Cryptography

“ He was evidently versed in cryptography, constructed this one as carefully as a mechanic putting together a piece of mechanism, fitting all the parts carefully into one another. The figures in the centre of the circle give the key to the outside figures: the outside figures are the key to the cryptographic table of letters from which the cryptogram is to be solved; there remains the key to be found. It is not likely that the composer of such an ingenious cryptogram would leave the keyword to guesswork. ”

“ Sometimes a slave’s head was shaved, and the crown written upon with some indelible coloring fluid; after which the hair being permitted to grow again, information could be transmitted with little danger that discovery would ensue until the ambulatory epistle safely reached its destination. Cryptography, however, pure, properly embraces those modes of writing which are rendered legible only by means of some explanatory key which makes known the real signification of the ciphers employed to its possessor.”
The key-phrase of this cryptograph is—“A word to the wise is sufficient.” ”

“ Cryptography as a science is supposed to enter largely into State diplomacy, secret correspondence being maintained by its means with the various State officials scattered over the globe. In the commercial world it is a fact that such correspondence is transmitted by telegraph with much saving of labour and money and with perfect secrecy, each correspondent possessing a key which enables him to translate into plain words and sentences the otherwise unintelligible jumble of signs. ”

“ Let be a group with generator used for public-key cryptography. Let be a key encapsulation method which takes a value in some space and outputs a private-public key pair of elements in the group . Then,
Where is a private key, is a public key, and is optional ciphertext in the ciphertext space containing securely encrypted information about . ”

“ Thus, the sentence given above yields a series 1, 3, 1, 2, 1, 4, 4, 1, 4. Using a biform alphabet, these are usually considered simply as odd and even; with a triform alphabet, some disposition must be made of numbers larger than 3.
The subject is fascinating, and the literature of cryptography is rich with examples. However, we need not delve further into what, after all, is only the stepchild of a legitimate science. The matter of telegraphic transmission alone will bar these ciphers for most general purposes, or the fact that a cipher once betrayed will never serve again. ”

“ Article 26
⁠Commercial cryptography products which concern national security, national welfare and people's livelihood, or public interests shall be listed in the catalog of critical network equipment and specialized cyber security products in accordance with law, and be sold or provided for use provided that they have passed the testing and certification conducted by qualified testing and certification bodies. ”

“ The transmission to our own times of this obvious mode of cryptography is due, probably, to the historical uses of the scytala, rather than to anything else. Similar means of secret intercommunication must have existed almost contemporaneously with the invention of letters.
It may be as well to remark, in passing, that in none of the treatises on the subject of this paper which have fallen under our cognizance, have we observed any suggestion of a method—other than those which apply alike to all ciphers—for the solution of the cipher by scytala. ”

“ The State encourages foreign investors to cooperate in commercial cryptography technology based on voluntariness and commercial rules. Administrative departments and their staff members shall not force the transfer of commercial cryptography technology by administrative means.
⁠The research, production, sale, service, import and export of commercial cryptography shall not endanger national security, public interests, or the legitimate rights and interests of others. ”

“ This method is very secure; yet it is possible to decipher any cryptograph written by its means—and it is greatly objectionable otherwise, on account of the time necessarily required for its solution, even with the key-volume.
It is not to be supposed that Cryptography, as a serious thing, as the means of imparting important information, has gone out of use at the present day. It is still commonly practised in diplomacy; and there are individuals, even now, holding office in the eye of various foreign governments, whose real business is that of deciphering. ”

“ Philip Thicknesse (A Treatise on the Art of Decyphering and of Writing in Cypher) , 1772; William Blair (the writer of the comprehensive article “Cipher” in Rees’s Cyclopaedia) , 1819; and G. von Marten (Cours diplomatique) , 1801 (a fourth edition of which appeared in 1851) . Perhaps the best modern work on this subject is the Kryptographik of J. L. Klüber (Tübingen, 1809) , who was drawn into the investigation by inclination and official circumstances. In this work the different methods of cryptography are classified. ”

“ In ElGamal encryption, as done in most public key cryptography encryption schemes, a symmetric key is established and then proceeding communication can occur using a symmetric-key based algorithm such as . ”

“ Even a basically weak cipher, in the hands of an expert, can be made to serve its purpose; and the strongest can be made useless when improperly used.
In the present text, we are likely to be found looking at ciphers largely from a military angle, which, apparently, has a more general interest than any other. In time of war, the cryptographic service, that is, the encipherment and transmitting service, is suddenly expanded to include a large number of new men, many of whom know nothing whatever of cryptanalysis, or the science of decryptment. ”

“ Any one of the multiple-alphabet ciphers may change keys at each new group instead of with each consecutive letter. As a rule, this kind of encipherment is never found except in connection with very simple ciphers, and the intact plaintext groups, each one standing on its own key-line, are readily discovered by the decryptor who takes the precaution of cutting out a segment from his cryptogram and “running down the alphabet,” first treating the original letters and then, if necessary, their complements. ”

“ Even book cipher, notably secure, however unwieldy in use, has been decrypted because of the encipherer’s very human tendency to use a substitute more than once rather than search for a new one among the hundreds at his disposal.
In book cipher, any agreed book, or other written or printed document, will serve as a key-volume, so long as it is one that is sure to be at hand when wanted. Words, or letters, can then be represented by a series of numbers usually indicating: page, (column) , line, serial position. One letter or one word may thus have a substitute such as 20-1-4-32. ”

“ Decryptment, too, can parallel that of the Vigenère: The period of a cryptogram can be found through repeated sequences, or, in their absence, through repeated single numbers, and individual frequency counts can be taken on the several alphabets of the period. If the arrangement of letters in the checkerboard is that of the figure, or any other strictly alphabetical one to which the order of the numbers can be adjusted, these frequency counts will all follow the graph of the normal alphabet, with allowance made for the missing letter. ”

“ A key-word, treated in the same way, is repeated often enough to pair one key-number with each message-number, and the final cryptogram is formed by adding these pairs of numbers. Decipherment, of course, will be the subtraction of key-numbers from the finished cryptogram and the resubstitution of letters. We have, then, another periodic cipher, not essentially different from those already seen. Any number in the checkerboard can become a key, to be applied periodically at some given interval, and thus may govern one of the 25 possible cipher alphabets. ”

“ Usually time is saved by taking cryptogram pairs just as they come and filling in as many letters as possible; in this way, patterns are sometimes brought out, and thus we come back to step 1: the identification of more pairs. With the key-square beginning to shape up, the “chart of probable position” may be used to good advantage. For instance, what about the letters H and B which were very high in the frequency list?
Once a beginning is made, the cipher is broken, though just how rapidly we may proceed with the solution depends chiefly upon the manner in which the square has been filled. ”

“ Knowing that a great many letters are going to be enciphered by B, a great many others by E, and a great many others by D, and having no wish to preserve word-divisions, we begin by writing our plaintext into three columns (or by grouping it conveniently) , and then encipher at a single writing all of those letters which are to be enciphered by any one same key-letter. That is, we apply one cipher alphabet at a time, as first explained. The modern practice will also require that the cryptogram be taken off in five-letter groups, and that the final group be made complete. ”

“ But, before leaving the simple for the complex, we must not overlook the celebrated key-phrase cipher, which discards the idea of multiple substitutes in favor of multiple originals! This cipher, shown in Fig. 79, is said to have been used for serious purposes. Its only difference from the ordinary simple substitution lies in the nature of the cipher alphabet, which must be a plaintext sentence, or phrase, containing the necessary 26 letters. The mysterious pronouncement, “One who has passed on is among us,” is the earliest example of which the writer has any recollection ”

“ Experience shows that the most cunningly constructed cryptograph, if suspected, can and will be unriddled.
An unusually secure mode of secret intercommunication might be thus devised. Let the parties each furnish themselves with a copy of the same edition of a book--the rarer the edition the better--as also the rarer the book. In the cryptograph, numbers are used altogether, and these numbers refer to the locality of letters in the volume. For example--a cipher is received commencing, 121-6-8. ”

“ The subject which we are about to study is the analysis and solution of cipher, though not including code, which is a very special form of cipher demanding something more than elementary knowledge; nor shall we enter at all into the subject of invisible inks, certainly a most important aspect of secret writing, but belonging to the province of chemistry rather than to that of cryptanalysis. Cipher machines, also, are not within our present scope. ”

“ On what principle had these letters been arranged? He who held the paper was alone able to tell. With such cipher language it is as with the locks of some of our iron safes—in either case the protection is the same. The combinations which they lead to can be counted by millions, and no calculator’s life would suffice to express them. Some particular “word” has to be known before the lock of the safe will act, and some “cipher” is necessary before that cryptogram can be read.
He who had just reperused the document was but a simple “captain of the woods.” ”

“ But it is still present; the most complex of ciphers has method of some kind, provided we can find it. Consider, for instance, the series of numbers, 11-8-25-6-3-21-19-16-5-14, which has been forming in Fig. 53. Examination here shows pairs of consecutive numbers, 11-8, 6-3, and 19-16, all having the same numerical difference of 3; that is, the plan of our present encipherment, whatever it is, has, on three separate occasions, caused some plaintext digram to appear in the cryptogram reversed, and with its letters three positions apart. ”

“ Thus the taking out of columns from the second block will, at times, select one each from two or
more different progressions of 6, and the new columns, throughout some portion of their length, will differ from one another by exactly 6, the original key-length.
We have seen, then, the general case in which the “enemy” decryptor, having several cryptograms of the same length, enciphered with the same key, is able to use a purely mechanical method in order to restore the plaintext, and afterward, by observing traces of a known cipher, to extract their key. ”

“ The term cipher implies a method, or system, of secret writing which, generally speaking, is unlimited in scope; it should be possible, using any one given cipher, to transform any plaintext whatever, regardless of its length and the language in which it is written, into a cryptogram, or single enciphered message. ”

“ We do not desire, however, to take off plaintext. And, to use this same key on a cryptogram, we should have to use it in the writing-in manner; that is, first lay out the series of key-numbers, and then, taking the cryptogram letters in their 1-2-3 order, place them, one by one, below their key-numbers. But once the plaintext has been restored, the plaintext letters (or columns) may also have serial numbers, and these new serial numbers, in the figure, have been added at the bottoms of the columns. ”

“ Transposition has already been explained as a form of cipher in which the letters of a message are disarranged from their natural order in accordance with any pattern, or key, agreeable to the correspondents. The fact that any plan may be followed will suggest the possible ramifications as to detail. Transpositions are, in fact, found in every conceivable degree of complexity. They are not even unanimous in their demand that there be two separate operations in the preparation of a cryptogram: (1) the writing down of the plaintext letters, and (2) the taking off of these letters. ”