CRYPTOGRAPHY. - It is the study of secret or conventional and concealed writings, employed by two or more correspondents to hide, wholly or in part, the content of dispatches from anyone who may come into possession of them unlawfully. There is therefore a military, diplomatic, commercial (banking) c., etc.
C. is extremely ancient; the Spartans, the Carthaginians, Julius Caesar made use of it. The ancient practice continued into the Middle Ages as well, when the most common system was the Byzantine one, consisting in the transposition of the letters of the alphabet. In this manner the letters were divided into three sections: α-β; κ-π; σ-ω. The first letter of each group was exchanged with the last; the second with the penultimate; the third with the third-to-last, and so on. The intermediate letters, that is, 1 and ρ, were represented, the first by the koppa 4 and the second by the sampi 3. The central letters of the individual groups, that is, ε, ν, ρ, remained the same. This system was very much in vogue in the subscriptions of inscriptions and codices, as can be seen in the many examples of the 9th-14th centuries. For example, St. Nilus the Younger, founder of the abbey of Grottaferrata, in his codex B. a. XX, signs himself Νεχολχ instead of Νεβλω.
On the other hand, c. was particularly developed by the diplomacy of the Renaissance; it declined at the end of the 18th century and in the 19th, and took on new vigor after the Franco-Prussian War of 1870. Today it has become a science to which mathematicians of the highest caliber contribute. Among the classics of c. mention should be made of Leon Battista Alberti, G. B. della Porta (De furtivis literarum notis, Naples 1563), Gerolamo Cardano (De subtilitate, Lyon 1554), Trithemius (Polygraphia, Frankfurt 1550 and Steganographia, ibid. 1606-22), Blaise de Vigenère (Traicté des chiffres ou secrètes manières d'escrire, Paris 1586). Today the invention of new cryptographic systems, theoretically unlimited, is instead subject to the limits imposed by the use of the telegraph and radiotelegraph, while concealed writings (with sympathetic inks and the like) are used only in espionage, by illegal associations (anarchists, etc.).
In c. a distinction is made between: encipherment, done by the sender of the dispatch and consisting in transforming the clear text into secret or enciphered text (cryptogram), according to the rules agreed upon between him and his correspondent; decipherment, done by the recipient of the dispatch, consisting in transforming the received cryptogram into the original clear text according to the agreed rules (the reverse operation of the preceding); decryption, done by one who is not the recipient of the dispatch and consisting in transforming the intercepted cryptogram into clear text without knowing the rules agreed upon between the correspondents.
Cryptographic systems can be classified into three groups: transposition, substitution, and mixed.
Transposition systems shift the letters of the clear text, according to a geometric figure or a key, so as to obtain an incoherent text.
Thus let there be, for example, the expression "abbiamo ricevuto," to be encrypted, and let the literal key be the word "Carlo," the numerical key the figure 21.534, which contains all the numbers from 1 to 5 in an order different from the normal order of succession. The phrase to be encrypted will then be arranged beneath the key word, obtaining 3 words of five letters from it as follows:
CARLO
abbia
morice
evuto
Once the literal key is replaced by the numerical key (21.534), another 3 words of five letters are formed, taking these in their vertical arrangement, from top to bottom, according to the order indicated by the normal succession of the individual numbers that form the key-cipher. One will then have:
 | 2 1 5 3 4 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| a b b i a | b | a | i | a | b | |
| m o r i c | o | m | i | c | r | |
| e v u t o | v | e | t | o | u |
and therefore the cryptogram BOVAM EIITA COBRU.
Transposition systems can be used with special grids (Cardano's, Sacco's), can be complicated with double transpositions, and can yield cryptograms that are truly difficult to decrypt.
Substitution systems replace every letter or syllable or word or entire phrase of the plaintext with: a letter or a group of letters, a numeral or a group of numerals. In the 16th century, signs of a cabalistic appearance were sometimes used as substitutes, soon abandoned because of the inconvenience of their use. They are the most effective at rendering a text obscure, but they have the drawback of requiring the existence of a written cipher book, which may fall into the hands of the decryptor. There are three types: a) monoalphabetic substitution; every letter of the plaintext is replaced by another letter (the following one, the corresponding one in the alphabet arranged in reverse order, and so on). By using pairs of numerals instead of letters, one can replace every plaintext letter with several two-digit numbers and institute some homophones and nulls.
| A | B | B | I | A | M | O | R | I | C | E | V | U | T | O |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 18 | 24 | 11 | 02 | 05 | 20 | 84 | 99 | 87 | 01 | 64 | 03 | 22 | 37 | 98 |
| homophones | ||||||||||||||
| null |
With this system, if well employed, cryptograms difficult to decrypt are obtained; b) polyalphabetic substitution (invented by Della Porta, perfected by Vigenère and Delastelle). Every letter of the plaintext is replaced by another letter drawn from ever different alphabets, that is, arranged in an order different from the normal one; in other words, if the word ROMA must be enciphered, the R will be replaced by a letter drawn from the 1st cipher alphabet; the O from the 2nd, the M from the 3rd, the A from the 4th. To employ these systems, special tables and keys are required. Modern cryptographic machines are based on the same systems, complicating them with an enormous number of keys and cipher alphabets, with which millions of different combinations are obtained; c) repertories or codes; every letter or word of the plaintext is replaced by groups of letters or numerals chosen from a repertory that may be of the most varied dimensions, from those of a pocket notebook to those of a large dictionary.
Mixed systems result from the promiscuous use of transposition and substitution systems.
All systems can be complicated in infinitely varied ways; one must only take care that the complication be substantial and not apparent, and that it not generate possibilities of error in enciphering and deciphering.
Decryption - While enciphering may be called a science, decryption may be called an art, because, although based on certain mathematical and linguistic rules, it relies above all on the intuition and skill of the decryptor. Decryption, as ancient as enciphering (a short treatise on decryption by Cicco Simonetta, secretary of Francesco and Galeazzo Sforza, who lived from 1410 to 1480, is cited), drives enciphering to continual progress; so much so that today, in the secrecy offered by cryptographic systems, one no longer seeks undecipherability in an absolute sense, but resistance to decryption for a period of time more or less long according to the importance and nature of the dispatch.
Decryption is based on three notions that the decryptor must possess: a) knowledge of the subject treated in the dispatch (if available); b) knowledge, therefore, of the type of language (diplomatic, military, commercial) and of the formulas or words or phrases that may occur; c) statistical knowledge of the language used. By statistics of the language is meant, in our case, the frequency with which in each language or, better still, in each type of language the letters and certain groupings of letters or certain words (conjunctions, auxiliary verbs, etc.) occur. In general, the longer the cryptogram, the more the statistics of its elements will approach the statistics of the language and the less difficult its decryption will be; several cryptograms enciphered with the same system are considered for this purpose as a single cryptogram. There are, however, systems whose decryption can be attempted even with only 30 or 40 elements at hand.
For example, let the cryptogram be (monoalphabetic substitution) 11. 22. 11. 08. 18. 38. 19. 43. 27. 19. 21. 39. 38. 27. 36. 18. 27. 41. 27. 39. 38. 11. 36. 18. 19. 36. 34. 11. 21. 27. 11. 36. 29. 08. 29. 34. 11. 24. 30. 11. 36. 36. 27, of which it is known with certainty only that the language employed is Italian.
By compiling the statistics of the two-digit numbers to learn their absolute and percentage frequency and which two-digit number follows each of them, one observes that 36 is followed by 36, that is, that 36. 36. replace a double letter, which in Italian can only be a consonant, and therefore 11 and 27 must be two vowels. One sees further that 39 is repeated twice followed by 38, while 38 is found once preceded by another two-digit number; therefore it is probable that this is an obligatory sequence, and then 39 will be Q and 38 U. One also observes that the greatest frequency is given by 11 (no fewer than 7 times) and by 27 (no fewer than 6 times out of 43 two-digit numbers); from the frequency tables for the Italian language one therefore deduces that these are respectively E and I.
One can therefore begin to make the substitutions:
11.22.11.08.18.38.19
e e u i q u i
27.39.38.11.36.18.19
i q u e e i e
11. 24. 30. 11. 36. 36. 27.
e e i
Observing now the series 27. 39. 38. 11., one notes that
i q u e the sequence ique in Italian is very rare ("liquefare" and derivatives); it is therefore probable that i is the end of a word, and QUE the beginning of another. QUE then begins questo or quello or derivatives, and since it is followed by 36. 18. it must be QUEST because if it were quello there would have to be a double letter. Two more letters, S and T, have thus been acquired, and they are substituted for the corresponding two-digit numbers. One notes then that 39. 38. 27.
q u i
is followed by 36. 18. 27., and therefore cannot be other
s t i than part of the words "acquisto" or "quistione." Trying with the first word, one deduces 19—A and 21—C. Thus, substituting step by step, in a short time one obtains the text "eventuali acquisti di questa specie sono permessi."
Today decryption is widely exploited in all armies, but it can also procure, if applied methodically, a very large harvest of historical information from the enciphered documents that lie in all archives.
Bibliography8 works
Carmelo Trasselli