The landscape at the Langley CIA complex includes
several unique items which are part of Kryptos. Near the main entrance, a copper plate containing
morse code is sandwiched between slabs of granite. Across the sidewalk are more slabs of granite,
on top of which is a compass engraved into the stone. The compass points across the slab to a lodestone
which sits on top of yet another copper plate. Next, a smaller triangular piece of granite
appears to pierce the surface of the ground. Within the courtyard, more slabs of rock flank
two sides of a still pool of water. Behind this building is the focal point of
the Kryptos installation which includes letters carved into a copper sheet, petrified wood,
another pool, and several large stones. A computer-generated model of the courtyard,
which contains the main parts of Kryptos, allows for a dynamic view of the sculpture. Manipulating the S-shaped copper sheet into
a flattened representation offers a more practical view. The copper sheet is actually composed of four
panels, each of which are about five feet tall by about nine feet wide. Panels three and four are reversed relative
to panels one and two. After the two panels are rotated, all of the
letters are moved onto a grid in preparation of attempting to solve the puzzle. The objects in these photos may hold clues
for solving the puzzle on the copper sheet. But then again, they might not. Mister Sanborn, in an interview with Wired
News, was asked this question: "So just by reading the text taken from Kryptos and posted
online, you can solve the puzzle?". To which Sanborn replied, "well, yeah". The text of Kryptos appears to have been designed
with a fictitious operative in the field in mind. Ed Scheidt, the man who taught cryptography
to Jim Sanborn, described the idea of getting a message to an operative and that the message
must contain the clues, or keys, for decrypting the message. What might an operative, who is trained in
cryptography, make of the text from the Kryptos panels? Scanning the characters of each line would
reveal that there are four question marks breaking up the text. A trained eye would easily recognize the Vigenere
Tableau. The operative might find it curious that three
alphabets surround the tableau, and that four extra columns have been appended to the right
edge. At least some of the message was encrypted
using substitution, because of the Vigenere Tableau. However, the operative would likely perform
a frequency analysis to expose any use of transposition. Many of the letters J K Q V X and Z will show
up in substitution. But only a few of these letters will exist
in a message encrypted using transposition. An analysis of each line reveals that there
is one section encrypted using transposition and two sections using substitution. The substitution sections were likely encrypted
using the provided Vigenere Tableau. Encrypting with a Vigenere Tableau implies
the use of one or more keywords. Keywords can often be recovered through an
analysis of the cipher-text. First, the operative would attempt to identify
the length of the keyword by looking for sets of repeating letters in the cipher-text. The first two lines contain the five repeating
letters V J Y Q T at 20 characters apart. This suggests a keyword length of at least
five. So either five or 10. The next two lines contain the five repeating
letters G W H K K at 16 characters apart. Therefore, the length of the keyword must
be five or more letters. So, it's most likely an eight-letter keyword. At lines 11 and 13, the letters N U V P D
repeat at 72 characters. Possible keyword lengths are 6 8 9 and 12. The spacing of other pairs of repeated letters
suggests a keyword length of eight. Because a longer message is easier to decrypt
than a shorter one, the operative might attack the lines three through 14 first. To begin, the letters are placed into rows
of eight, leaving out the punctuation. The two alphabets, written at the top of this
grid paper, are for reference. The first is the Kryptos alphabet taken from
the first row of the vigenere tableau. Below the letters are written the numbers
0 through 25. The second is just the regular alphabet. Below this alphabet are numbers from the Logarithmic
Weights of Letter Probabilities, in chapter nine of the 1990 Army Field Manual on Basic
Cryptanalysis. These numbers were assigned to each letter
based on how often the letter appears in the English language. To begin the analysis, the first column of
cipher-text is written along the left side of the grid paper. The letter A is placed at the top of two columns
to the right. Using the Vigenere Tableau, each letter of
the cipher-text is decrypted using the letter A as the key. The short-hand method is to subtract the key
from the cipher-text. The numbers associated with each letter come
from the first alphabet at the top of the grid paper. When the result is a negative number, 26 is
added. Next, the plain-text letters are each assigned
a weight value from the logarithmic weights alphabet. These numbers are totaled at the bottom of
the column. This entire process is repeated 25 more times
using each letter of the alphabet as the key in the formula. Now the column with the highest total will
reveal the first letter of the eight-letter keyword. Here, column A has the highest total of 350. So, the keyword likely begins with A. This entire process is repeated with each
of the eight columns of cipher-text. When finished, the keyword ABSCISSA is revealed
by the eight columns which have the highest totals. The eight columns with the highest totals
also contain the plain-text which, when brought together, reveals the deciphered message. This process doesn't work as well when the
amount of cipher-text is small, as is the case with the first two rows. As discovered earlier, the keyword length
could be either five or ten, so the cipher-text is placed in rows of both five and ten letters. Using the same process as before, the highest
totals for the five columns results in a keyword of: P E L J K. The highest totals for the ten columns results
in a keyword of: P A L I Z P E G J S. Because both keywords are non English words,
the plain-text under both keywords is examined to see if any whole or partial English words
stand out in any or all of the rows. The text under the ten-letter keyword looks
the most promising. The word BETWEEN is apparent in the first
row. The fifth column should be replaced so that
an E is at the top. An E at the top is found under the key letter
M. The seventh column should be replaced so that
an N is at the top. An N at the top is found under the key letter
S. Now the keyword can be made out and the rest
of the cipher-text is easily decrypted. The portion of the cipher-text which involves
the use of transposition will be addressed next. The simplest form of transposition is the
rotation of a block of letters which have been arranged into a square. This method will be attempted first. The number of letters in the Kryptos transposition
cipher will determine the size of the square to be used. The total is 336, and the square root of 336
is 18.33. An exact square is not possible. Therefore, several integer-pairs are calculated
which are close to 18.33 and are a factor of 336. These integer pairs are: 12 and 28, 14 and
24, and 16 and 21. The number pair closest to forming an exact
square is 16 and 21. The 336 letters are rotated and placed into
rows of both 16 and 21 letters. Clockwise is the standard direction of rotation. One of these rectangles is selected to work
with. A new rectangle is then started, bottom up,
by taking five letters at a time starting at the lower right corner of the chosen rectangle. If an English word doesn't start to form in
the left-most column a new rectangle is started using six letters at a time, then seven, and
so on. If not successful with the first selected
rectangle, the other rectangle will be selected. Success is achieved, when 12 letters at a
time are taken from the 21 by 16 rectangle. The word SLOWLY appears in the left-most column. And more English words appear in other columns
as well. Working from bottom to top, the remaining
letters are placed into the rows of twelve. The rectangle is rotated one last time to
make it easier to read. Here, the final result is placed into 12 rows
of 28. The first encrypted message, referred to as
K1, appears to make reference to the lower atmosphere, outer space, the northern lights,
and the earth's magnetic field. Between subtle shading, and the absence of
light, lies the nuance of illusion. The word illusion contains the letter Q in
place of the first L. The importance of this Q will be made apparent
later in the recovery of keywords from the text of Kryptos. The second encrypted message, which is referred
to as K2, is composed of several individual messages which are separated from each other
by the letter X. The first message of K2 may be describing
the act of hiding an entire ship from being detected by radar. The next three messages seem to share a common
but vague topic. The word underground, however, is misspelled. The extra letter U will play a part later
in the recovery of keywords. The fifth message contains numbers in the
form of latitude and longitude coordinates. These numbers will become important later
as part of a proposed algorithm used in solving the fourth message. The sixth message, which appears to be part
of the fifth message, simply says, I D BY ROWS. However, mister Sanborn offered a correction,
saying that a letter S had been omitted. The corrected message is preceded by an X
and says LAYER TWO. This message will also play a part later in
the recovery of keywords. The third encrypted message, which is referred
to as K3, describes the act of opening the tomb of King Tutankhamun. The first line contains three raised letters,
and the word desperately, which is misspelled with an A in place of an E... and also has
a missing E before the L Y. All of these are clues in the recovery of
keywords. The letter Q, just before the question mark
at the end of K3, will also play a role later in the recovery of keywords from the text
of Kryptos. The first part of this video was created in
order to establish a mind-set. This was done by demonstrating some of the
standard analytical techniques involved in working with an encrypted message. The remainder of this video will focus on
the final 97 letters of Kryptos referred to as K4. Since K4 appears to be a substitution cipher,
keyword recovery would be attempted next. However, it becomes difficult when there are
only short sets of repeating letters. K4 was designed to be more challenging. The keywords for K4 are actually hidden in
the text of the sculpture. They must be found before K4 can be decrypted. After the keywords are found, there is a specific
technique which was used in K4 to mask the English language. And that technique must be discovered as well. The next part of this video will cover an
idea of what the keywords are and where to find them, as well as present the masking
technique which may have been used to arrange and encrypt those last 97 letters. First, the masking technique. K4 appears to have been encrypted by first
placing the letters into rows below two keywords. For now, call the keywords A and B. Keyword A is seven letters and keyword B is
eleven letters making a total of 18. K4 is placed into five rows of 18 and then
one row of seven below the two keywords. K4 is then divided on the keyword boundary
making two puzzles. At first glance it appears that K4 was split
and each side was encrypted with its own keyword. The two sides were then put back together
to appear as a single puzzle. Analysis of side A will produce valid results. So will analysis of side B. But, analysis on K4 as a single puzzle will
fail. The English language won't be exposed. And we have uncovered the masking technique. If only it was that simple. It appears that the masking technique is more
complicated than that. Encrypting requires the use of an alphabet. But with K4 it appears that each row segment
in each half of the puzzle may have been encrypted with its own alphabet. Or rather one of six possible alphabets. The six alphabets would be numbered three
through eight to match the same numbers used in the latitude and longitude coordinates
provided in K2 which use only the numbers: 3 4 5 6 7 and 8. The latitude coordinate numbers 3 8 5 7 6
5 are placed alongside puzzle A. And the longitude coordinate numbers 7 7 8
4 4 are placed alongside puzzle B. The first row of puzzle A, for example, would
be decrypted using alphabet number three. The second row would use alphabet number eight,
and so on. There may be even more to the masking technique
than this. Instead of two keywords, there may be eleven
keywords, one for each segment. Ed Scheidt made the comment that the key is
the algorithm or the instructions of how to proceed. The keywords A and B give instructions to
use two streams of letters as keywords. Instructions for where to get the streams
of letters was not provided. However, the text of Kryptos would be a likely
source for an operative in the field to find these key-streams. Unlike an operative in the field, we have
the advantage of seeing part of the original encryption sheets which were supplied to the
media by Mister Sanborn. Using clues provided on this code sheet, it
appears that the cipher-text of K1 and K2 provide the two streams of letters. K4 has been arranged into rows of 18 letters
and on the code sheet can be seen marks at the 18th character on the first lines of both
K1 and K2. Two arrows are also drawn on K1 to show the
direction in which the key-stream is to be taken off... from left to right on the first
row... and from right to left on the second row. Another mark found on the second line of K1
indicates where to stop. Eighteen letters from K1 brings us to the
first mark. Two more sets of 18, and a set of seven letters
brings us to the stop mark, with a total of 61 letters from K1. Eighteen letters from K2 brings us to its
mark. Then eighteen more makes 36 letters from K2,
and a total of 97 letters from the two streams. Another possibility is to take the two sets
of 18 letters from K2 and place them before the letters from K1. Some trial an error will obviously be required
to determine which arrangement is correct. The masking technique appears to have been
accomplished by dividing K4 into eleven puzzles, using two key-streams as eleven keywords,
and eleven numbers as indices into six alphabets. If K4 was designed to be this complex, then
it explains why Ed Scheidt said, "you need to solve the technique first, and then go for the puzzle". As previously indicated, six alphabets are
to be used. Where can they be found? The six alphabets are actually created from
one alphabet by using something called decimation. An alphabet is decimated when it is systematically
reordered using a selected integer, such as three. The third letter is taken first, then the
sixth, ninth, twelfth, and so on. When the end of the alphabet is reached, counting
continues by wrapping around to the start. When all 26 letters have been taken, the alphabet
has become a decimated alphabet. This doesn't work with some integers, such
as four. Every fourth letter is taken until the end
of the alphabet is reached, then counting wraps around to the start. After the second loop, it wraps around to
a letter which has already been taken. The only integers which can be used to decimate
an alphabet must be co-prime with the length of the alphabet, which is 26 in this case. These integers are: 1 3 5, 7 9 11, 15 17 19,
21 23 and 25. What is needed are six alphabets decimated
using the numbers 3 4 5 6 7 and 8. So, a 26-letter alphabet cannot be used. What can be used is a 31-letter alphabet because
31 is a prime number and all other integers are co-prime with 31. This is why four extra columns were added
to the vigenere tableau. Each row now contains a 30 letter alphabet,
and one of the rows has a 31 letter alphabet. The six required alphabets are obtained by
decimating this alphabet using the numbers 3 4 5 6 7 and 8. Now for the recovery of keywords from the
text of Kryptos. Up to now the two main keywords have been
referred to as A and B. Together, they have the meaning of two key-streams. Keyword A is the seven letter word LETHEAN,
which is a certain river in Greek mythology. Keyword B is the eleven letter word PARASYSTOLE,
which indicates the existence of a second pacemaker. Applying these words to cryptography, the
role of a keyword is equated to being a pacemaker, with there being two. And the river is equated
to being a stream. Combined, there are two key-streams. These two keywords have been hidden somewhere
in the text of Kryptos. Not only did Mr. Sanborn have to figure out
how to hide these two keywords, but he also had to figure a way to specify that they should
be joined end to end. And that the word LETHEAN should be placed
before the word PARASYSTOLE. The keyword PARASYSTOLE is the easiest to
discover. It is found in the plain-text at the start
of K3. The two words, SLOWLY and DESPERATELY, possess
most of the necessary letters in which to hide the word PARASYSTOLE. Two A's are needed, but there is only one A available. So an E was switched to an A. The W, and the second L of the word SLOWLY
are not needed... as well as the D of DESPERATELY. So these three letters were raised as an indicator
to get rid of them. All that is needed now is a way to communicate
where to stop taking letters from the start of K3. Removing a letter would signal where to stop. So this is why the letter E was removed. The three raised letters, W L and D, are replaced
(after the transposition process has been completed) by the letters Y A and R. So, it's the position of the raised letters
Y A and R that's important, not the letters themselves. The keyword LETHEAN is much more difficult
to recover from the text of Kryptos. The keyword PALIMPSEST, from K1, offers one
of two clues. Palimpsest refers to layers of writing. The other clue can be found in the words,
LAYER TWO, located at the end of K2. If this top panel is layer two, then the bottom
panel must be layer one. By placing one layer of this text on top of
the other, a few of the same letters of both layers will become aligned. This is a type of steganography and it is
how the letters of the keyword LETHEAN were hidden in the text of Kryptos. Rather than showing how to find the keyword,
it might be beneficial to see what steps were required to hide the keyword LETHEAN. To begin, the text was originally placed into
rows of 31 characters, with two necessary exceptions. Also at this stage, the words ILLUSION and
UNDERGROUND are spelled correctly. The letter Q, placed at the end of K3, is
intentional. It will act similar to a registration mark
used by professional printers to align color layers. The ideal position for overlapping the two
layers must be found next. By moving layer two, nine rows down, and one
column to the right, five of the seven letters of the keyword LETHEAN are either aligned,
or close to being aligned. The first letter is brought into alignment
by shifting the corresponding row of layer one by two columns to the left. The two left-most letters are then moved up
and to the end of the row. The second letter is brought into alignment
by shifting the corresponding row of layer two, one column to the left. The left-most letter is also moved up and
to the end of the next row. The fifth letter is brought into alignment
by shifting the corresponding row of layer two, one column to the right. A letter is then borrowed from the end of
the row above in order to fill the void at the left. An operative in the field will need to know
how to align these two layers correctly. To mark this exact position, the letter Q
on layer one is located. And then the letter directly beneath the Q,
on layer two, is forced to become a Q when decrypted. It just happens to be the first L in the word
ILLUSION. Aligning the letter Q of both layers will
bring five letters of the word LETHEAN into alignment. The remaining two letters of the word LETHEAN
are to be aligned by first taking the top nine rows of layer one and moving them down
to cover the bottom nine rows of layer two. Two letters are already aligned on the next
row to be used. A letter T is wanted, but not the letter N. There happens to be another letter T which
can be used. This letter T is brought into alignment by
shifting the corresponding row of layer two, one column to the right. Doing so takes the letter N out of alignment. One letter is borrowed again from the end
of the row above in order to fill the void at the left. Six of the seven letters of the word LETHEAN
have been aligned on both layers. The final required letter is an E. However, there happens to be ten more letters
which are already aligned just by coincidence. Assuming the final letter E is aligned, an
instruction must be left to use only the first seven letters to make a word. This is accomplished by finding the next available
letter E, on layer one, and then forcing a misspelling of the word beneath it, on layer
two. The desired effect will be to draw attention
to the letter and raise the question of why it is there. The answer, of course, is to take the letter
E which is above the misspelled letter U and unscramble the letters up to that point. One final task remains. An instruction must be included to place the
word PARASYSTOLE after the word LETHEAN. If one more random letter was brought into
alignment, there would be eleven random letters after the seven letters which make up the
word LETHEAN. A letter E on each layer has a separation
of only one column. These are brought into alignment by shifting
the corresponding row of layer one, one column to the left. The left-most letter is again moved up and
to the end of the row. This brings the total to eleven. However, to insure additional words or phrases
are not to be made from these random eleven letters, several letter-swaps will be made. The row with the aligned letter C has two
letters on each layer which are each separated by two columns. The row on layer one is shifted one column
to the right, and a letter is borrowed from the end of the row above. The row on layer two is shifted one column
to the left, and the left-most letter is moved up and to the end of the row. The letter C is replaced by the letters A
and N. Next, the letters H and S are both removed. They are on the same row, so they are tied
to the same action. The row on layer two is shifted one column
to the left, and the left-most letter is moved up and to the end of the row. The removal of those two letters leaves one
space to be filled. The next row contains the letter E which is
only off by one column between the two layers. The row on layer one is shifted one column
to the right and a letter is borrowed from the end of the row above. With the alignment of the letters completed,
the rows are restored to their original positions. The jagged right edge of the two layers is
explained by the adjustments which were made in order to align the 18 chosen letters. Imagine an operative in the field receiving
only a sheet of paper with the transcribed text of Kryptos. The design of Kryptos was oriented toward
a fictitious operative in the field. And the text of Kryptos contains both the
message and the keys. Mister Sanborn revealed that the text is the
only item required for decrypting its messages. Half of the text contains encrypted messages. The other half contains a Vigenere Tableau. Letter frequency analysis reveals the use
of both substitution and transposition ciphers. Groups of repeating letters in the top half
reveal that two keywords are used, and that the top half contains two puzzles. Keywords for the two puzzles are recovered
by calculating the logarithmic weights assigned to all possible plain-text letters for each
puzzle. The columns with the highest totals reveal
some or all of the keyword letters. The last question mark reveals the end of
the third puzzle, which utilizes a transposition cipher. It is decrypted by first rotating the 336
letters clockwise and into a block. This is followed by a restructuring of the
block of letters to discover English text. Then one final rotation of the letters makes
it readable. The solution to K4 comes in two stages, the
first of which is to figure out how the puzzle was structured so that the English language
will not be revealed through standard analysis techniques. The process begins by discovering two keywords
in the text of Kryptos. One keyword is found at the start of the K3
plain-text by taking the letters up to the missing E in the word DESPERATELY, and then
discarding the three raised letters prior to unscrambling the remaining letters. The other keyword is found by first aligning
the two Q's on the bottom and top halves of the puzzle. Five of the same letters will become aligned
on the two layers. Bringing the top nine rows down will reveal
the alignment of twelve more letters. The letter E, which is on top of the letter
U in the misspelled word UNDERGROUND, is also included. The first seven letters are unscrambled to
reveal the keyword LETHEAN. The remaining eleven letters are a placeholder
for the keyword PARASYSTOLE. The 97 letters of the fourth puzzle are then
placed in rows below the two keywords. The puzzle is then divided on the keyword
boundary, making a total of eleven row segments. Next, the eleven numbers provided in K2 as
latitude and longitude coordinates are placed alongside the eleven row segments. A specific alphabet in the center of the tableau,
which is 31 letters in length, is decimated using the numbers 3 through 8 in order to
make six unique alphabets. The integers which make up the coordinates,
are used as indices into the list of six alphabets. The definitions of the two keywords LETHEAN
and PARASYSTOLE lead to the idea of using two key-streams. The source of the key-streams must be available
to the operative in the field. The cipher-text of K1 and K2 offer streams
of random letters as a source for the two key-streams. The puzzle called K4 appears to actually be
eleven puzzles, each encrypted as a one-time-pad. This arrangement resembles the rows and divisions
of the Berlin Clock. The two words, BERLIN and CLOCK, are the solution
to the 64th through the 74th letters of K4. The question now is, what algorithm was used
to encrypt BERLIN CLOCK to N Y P, V T T, M Z F P K.
