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Gronsfeld Ciphers SOLVING CIPHER SECRETS Edited by M. E. Ohaver HERE IS THE WAY TO SOLVE THE NIHILIST CIPHER AND SOME CIPHERS TO TRY YOUR SKILL ON N our issue of March 28 we offered a sample of the famous Nihilist code which was a challenge to our readers to send us messages that Mr. Ohaver could not translate. I Many of the correspondents doubted his ability to do it without the keyword and hoped that he would reveal the secret of his method. It is no secret. Skillful cryptographers the world over know it, and as Mr. Ohaver says, this method is about as safe as a leaky rowboat in the middle of the Atlantic. It's all in knowing how. In the department this week Mr. Ohaver explains one deciphering method. He says it's easy. Maybe it is. Try it for yourselves. Incidentally he offers some more ciphers from readers and gives the key• words of a lot of Nihilist messages we have received. Your own may be among them. F the numerous correspond• Nihilist cipher in FLYNN'S for April 25. ents who submitted Nihilist But for the benefit of the many who were ciphers for solution in re• tmable to do this, we have decided in re• sponse to our invitation in sponse to insistent requests to publish here FLYNN'S for March 28, for the first time a full exposure of the some were absolutely cer• method used in deciphering this kind of tain that their messages could not possibly cipher. be read without the keyword. To begin with, the Nihilist cipher, while Others, not so confident as these, thought bearing certain other earmarks that assist we might be able to decipher their crypto• in its identification by the initiated, is easily grams, saying, however, that they were recognizable from the fact that its num• completely in the dark as to how it could bers are never lower than 22 nor higher be done. than no. But almost to an individual they wanted If this cipher be carefully examined with to know, i/ we succeeded in deciphering a view to discovering weak points in its their communications, by what method this structure, it will be found to consist in the could be accomplished. use of a number of cipher alphabets in suc• A few of the more experienced fans suc• cession. Like the Gronsfeld cipher, it is of ceeded without the key in deciphering the the polyalphdtbetical type, each of its sev- 794 SOLVING CIPHER SECRETS 795 eral alphabets being formed from the orig• direct evidence against him. Just so, if we inal simple numerical alphabet by modify• can prove that the period of a cipher is ing the latter with one of the numbers of nothing other than four, for example, then the secondary or variable key. jour must be the guilty party. A Nihilist cipher written with a key word By consulting the full description of the of ten letters thus would use a fixed series Nihilist cipher in FLYNN'S for March 28 of ten cipher alphabets in a fixed order, you will find that the twenty-five numbers and, in cipher parlance, would be said to of the original alphabet, or primary key, have a period of lo. are formed from the various combinations The Nihilist cipher is, as far as safety is of the figures i, 2, 3, 4, 5, and that the concerned, just about as valuable as a row- numbers of the final cipher result from ad• boat shot full of holes in the middle of the ditions of two of these figures. Atlantic Ocean. This cipher cannot hold a This being the case, it is possible to de• secret, for it is as leaky as a sieve. termine when two numbers cannot have Under favorable conditions it may be been enciphered by the same key number solved by the method of trial guessing ex• by the following simple rule: It is impossi• plained in the article on the Gronsfeld ble for any two numbers whose units or cipher in FLYNN'S for June 6. Or it may whose tens differ by more than 4 to have be resolved by a general method for poly- been enciphered by the same key number. alphabetical ciphers worked out by a Ger• In taking these differences a zero in the man major, F. W. Kasiski, and described units place is counted as ten. And the only in his book, " Die Geheimschriften und die exception to the rule is when a number Dechiffrirkunst," published in 1863. ends in zero. This always results from the Treatment by the Kasiski method con• addition of two fives, and causes the tens sists first in the mathematical determina• digit to be increased by i. Consequently, tion of the period, and then in the develop• in applying the rule, i must always be ment of the several alphabets. All of these deducted from the tens figure of any num• theories will be fully treated in later articles. ber ending in o. But for the present we shall confine our• To illustrate the full application of the selves to a much more ready method, that method, nothing could be much more ap• will neither require as long a message as propriate than to use it in solving one of does Kasiski's, nor as much time in its ap• the recently submitted Nihilist ciphers. And plication. for this purpose the cipher of Thomas J. Now, to get down to brass tacks, this Sullivan, New York City, has been selected special method consists in the determina• as especially fit in illustrating all of the tion, first, of the number of letters in the" necessary points. key (that is, of the period of the cipher); For the purposes of this explanation, his and, second, of the identity of each one of cipher has been rewritten and numbered by these key letters. This latter step is, of fives, making it easy to tell at a glance the course, equivalent to the determination of serial position of any particular cipher each cipher alphabet. group: By the Kasiski method a period is dis• (5) (10) (15) covered by finding out the only one that 55-38-85-48-78- 79-48-49-62-55- 89-102-30-96-69- (20) (25) (30) it could possibly be. But by this method, as paradoxical as it may seem, it is deter• 79-47-42-84-67- 85-48-93-50-78- 57-46-64-48-74- (35) (40) (45) mined by discovering what it is impossible 39-73-59-77-78- 44-55-59-74-30- 84-87-58-78-54- for it to be. (50) (55) (80) This is what detectives would call iden• B5-69-95-50-63- 50-59-49-85-83- 58-93-29-53-68- tification by elimination. If it is absolutely (65) (70) (75) certain, say, that one man out of a dozen 48-58-74-76-33- 94-39-86-79-57- 58-74-4466-105- (80) (85) (90) has committed a murder, and eleven can 50-86-80-56 70- 42-74-43-84-58- 87-70-69-68-73- prove their innocence, then the twelfth must (93) (100) (105) be guilty, even though there may be no 72-58-72-471961 48-68-67-75-46. 57-95-39-78-79. 796 FLYNN'S In the subjoined table you will find all of divisible into 12 are thus automatically dis• the data required to determine the period posed of. of this particular cipher. But the elimination of a given number For example, if the period is i, this would as a period does not eliminate the multiples mean that the key consisted of but a single of such a number. Thus, if it is found that letter, and that consequently every number 3 cannot be the period, it does not follow in the cipher had been equally increased that 6, 9, 12, 13, et cetera, must on this by the same number. The discovery of ground also be rejected. any two numbers not so enciphered would It is always good policy to test each elim• eliminate this period as a possibility. Two ination by two or three trials with other such numbers are given in the first line of groups. Also it is best before going further the table. to verify the interval not eliminated by Incidentally, a Nihilist cipher with only thorough tests for positive results through• a single letter as the key would be equiva• out the cipher. In the present case there lent to a simple substitution cipher, and will be found no instance where any groups could be solved by any method commonly separated by an interval of 9 provide a dif• used with such ciphers. ference larger than 4, as per the rule. In the case of a period of 2, every second Having rejected every period but 9, it letter would have to be enciphered with may therefore be tentatively assumed that the same key number. The discovery of the period of the cipher is 9, because it is any two numbers separated by an interval not found possible for it to be anything of 2, which, according to the rule, were not else. so enciphered, would eliminate this period. Things now begin to look pretty black Two such numbers are (group 9) 62, and for Number Nine, don't they? So far, noth• (group 11) 39, which have a unit's differ• ing but circumstantial evidence has been ence of 7.
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