expressed in numbers, as 55-7-5. To the decipherer, this would mean to look in a chosen book on page 55, line 7, for the 5th word. Naturally the sender of the message and the recipient must, by agreement, have a copy of the same book; this might be a dictionary, a novel, or whatever. Special books of commercial codes in which the meaning of groups of numbers are printed (as, 34567 = January) are common, and are cross indexed.
Crib From Webster: "a small theft; a plagiarism; hence a translation to aid a student in reciting." In cryptanalysis, if a word or phrase is known, or suspected, to be contained in an undeciphered message (a "probable word"), then that word can be used as a crib to greatly assist in cryptanalysis.
Cryptanalysis This is the usually difficult process of reading a cryptogram without having the secret key. The word contrasts with "deciphering"; the decipherer is assumed already to have the key, so as to read a message without any obstacle. Again, both words are used loosely in general discussion.
Cryptogram After the plaintext message is enciphered and transformed into ciphertext, the result is a cryptogram. It may be deciphered by one having the key or it may be solved by a cryptanalyst who does not have the key.
Cryptography The science of concealing a message, although the outward form (e.g., five letter "code" groups) may patently show that a cipher system has been used. This is to be compared to steganography, a process of encrypting a secret message within an ordinary looking "open text."
Cryptology This refers to the science of cryptography and cryptanalysis, but the term as it is used now also includes systems of either making message signals secure or of extracting information from them. Such extensions refer to electronics, RADAR, radio communication jamming and so on. It is a general term, loosely used in ordinary discussion.
Decipher To read an enciphered message while knowing the key.
Decrypt Another term meaning to cryptanalyze. Encrypt describes the reverse process.
Doubles The determination of letter frequency in aid of cryptanalysis can sometimes be defeated by doubling ciphertext letters, such as "YY" or "AA".
Encipher The opposite of decipher: to convert a plaintext readable message into a ciphertext while using a cipher system for transmission to an ally who knows the cipher key and can decipher it.
Encrypt (Opposite of Decrypt) A rule by which the cryptographer may specify the arrangement or number of letters in a cipher alphabet for purposes of substituting one letter for another; or of transposing the letters of an alphabet; or of making mechanical settings on a cipher machine; or of using an algorithm or mathematical formula to program a computer. More than one key may be used in composing a cryptogram.
Keyword An easily remembered word used to disarrange an ordinary alphabet. If the keyword is "DOG", then the cipher alphabet may read "D O G A B C E F H I K L M N P Q R S T U V W X Y Z". The letters of the keyword are used up first and the remaining letters are written in normal order afterward. There are, of course, methods to complicate the process.
Message The text of the information intended to be communicated. If it is enciphered it is called plaintext; if not it is called cleartext or sometimes opentext.
Monoalphabetic Cipher A cipher based upon only one series of letters of the alphabet; however that alphabet may be scrambled or truncated.
Null A letter of the plaintext or of the ciphertext which is not meaningful. Often these, or multiples of them, are included in cryptograms to confuse the cryptanalyst.
Opentext A series of words or sentences having ordinary meaning. Historically, innocent appearing "opentexts" have been found to be steganographic ciphertexts and to contain enciphered letters intended for use in an acrostic cryptogram.
Plaintext A message in its original, readable form before it is converted by a cipher system into ciphertext. Successful decipherment or cryptanalysis of the cipher system returns the ciphertext to plaintext.
Probable word A word which the cryptanalyst has cause to believe might be found in a ciphertext. See Crib .
Solution A successful conversion of ciphertext to plaintext, either by decipherment or cryptanalysis.
Steganography Any method of concealing the actual existence of a cipher, such as Bacon's Bi-literarie system. Individual acrostic letters in an ordinarily-worded text may be enciphered. Microdots, invisible inks and grille ciphers are other examples of ways of hiding a message so that no suspicion is aroused. A steganographic solution may be doubly or triply enciphered so as to require further cryptanalysis.
Substitution The process of replacing the letters of a message with cipher letters in a regular pattern so as to produce a plaintext when they are deciphered. See Cipher .
Superencipherment This often refers to the conversion of code words by a cipher system into ciphertext. It may also mean the re- encipherment of letters of the alphabet which have already been converted by a cipher system into a ciphertext.
Transposition The process of rearranging the original letters of a plaintext message into a different, unintelligible sequence according to a fixed rule. See Cipher .