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Articles on Ciphers
« on: December 03, 2008, 08:03:46 AM »
From ‘MATHEMATICAL MONTHLY’ Vol.1 March 1859 No.VI p.194

By Pliny Earle Chase, Philadelphia.

The ciphers usually employed for secret correspondence, are formed by the mere substitution of symbols for letters of the alphabet, one symbol only being appropriated to each letter. The comparative frequency with which the several letters recur in our language, is well known, therefore all ciphers of this kind are of little worth, as they may be easily translated by any expert into whose hands they may fall.
By the alternative use of two or three different symbols for each of the most common letters, the difficulty of translation is increased, and the value of the cipher proportionally enhanced. But even in this case the law is so simple, and the number of constants so great, that the key can generally be found after a few trials.
A holocryptic cipher should not only conceal the message that it is intended to convey, but it should also effectually hide the key to the message, which it can hardly do unless it destroys all symbolic uniformity, so that any given letter will be as likely to be represented by one symbol as by any other. The various operations of Mathematics, - Addition, and the other simple rules of Arithmetic, Logarithms, Curvefunctions, &c., furnish an infinite variety of methods that will accomplish this end.
Let two correspondents, for instance, commence by arranging an alphabet in rows and places, in a manner similar to the following:-

R     1  2  3  4  5  6  7  8  9  0
O  1  X  U  A  C  O  N  Z  L  P  φ
W  2  B  Y  F  M  &  E  G  J  Q  ώ
S  3  D  K  S  V  H  R  W  T  I  λ

According to this alphabet the word “Philip” may be designated by
, the upper line denoting the row, and the lower line the place, of the several letters.
If we multiply the lower line by 9, we obtain for our cipher
8639091 = Lnsiώix.
If the key that has been agreed upon, is the addition of 7854 (repeated as often as necessary), 959899+785478=1745377. The left-hand figure of this sum may be rejected, as it will be readily known when the cipher is retranslated. We then obtain for our cipher
If a logarithmic key has been adopted, we may obtain the following cipher: log 959899**=982229;
The following examples will illustrate the method of interpreting the three foregoing varieties of mathematical cipher.

1. Eώntxbxxdheokj=22131211332132 divide by 8
2. Ωpcpwiλmaopiag=21113332111312 subtract 709
3. Ωlgpntufkygl  =212113123221       log.

Dividing th place-row, in the first example, by 8, we obtain
7585138894566= Go to Baltimore
Subtracting 70970970970970, from the place-row in the second example, we obtain
38526933388967= Flour is falling
In the third example, 08796= log 12245; 82322 = log 66562; log 78 = 6. Then
12245665626 = Buy corn and rye.

These illustrations, I think, are sufficient to show that a very simple arithmetical process may effectually conceal the meaning of a message from every one but the persons who hold the key to the cipher. The obscurity and consequent security may be increased to any desired extent, by adopting processes that are more intricate. But the simpler the cipher, provided it is effectual, the better, and I know of no simpler methods, that merit the name holocryptic, than those I have just indicated.

* The first letter may be either L, J, or T.
** The index of the logarithm, is disregarded.
« Last Edit: December 03, 2008, 08:29:17 AM by tonybaloney »


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Re: Articles on Ciphers
« Reply #1 on: December 03, 2008, 08:28:14 AM »
From ‘Tracts in Shorthand’ 1887


Cipher writing is commonly regarded as being impenetrable in proportion to its arbitrary complexity, yet it is understood to be a maxim among cryptographers that any cipher can be discovered. In this matter, as in “Shorthand without complications,” I seek to attain my end by simple means. Again, the plan on which an ordinary cipher is arranged is peculiar to itself, and is kept, if possible, a close secret. I give a general or common plan, on which countless ciphers can be constructed, with greater or less intricacy according to the purposes to which they are to be put.

All these ciphers are made out of the signs 1,2,3,4,5,6,7,8,9,0. But as twenty-six letters have to be provided for, while these signs are but ten in number, it is clear that combinations of figures must be employed. When figures are thrown together, they must, therefore, in a cipher, be distinguished in some way. If an arbitrary mark be used, it at once attracts attention. Therefore, I propose to make a figure serve the purpose of dividing the figures. Any single figure may be taken, but the one selected must not then be used in representing any letter of the alphabet. The figure selected I term a “spacer,” its function being to “space off,” one representative of a letter from another. If the 0 be taken, and figures (always excluding the 0) be used up to 100, there are 90 sets of figures to choose from, the tens containing the 0 being excluded. These 90 sets will suffice to form a practically infinite number of alphabets, so that there need be no fear of an alphabet drawn up by one person being identical with one compiled by another. Taking 0 as the “spacer,” an alphabet may be formed on this model:-

A 86    G 62    M 44    S 16    Y 14
B 25    H 11    N  7    T  9    Z 92
C 43    I 55    O  6    U 19
D 97    J 18    P 63    V  8
E 74    K  5    Q  1    W 13
F 38    L  2    R 21    X 45

The figures are taken at random, the only things to be careful about being (1) to omit the “spacer” figure from the alphabet, and (2) not to allot the same sign to two letters. A message may now be written, the “spacer” being placed after the sign for each letter, and doubled at the end of a word, as in –

A person writing a cipher communication to a correspondent must, of course, use a key, and his correspondent must have a duplicate of the key. The receiver of this cipher, having the key given above’ will draw his pen through the “spacer” wherever he finds it, and will then, by referring to his key, find the figures to mean –


The cipher code here set forth is the most elementary form in which the plan can be applied, but it would probably be found safe enough for all occasions on which great precaution was not required. It may be made a little more difficult, however, by omitting the second 0 at the end of a word, and treating the whole message as continuous letters thus –
– equivalent to –

It does not need much ingenuity to divide these letters into words.

Any one of  the single letters may be used as a “spacer,” instead of 0, and then 0 can be used in the alphabet. Still keeping the alphabetical symbols within two figures, the number of distinct alphabets which could be constructed is practically, though not theoretically, as exhaustless as before. With 2 as the “spacer,” and therefore not employing 2 in the alphabet, we may draw up a plan or key on this model:-

A  5    G 48    M  3    S  8    Y 66
B 17    H 61    N 55    T 40    Z 99
C 81    I 00    O 33    U 90
D  1    J 30    P  4    V  7
E  6    K 64    Q 10    W 50
F 19    L 46    R 01    X 18

Supposing that one of those singular beings, who have only to withdraw for a few days from the family circle in order to obtain anything they wish, should have practised on this alphabet and left a key behind him, we might see in an “agony” column something like the following, which would be rather more puzzling than the guileless ciphers often advertised:-

Treating this like the former illustration – drawing the pen through every 2, and referring to the key, the message is translated thus:-

“dearrobertreturnhomeandallshallbeforgivengovernorsquared;” or

DEAR ROBERT.- Return home, and all shall be forgiven. Governor squared.

If these ciphers should be employed in the service of love, I would recommend ladies to insist on offers of marriage being made in longhand. Jurymen are naturally inclined to look favourably on a fair plaintiff, but it would be a rude shock to their feelings to learn that the declaration, “Darling, I adore you. Only say you will be my wife,” was conveyed in a prosaic row of figures. This sort of thing might affect the amount of damages.

The repetition of the “spacer” would probably attract the attention of the curious, and therefore the next step in ensuring secrecy is to disguise the “spacer.” The most simple way of doing this is to employ two “spacers,” used alternately. The withdrawal of two figures (neither being 0) from those available for the alphabet somewhat reduces the supply of material, but yet leaves enough for variety, the number of combinations now possible – keeping to only two figures – being still many trillions. Taking 4 and 7 for “spacers,” an alphabet may be made thus:-

A 18    G 29    M 20    S  5    Y  6
B  2    H 22    N 30    T 60    Z 99
C 68    I 15    O 50    U 13
D  1    J 11    P 66    V  8
E 03    K 81    Q 36    W  9
F 55    L 39    R 33    X 10

On this plan we will suppose a commercial telegram to be sent –

“Syndicate concerning Silk. Buy.”

But there is no reason, apart from cost of telegraphing – that is to say, with regard to communications by letter there is no reason at all – why the signs should be confined within two figures, and when higher numbers are taken the variety of combination is vastly increased. Indeed, two letter “spacers” and a word “spacer” might then be employed, and the liability of the “spacer” to draw too much attention to itself would be considerably diminished.

Where communications are constantly passing, several alphabets might be arranged, the order of which could be settled by the person sending the message. Supposing 9 such alphabets to be drawn up, and numbered, and the duplicates correspondingly numbered, the person sending a communication could fix the order in which they should become the keys to the message. It would be understood between the two correspondents that so many words – say ten – should be translated by means of each key in turn. Then the order of the keys could be made the first nine figures of the communication – thus: 762814953. The receiver of the message would place his keys in the order indicated, and then translate. Each key would have its own “spacer.”

A government might employ 365 different alphabets or codes, each with its own word and letter “spacers,” copied in one book, and each code bearing a date, the diplomatic agents having duplicate books. A year would thus be covered. The date could be telegraphed or written without concealment, and would indicate to the recipient the key to the message. It is hardly conceivable that an artfully-arranged figure cipher such as I Have explained could be read by another Foreign Office; but supposing it to be possible, and to be done, the discovery would throw no light upon any message transmitted at another date. The entire book could be changed annually.

The last kind of cipher to be set forth is one to which I give the name of the “lockstitch,” each letter being a cipher by itself, so that the repetition of a letter in the message would not involve the repetition of a sign in the cryptogram, and the “spacer” would be changing all the time. A set of alphabets must be drawn up, each having one of the nine single figures, or 0, as its “spacer,” and the message must be taken letter by letter from each alphabet in turn. This plan need only be adopted where no labour would be too great to make assurance not merely doubly sure, but sure a hundred times over. I will suppose the following message to be sent by “lockstitch” cipher:-
“War Imminent. Rely on this. Act accordingly.”

Here are 85 letters. Space does not permit of 35 alphabets being set out in full, but the reader will please to suppose that they exist, and that the necessary letters are taken from them thus (the figure after the hyphen represents the “spacer” allotted to each alphabet):-

W 486-3  I 13-4  E   3-6  H  9-1  A  21-0  I  26-1
A   0-5  N 10-6  L 628-7  I 11-4  C  02-3  N   7-4
R  91-8  E  5-0  Y  00-9  S 83-5  C 938-2  G  39-7
I  34-2  N 60-1  O  90-1  A 95-7  O  28-9  L  57-0
M   6-9  T  4-7  N  81-2  C 32-6  R 329-5  Y 631-9
M  09-2  R 07-3  T  20-8  T 50-9  D   8-6

Each letter is here represented by a different sign, but that is not necessary; indeed, the complexity would, if possible, be increased by having the same numbers to different letters here and there. The “spacer” number follows the letter-sign, and must, therefore, be struck out as each letter is translated. The 35 alphabets would, of course, be numbered, and the numerical order, or order agreed upon, would be followed. The above message, as telegraphed or written, would look as follows:-

The “spacers” are here, to the uninitiated, utterly confounded with the letter-signs.



In conclusion, I beg to submit the following cipher to cryptographers of all nations, informing them, for their guidance, that it is not a “lockstitch” cipher, though taken from more than one alphabet, and that it enshrines ordinary English words. Solutions are respectfully invited:-



Not being able to figure this one out and not having come across the solution anywhere, I'm hoping someone with a good head for figures will be able to give me the key.
« Last Edit: December 03, 2008, 08:30:44 AM by tonybaloney »


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Re: Unsolved 1999 Missouri case ... two codes in the dead man's pocket
« Reply #2 on: November 07, 2011, 08:11:07 AM »
One of my old Army buddies who worked at NSA for 40 years sent me this cipher:

I worked on the frequency distribution, and repeated patterns and made little progress.

Has anyone on this web page made better progress?

Milo Gardner


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Re: Articles on Ciphers
« Reply #3 on: November 09, 2011, 06:52:16 PM »
Taken from offers two short discussions.

The FBI cipher recorded 11 symbols used over 28 times: b, c, d, e, l, m, n, p, r, s, and t,

a language distribution may  match with English which uses: a, d, e, h, i, l, n, o, r, s, t  (11 letters).

So let's look closer, at the low frequency letters from 1 to 15 cipher: a, f, g, h, k, o, v,w, x, z (10 letters)
English uses:  b, f,g,j,k, p q, u, v, x, y z (12 letters) ..

sadly I can not rule out English ... even though I suspect another language or code is hidden in the two pages.

Rigorous statistical tests can compare the FBI cipher raw to the 'norm' English distribution of letters  the way Linear A was proven not to be Linear  B, topics easily researched on Wikipedia.

Some ciphers do not offer sufficient data to be broken, was is the case with Linear A, especially if a two layer Navajo code talker code built the structure of the two pages of 1999 information.

I have the time, but not the code breaking programs on my computer to probe this 1999 issue further. A vowel pattern program for English and other possible languages distribution program comparisons would be needed to to proceed to the second step.  If a needed program or two, or other data drop into my email in-box , I'll be appreciative.