The encoding chart, unfolded

In November 2010 the New York Times published two sheets of Jim Sanborn’s handwriting: the worksheet on which he enciphered the first two sections of Kryptos. Two days later he told NPR that if people studied the sheets “in a forensic manner, there might be revelations in there.” We took him at his word and read the published chart cell by cell. This page is what we found, what we did not find, and one way the sheets may have folded.

Still from the animation: the K1 and K2 chart pieces laid out one above the other, with their taped joins marked. — One possible reconstruction of how the K1/K2 encoding worksheet could have folded at its taped joins. The fold locations, directions and sequence are unverified, and no K4 mechanism is established. The animation is built from the tape and margin evidence described below, not from a photograph of the folded object. The handwriting is Sanborn’s; the paper motion is ours. 58 seconds, silent. Download as GIF (7.5 MB)

In plain English: the chart is a working sheet on pad paper, most likely taped page to page so it could fold like a small scroll. Every mark on it that is not a letter looks like ordinary bookkeeping. Its rows break in different places from the letters on the copper. The one thing it settles is that the two famous misspellings in K1 and K2 happened at different stages: one on this sheet, one after it.

What Sanborn actually said

The remark comes from NPR’s All Things Considered on November 22, 2010, two days after the Times published the charts alongside the BERLIN clue. Asked whether releasing a clue meant he wanted the puzzle solved, Sanborn answered:

“I also divulged, or gave images, of my original decoding charts, the ones that I, well, actually, for me they were encoding charts. And I think once the Krypto-philes study it in a forensic manner, there might be revelations in there. So in a way, I gave more than just Berlin.”

Three things he did not say are worth stating plainly:

He named no kind of examination. Paper, handwriting, corrections, erasures and margins are all the community’s later elaboration.
He was talking about these two K1 and K2 sheets only. The K3 chart was not shown until 2013, and the K4 material was not public in 2010.
He did not say the charts contain a clue to K4. “Revelations” is left open.

One later report points somewhere specific. An attendee at a 2013 American Cryptogram Association dinner wrote that Sanborn urged people to study the released charts “particularly regarding misspelled words.” That is an unrecorded second-hand account Unverified, but it matches what the chart turns out to carry, so we come back to it below.

What the chart is

Two pieces of green-grid computation paper, photographed separately. Each line of the message takes a block of four ruled rows: the plain text, the keyword written out letter by letter beneath it, the resulting cipher text, and a blank row. The keyword for K1 is PALIMPSEST and for K2 is ABSCISSA; how those keywords drive the letter substitution is explained on the About page. Rows are numbered 1 to 8 in the left margin and every row is 31 cells wide.

The full K1 and K2 encoding chart with the paper tone flattened so the pencil reads evenly: an upper piece holding rows 1 and 2 under the heading PALIMPCEST, and a lower piece holding rows 3 to 8 under the heading ABSCISSA. Each row is three lines of capital letters in a printed grid, with a blank line between rows. — The published chart with the paper tone flattened by dividing out a wide median of the background. This is the same photograph the Times ran, not a new image; the processing only evens the lighting so faint pencil and tape edges can be compared across the sheet.

Chart row	Section	Cells with letters	Notes
1	K1	31	The header line above it reads PALIMPCEST, spelled with a C.
2	K1	31, plus one	K1 has 63 letters. The 63rd is written as a little vertical stack, N over L over D, in the first column below the block.
3	K2	31	The header ABSCISSA sits in the unruled top margin, on the tape.
4	K2	30 and a `?`	The question mark takes a cell and is copied down through all three lines. The keyword does not advance on it.
5	K2	32	One cell too many for the grid. The extra letter, its key letter and its cipher letter are boxed by hand in the left margin.
6	K2	31	The cipher line is written in a band with no printed grid, between rows 6 and 7.
7	K2	31
8	K2	30 and a `?`	The photograph ends here. K2 continues on sheets that were not published.

We checked every one of the 744 cells against the K1 and K2 text using the same cipher code that reproduces the solved sections. Reading the K1 cipher rows in order, including the stacked D, gives the 63 carved K1 letters exactly. The K2 rows give the first 185 carved letters with one exception, described below.

How it was physically put together

This is the part of the chart that a levels adjustment in an image editor tends to miss, because it is about the paper rather than the pencil. Six things are visible once the tape and the paper edges are isolated by colour.

The chart with red rectangles drawn around the areas whose colour matches aged adhesive tape: several patches along the bottom edge of the upper piece and the top edge of the lower piece, a run along the left margin, and three separate patches in the band between rows 6 and 7. — Regions whose colour matches yellowed adhesive, outlined in red. They cluster at the join between the two pieces, along the left margin, and in three separate patches on the band between rows 6 and 7.

The two pieces were taped together and later separated. Tape residue at the join is in several separate patches, not one continuous strip, on both the bottom edge of the K1 piece and the top edge of the K2 piece. The exact way they bridged cannot be recovered from this photograph.
There is a second join inside the K2 piece. Between rows 6 and 7 runs a full-width band with no printed grid. The printed grid below it is shifted about 2 pixels sideways from the grid above it, and three tape patches sit on the band, left, centre and right. Rows 3 to 6 and rows 7 to 8 are two pieces of paper.
Three lines of writing sit in unruled margins, and all three are on tape: the stacked D at the foot of the K1 piece, the ABSCISSA heading at the top of the K2 piece, and the whole cipher line of row 6, written freehand across the band with no cells to guide it.
Overflow was handled two ways. K1’s 63rd letter went below the block in the first column. Row 5’s 32nd letter went to the left of the grid in a box drawn by hand, with its key letter and cipher letter boxed beneath it. Same problem, two different fixes.
A crease runs along the top of the row 4 cipher line, a thin yellow-brown line the full width of the sheet. The letters beneath it are not degraded.
Two pale blue-grey rectangles sit in the left margin, each about a cell wide and a cell and a half tall, beside row 3 and again beside row 7. Each is at the head of a piece of paper. We return to them below.

Close view of the bottom left of the K1 piece: the letters N, L and D stacked vertically in the first column of three otherwise empty grid rows, with the D sitting below the last printed rule on a strip of tape. — The 63rd letter of K1. Plain text N, key letter L, cipher letter D, stacked in the first column below row 2 because the row was full. The D is written on the tape at the foot of the sheet.

Close view of the left half of the row 6 cipher line: the letters G Z L E C G Y U X U E E N J T B written freehand on a band of paper with no printed grid, below a ruled row of keyword letters. — The row 6 cipher line, written on the unruled band between the two pieces of the K2 sheet. Its pencil is measurably darker than the lines in the grid above, as is the ABSCISSA heading, which also sits on tape.

Why not a larger sheet?

Computation pads have unruled margins at the top and bottom of every page. The simplest account of everything above is that when a three-line block ran off the ruled area of a page, Sanborn wrote the third line in the margin rather than start the block again on the next page, which keeps plain text, key and cipher text lined up vertically. That is the whole point of the worksheet. The next page was then taped on underneath, in patches rather than a sealed strip, so the join could fold. The result is a long, hinged run of pad pages carrying the whole encipherment in one unbroken keyword sequence, later cut back apart at the joins, plausibly for framing or photography. The 31-cell width is the pad’s width and the copper’s. It was the page height that ran out, and tape is how a pad becomes a scroll.

That is what the animation at the top of the page shows, and it is a reconstruction, not a record. One more caution before anyone measures anything: the two pieces were placed and resized separately when the photograph was assembled. The upper piece is reproduced about 1 percent wider and 2 percent taller than the lower one. The published image cannot be used to compare the chart’s dimensions with the sculpture’s.

The row breaks do not match the copper

The chart breaks every row at 31 cells, with the two overflow tricks above. The lines cut into the copper do not. Reading down the left panel of the sculpture, the K1 and K2 lines run 32, 31, 31, 30, 31, 32, 31 and 31 letters.

Line	Letters on the copper	Letters on the chart row
1	32	31
2	31	31, plus the stacked D
3	31	31
4	30	31, counting the `?`
5	31	32
6	32	31
7	31	31
8	31	31, counting the `?`

Concretely: the J that ends the first carved line is the first cell of the chart’s row 2. The T that begins the fifth carved line is the last cell of the chart’s row 4. The D that ends the second carved line is the chart’s little stack below row 2. The letters are the same sequence in the same order, poured into different line lengths.

Sanborn explained why in the same NPR interview: “there were several ways I could manipulate the lines of text so I would end up with a panel that’s square on the sides.” The chart is the encipherment draft at a steady 31 per row. The line lengths on the copper were adjusted afterward for the look of the panel’s edge. Anyone using the chart’s row breaks as evidence about the copper layout, or the other way round, should know they differ.

The chart with the detected printed grid drawn over it: thirty-two vertical lines in blue on the upper piece and red on the lower piece, with horizontal lines in green, showing 31 columns on both pieces. — The printed grid as detected by the software: 32 vertical rules on each piece, so 31 columns. The cell pitch is about 34 pixels on both pieces, but not the same 34 pixels, which is how the separate resizing of the two pieces was found.

The two misspellings happened at different stages

The copper spells ILLUSION as IQLUSION in K1 and UNDERGROUND as UNDERGRUUND in K2. Both words are spelled correctly on the chart. Of the 744 cells on the sheet, two letter positions, four written cells, disagree with what is on the copper, and they disagree in opposite directions.

Chart cell	Line	Expected	On the chart	On the copper
Row 2, column 25	plain text	Q (as carved)	L (ILLUSION)	—
Row 2, column 25	keyword	S (PALIMPSEST)	C (PALIMPCEST)	—
Row 2, column 25	cipher text	K	K	K, matches the chart
Row 6, column 21	plain text	U (as carved)	O (UNDERGROUND)	—
Row 6, column 21	cipher text	R	E	R, does not match the chart

Columns are counted from 0, as everywhere on this site.

Enlarged cells from row 2 of the chart: the plain text reads E O F I L L U S, the keyword row beneath reads L I M P C E S T, and the cipher row reads Y Q T M K Y R D. The C of the keyword sits under the first L of ILLUSION. — Row 2, columns 21 to 28. ILLUSION is spelled correctly in the top line. The keyword beneath it is written PALIMPCEST, and the letter C under the first L produces the cipher letter K, which is what was carved. Decoding K with the correct keyword letter S gives Q, hence IQLUSION.

Enlarged cells from row 6 of the chart: the plain text reads N D E R G R O U N, the keyword row reads I S S A A B S C I, and the cipher line below the grid reads B J L B Q C E T B. The O of UNDERGROUND sits above the cipher letter E. — Row 6, columns 15 to 23. UNDERGROUND is spelled correctly, the keyword letter under the O is S, and the cipher letter Sanborn wrote is E. The copper has R at that position. The O beside a clearly open-topped U in the next cell shows the hand distinguishes the two letters.

The letter arithmetic, checked against our cipher code

K1 and K2 use the keyed-alphabet substitution described on the About page. Running our implementation of it on the four cells in question:

enc(L, key C) = K   chart row 2, col 25  -> the carved K1 letter
enc(Q, key S) = K   expected             -> same letter by a different route
enc(O, key S) = E   chart row 6, col 21  -> the letter on the chart
enc(U, key S) = R   expected             -> the carved K2 letter

Replacing the single keyword letter at K1 position 56 with C, and keeping the plain text ILLUSION, reproduces all 63 carved K1 letters. The chart was read at three to nine times magnification, with an independent template matcher as a second reader; at both cells the matcher ranked the chart’s letter above the expected one, and it ranked the expected letter first at neighbouring control cells.

So the two errors have different histories. IQLUSION was made on this sheet: the keyword was miswritten as PALIMPCEST, the same spelling that heads the page, and the cipher letter Sanborn computed from it is the one on the copper. The sculpture faithfully reproduces a worksheet that was already wrong. UNDERGRUUND was made after this sheet: the worksheet is entirely correct, and the wrong letter appeared somewhere between this page and the copper. Both conclusions had been reached by the community from the published image. What is new is that they are now verified cell by cell against the cipher code.

That matters for any theory that treats the misspellings as deliberate signals. At the moment of encipherment, ILLUSION was spelled correctly in front of him. Whatever IQLUSION means, it was not visible as a choice on the plain text line when the cipher was made.

What we looked for and did not find

Because Sanborn left “revelations” open, we also looked for things that were not letters. All of the following are results about this one published photograph, a 1.5-megapixel web JPEG that passed through the photographer, the newspaper and an image editor before it reached us.

Cells read 744

Positions differing from the copper 2

Hidden marks recovered 0

No faint or erased writing. A letter-sized detector was run over every blank region: the header band, the blank rows, the gaps between rows, the margins, both joins and the strip below row 8. Its noise floor is 2 to 3 grey levels; the faintest real pencil letter on the page scores 12.4. Anything about half as faint as the faintest real letter would have shown, and nothing did. This says nothing about pressure marks with no tonal trace, which need raking light on the object itself.
No second ink. Every stroke on the sheet falls into one colour class once the paper tone is removed. Within what this image can separate there is no second pen, though that does not prove one pen or one sitting.
No hidden pattern. The frequency picture of the image contains the printed grid, the four-row block rhythm and nothing else.
Thirty-one marks that are not letters, all catalogued with coordinates: row numbers, two arrows, a check mark, ticks, corner brackets, isolated dots, a heavily traced S and Y, a struck-through H, lower-case letters inside BURIED. None has more than one indicator pointing beyond place-keeping while working across several hundred cells by hand.
The “bleed-through” is grain. Pushing the levels of this JPEG to extremes fills the blank cells with coloured speckle. That is paper texture and compression noise amplified about 25 times, with each printed cell clipping slightly differently. It is not writing on the reverse side.

Enlarged left margin beside row 7 of the chart: the row number 7, the first cells of the three lines K, I and I, and to their left a faint pale blue-grey rectangle about one cell wide and a cell and a half tall. — The left margin beside row 7, enlarged four times. The faint blue-grey rectangle to the left of the grid has a twin beside row 3.

What would settle the open items

Each of these needs the physical sheets or new photography of them, not another pass over the published image.

Raking light across the surface, to separate pressure impressions from surface pencil.
Light through the paper, to show anything on the reverse side, what the tape covers, and what the two margin rectangles are.
Measurement in millimetres and a look for a watermark, to establish whether the three pieces are from the same pad.
The remaining K2 sheets, which the 2010 photograph does not include.

How confident we are

What we know and don’t know

Everything on this page rests on one published photograph and on cipher arithmetic that anyone can repeat. The arithmetic is certain. The physical readings are as good as a 1.5-megapixel web image allows, and a better image or the object itself could overturn the medium-confidence ones. The animation is a reconstruction of one way the sheets could have folded, and it should be read as an illustration of the tape evidence, not as a record of what Sanborn did.

High: the row breaks differ from the copper; row 5 has 32 cells; the two misspellings differ from the copper in the way described; no faint writing is recoverable from this image.

Moderate: the second join at rows 6 and 7; the tape readings at the main join; the pad-page account of how the sheet was assembled.

Low: what the two blue-grey margin rectangles and the row 4 crease are. Present, nature unknown.

Images. The chart is Jim Sanborn’s work. The photograph of it was published by The New York Times with John Schwartz’s article “Original Decoding Charts for ‘Kryptos’” (November 2010) and is reproduced here at reduced size, with enlarged and tone-flattened details derived from it, for commentary and education on a non-commercial research site. The animation is built on period screenshot copies of the same publication hosted by Kryptos–Beyond K4. If you hold rights in any image here, write to us and it will be credited or removed the same day, whichever you prefer.

Sources. NPR, All Things Considered, November 22, 2010, Mary Louise Kelly interviewing Jim Sanborn. The New York Times, November 21, 2010 (posted online November 20). The full working note with cell coordinates, measurements and the corrections made along the way is on GitHub. For how we grade claims, see How we test.

About Kryptos & how the cipher works → · Sanborn’s other working papers → · What we’ve learned about K4 →