It was Paracelsus as I recall who said to the vulgar speak only of
vulgar things.....men such as Paracelsus were essentially geniuses but
they seemed to be a secret society unto themselves.
My old friend Sybil Leek said Trithemius she thought at devised the
calendar/code which I had at his abbey.....the one book he wrote
Stenographia - consider a court reporter using a machine which to us
would be coded who knew nothing of it, or a secretary using short hand,
etc........
Kings and Queens kept control through the fear of a God whom they said
ordained them to rule.......that is why family trees are so important to
those in any aristocratic and royal society - they still claim divine
right to rule but have to be able to prove their pedigree.
There are two forces using this calendar/code - one for good the other
evil.......in Daniel, the Chaldeans are the astrologers.....and in
Ezekial you find the symbolism of our President -Ezekial 38 and 39 time
to murder of JFK, even to Jeanne Dixon on November 15 which was seven
days before the death of JFK, this woman said the dark cloud was
beginning to descend.......from whom did she receive her salary?
So she was in on it.......murders set for time and date certain, and a
real cabal timed to near perfection.....easy to get someone going to
lunch at high noon when sun in zenith - like Reagan too, leaving the
Temple of Labor and nearly murdered like another brother Hiram.
So I sent you this story on Trithemius which dates way back.....the men
of Spandau had this calendar/watchword code...they also used a bird code
and the Russians knew what they were up to....only high ups had this
stuff and had to be military connected when it comes to
Ordnance.....Ordnance is key word.....supplies in Acts is a key word
used over and over in this one chapter.
Only numbers if my code are Chapter and verse and date and
times....astrology involved.
So hope those interested enjoy this.......
Saba
Reproduced for your convenience, but pull up original if you wish.
Ivars Peterson's MathTrek
May 4, 1998
Cracking a Medieval Code
The first printed book on cryptology was written by Johannes Trithemius
(1462-1516), an abbot in Spanheim, Germany, who was one of the leading
intellectuals of his day. Bearing the title Polygraphiae libri sex ("Six
Books of Polygraphy"), it was published in 1518 after Trithemius's
death.
The first of the six books contains 384 columns of Latin words, two
columns per page. Each word stands for a letter of the alphabet. Here's
a sample from the first page:
aDeusaclemensbCreatorbclementissimuscConditorcpius
By taking the words standing for the letters of a secret message from
consecutive columns, it's possible to construct passages that make sense
as innocent prayers. For example, enciphering the letters of the word
abbot would generate the Latin sentence DEUS CLEMENTISSIMUS REGENS AEVUM
INFINIVET.
The remaining books of Polygraphia introduce additional cryptographic
schemes, accompanied by lengthy tables, for ingeniously hiding
information.
Polygraphia wasn't Trithemius's first venture into cryptology. In 1499,
he had composed a controversial, cryptic volume called Steganographia
(meaning "covered writing").
For years, it circulated privately in manuscript form before finally
being printed in 1606, then placed on the official list of prohibited
books in 1609. Ostensibly, it explained how to employ spirits to send
secret messages.
The first two books of Steganographia contain numerous examples of some
simple types of ciphers. For instance, in the message beginning
PARAMESIEL OSHURMI DELMUSON THAFLOIN PEANO CHARUSTREA MELANY LYAMUNTO .
. . , the first nonsense word signals the specific cryptographic system
being used. The decipherer then knows to extract every other letter of
every other word, starting with the second word, to get the message (in
Latin):
Sum tali cautela ut . . . .
Book III consists largely of tables of numbers, whose columns are headed
by zodiacal and planetary symbols, suggesting astronomical data. Unlike
the first two books, however, there are few clues to help decipher the
contents.
For centuries, scholars debated whether the incomplete third book of
Steganographia contains any examples of enciphered messages. Many
concluded that it does not hold cryptographic secrets and merely
represents magical operations of interest only to occultists.
Nonetheless, the preface of Book III begins by announcing the
provocative goal of presenting a method of transmitting messages afar
without the use of word, book, or messenger.
Trithemius warns, however, that he has deliberately expressed himself
obscurely:
*******************
"This I did that to men of learning and men deeply engaged in the study
of magic, it might, by the Grace of God, be in some degree intelligible,
while on the other hand, to the thick-skinned turnip-eaters it might for
all time remain a hidden secret, and be to their dull intellects a
sealed book forever."
**********************************************
Those are fighting words to a cryptanalyst, and Jim Reeds of AT&T Labs
in Florham Park, N.J., couldn't resist taking on the centuries-old
challenge.
"On receiving a photocopy of the Steganographia, I decided to see ifI
could find any hidden messages in Book III," Reeds recounts in a paper
to be published in the journal Cryptologia. "I knew that Book III was
probably in a draft state. Hence, it might be missing important
information; the printed version had of course not received the author's
proof corrections."
At the same time, he notes, "if Book III was anything like Books I and
II, it was probably pointless to try to follow the instructions given in
the text. Moreover, I could expect that any plain [deciphered] texts
would be short and banal."
Reeds made a lucky guess. He assumed that the cipher was numerical and
that the tables were to be read in columns vertically. He also decided
that the table accompanying the preface was in the form of a key, in
which successive lines describe blocks of 25 numbers each, which might
specify distinct letters-to-numbers encryption formulas.
Reeds started by rewriting the first numerical table, turning the
columns into rows, excluding all headings and data not appearing within
the original columns, and replacing any nonnumerical symbols with a /
sign. Here's a sample:
/ 644 650 629 650 645 635 646 636 632 646 639 634 641 642 649 642 648
638 634 647 632
630 642 633 648 650 655 626 650 644
638 633 635 642 632 640 637 643 638 634 / 669 675 654 675 670 660 675
661 651 671 664
659 666 667 674 667 673 663 659
672 657 655 667 658 673 675 660 651 675 669 663 658 660 667 637 665 662
668 663 659 /
694 700 679 700 695 685 696 686
He noticed that the slashes divide the first 160 numbers into four
blocks of exactly 40 numbers each. Moreover, almost all the numbers in
each block fall within a particular numerical range.
Reeds wrote the four, 40-number blocks in four rows, one underneath the
other, to see if there was any similarity in structure among the rows:
644650629650645635646636632 646. . .669675654675670660675661651671. .
.694700679700695685696686632696. . .719725704725720710721711707721. . .
He found that, with few exceptions, a number in a given row is 25
greater than the corresponding number in the row above.
"Although I still did not know that there was a cipher present," Reeds
says, "it was clear from the emergence of this pattern that there was
enough truth in my initial guesses about column reading and the
importance of the number 25 to continue further."
"And if there were a cipher present, this finding would surely be due to
the presence of four copies of an isolog: four copies of the same plain
text encrypted in different but related ways," he continues. "If I knew
how to read those parts of the text encoded with numbers in the range
626 through 650, I could probably use the same recipe to read those
parts encoded with numbers in the range 651 through 675: Simply subtract
25 from each number and proceed as before."
Reeds went on to check how often each of the 25 different numbers of a
row were used:
626 1631 0636 1641 1646
2627 0632 3637 1642 4647
1628 0633 2638 3643 1648
2629 1634 3639 1644 2649
1630 1635 2640 1645 1650 4
The counts looked uneven enough to be consistent with a Latin or German
text rather than just random outcomes.
A little bit of experimentation revealed that a reversed 22-letter
alphabet apparently fit the observed frequency distribution: 650 = A,
649 = B, and so on, through an alphabet consisting of the letters A, B,
C, D, E, F, G, H, I, L, M, N, O, P, Q, R, S, T, U, X, Y, Z, along with
three additional symbols beyond Z (arbitrarily labeled alpha, beta, and
gamma).
Applied to the 40 letters of the first row, this guess yields:
gazafrequenslibicosduyitca?[gamma]agotriump
hos. That's certainly pronounceable, and it has hints of meaningful
Latin words.
Additional clues helped Reeds unveil the scheme that Trithemius had
used. For example, the symbol beta is really the common German letter
sequence sch, and what Reeds had thought to be x is w. He then
discovered that alpha is tz and gamma is th.
"One final piece of luck cinched the identification of the cipher
alphabet," Reeds says. He performed an Internet search for the two-word
phrase gaza frequens and came up with the Latin passage Gaza frequens
Libycos duxit Carthago triumphos. . . . This confirmed that gamma is th
and suggested that the letter Reeds had labeled as y is actually x.
The Book III ciphers turn out to be numerical substitution ciphers, with
multiple numerical equivalents supplied for each plain text letter,
Reeds concludes.
ThSchTzZXWUTSRQP010203040506070809101112262728293031323334353637515253545556575859606162767778798081828384858687
ONMLIHGFEDCBA131415161718192021222324253839404142434445464748495063646566676869707172737475888990919293949596979899
00
What did Trithemius go to so much trouble to encipher? The text turns
out to be somewhat garbled, probably indicating that pieces have been
lost over the years or were missing to start with. Thus, the text now
available represents little more than a collection of isolated sentence
fragments. Those fragments reveal nothing astonishing: mundane Latin and
German phrases, including one that can be loosely translated as
"the bringer of this letter is a bad rogue and a thief."
"Book III contains cryptograms," Reeds says. "Like those in Books I and
II, they are disguised and presented in a context of angelic magic."
However, the cryptographic technique is different because the letters
are represented by numbers, disguised as astronomical data, instead of
being hidden within a larger mass of letters.
Trithemius might have chosen angel language not to promote magic but as
a ploy to capture the reader's interest. "If so," Reeds says, "he was
vastly successful, even if he completely miscalculated how his book
would be received."
In one final twist to this tale, it turns out that Reeds was not the
first to reveal the ciphers in Book III of Trithemius's Steganographia.
Thomas Ernst, now a professor of German at La Roche College in
Pittsburgh, had resolved the problem several years earlier as a graduate
student at the University of Pittsburgh. He had written a paper in
German describing his solution, which was published in 1996 in the Dutch
journal Daphnis, but apparently no one had paid much attention to it.
In 1676, an obscure figure named Wolfgang Heidel had also claimed that
he had deciphered Book III, but his findings were disputed when he
insisted on writing about the discovery in his own secret code. Ernst
now strongly suspects that Heidel had actually figured out Trithemius's
code. (Hidell was code name for Oswald,,,,,,in Daniel he stands by
river Hidekell.....no K in ancient cyphers my note SABA)
The magic of Trithemius's cryptic work has finally evaporated in the
face of determined code-breaking.
(My Note: Took them nearly 500 years to break with modern
technoloty......but these guys were snobs and blue noses for sure - a
thief could be hired to deliver a message containing his own draconian
death warrant)
Copyright 1998 by Ivars Peterson
References:
Beutelspacher, A. 1994. Cryptology. Washington, D.C.: Mathematical
Association of America.
Kahn, D. 1996. The Codebreakers: The Story of Secret Writing. New York:
Scribner.
Kolata, G. 1998. A mystery unraveled, twice. New York Times (April 14).
Reeds, J. In press. Solved: The ciphers in Book III of Trithemius's
Steganographia. Cryptologia. (Available at
http://www.research.att.com/~reeds/.)
The Latin text of Trithemius's Steganographia can be found at
http://www.avesta.org/tritheim/stegano.htm.
You can visit the National Security Agency's National Cryptologic
Museum, which includes material about Trithemius, at
http://www.nsa.gov:8080/museum/tour.html.
Comments are welcome. Please send messages to Ivars Peterson at
[EMAIL PROTECTED]
Ivars Peterson is the mathematics/computers writer and online editor at
Science News (http://www.sciencenews.org/). He is the author of The
Mathematical Tourist, Islands of Truth, Newton's Clock, Fatal Defect,
and *The Jungles of Randomness. His current work in progress is
Fragments of Infinity: A Kaleidoscope of Mathematics and Art (to be
published in 1999 by Wiley).
NOW AVAILABLE The Mathematical Tourist: New and Updated Snapshots of
Modern Mathematics by Ivars Peterson. New York: W.H. Freeman, 1998. ISBN
0-7167-3250-5. $14.95 US (paper).
http://www.maa.org/mathland/mathtrek_5_4_98.html
