> **Source:** glthr.com, the blog of Guillaume Lethuillier > **Page:** Kryptos K4 as a 5 × 19 Grid > **Address:** https://glthr.com/k4 (interactive: hover a letter, a segment or a structure to read its notes) > **Articles:** A Fresh Perspective on Kryptos K4 (2024), https://glthr.com/a-fresh-perspective-on-kryptos-k4.md; Kryptos K4: The W-Rectangle and Its Half-Turn (2026), https://glthr.com/kryptos-k4-a-rectangle-hidden-in-the-cipher.md > **Other pages of this site, for AI agents:** https://glthr.com/llms.txt # Kryptos K4 as a 5 × 19 Grid K4 has 97 letters. Written in rows of 19, its first 95 letters fill a grid of 5 rows and 19 columns, and A and R are left over. Positions are counted from 1; row 1, column 1 is position 1, and position p is in row ⌈p / 19⌉. The grid holds 95 of K4’s 97 letters. The final AR remains unexplained and must be accounted for in any decryption. The grid’s center is position 48; the complete text’s center is position 49. ## The ciphertext The frame marks the rectangle formed by four of the five W’s, one cell in from each corner of the grid (rows 2 to 4, columns 2 to 18). The fifth W is in row 3, column 11, one cell right of the center cell (row 3, column 10). ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 O B K R U O X O G H U L B S O L I F B +--------------------------------------------------+ 2 B |W F L R V Q Q P R N G K S S O T W |T 3 Q |S J Q S S E K Z Z W A T J K L U D |I 4 A |W I N F B N Y P V T T M Z F P K W |G +--------------------------------------------------+ 5 D K Z X T J C D I G K U H U A U E K C + A R ``` ## The known plaintext Sanborn’s two clues, EASTNORTHEAST (positions 22 to 34) and BERLINCLOCK (positions 64 to 74), under the same layout; X marks the five W cells under the stop hypothesis; a dot is an unknown letter. ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 . . . . . . . . . . . . . . . . . . . +--------------------------------------------------+ 2 . |X E A S T N O R T H E A S T . . X |. 3 . |. . . . . . . . . X . . . . . . . |. 4 . |X . . . . B E R L I N C L O C K X |. +--------------------------------------------------+ 5 . . . . . . . . . . . . . . . . . . . + . . ``` ## Segments and groups The W’s split K4 into six segments, assigned alternately to Group A and Group B. In the grid below, each letter is replaced by the number of its segment; the W’s are shown as W. ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 W 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 W 3 3 3 3 3 3 3 3 3 3 3 3 W 4 4 4 4 4 4 4 4 4 4 W 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 W 6 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 + 6 6 ``` | Segment | Group | Positions | Letters | Ciphertext | |---|---|---|---|---| | 1 | A | 1–20 | 20 | OBKRUOXOGHULBSOLIFBB | | 2 | B | 22–36 | 15 | FLRVQQPRNGKSSOT | | 3 | A | 38–48 | 11 | TQSJQSSEKZZ | | 4 | B | 50–58 | 9 | ATJKLUDIA | | 5 | A | 60–74 | 15 | INFBNYPVTTMZFPK | | 6 | B | 76–97 | 22 | GDKZXTJCDIGKUHUAUEKCAR | - **Segment 1:** Start of K4 up to the first W. It fills row 1 and one cell of row 2. Half-turn: lies on segment 6 (22 letters); the two extra letters of segment 6 are the AR tail. - **Segment 2:** Carries EASTNORTHEAST (its first 13 letters) and two unknown letters (positions 35-36). Same length as segment 5 (15). In the half-turn it lies exactly on segment 5: the two crib segments are stacked. Top edge of the W rectangle. - **Segment 3:** Ends with ZZ right before the central W. Half-turn: nine letters land on segment 4. The Z at position 47 lands on the central W; the Z at position 48 stays at the center. - **Segment 4:** The shortest segment, between the central W and the W of position 59. - **Segment 5:** Four unknown letters (positions 60-63), then BERLINCLOCK up to the W. Same length as segment 2 (15). Bottom edge of the W rectangle. Knowing positions 60-63 would make this segment fully known. - **Segment 6:** From the last W to the end, including the AR tail. Half-turn: lies on segment 1. ## Structures ### W rectangle - Four W’s one cell in from each corner: (2,2), (2,18), (4,2), (4,18). They are symmetric left-right, up-down and under a half-turn. - Among random 97-letter texts, about 1 in 10,000 shows a rectangle with these inset corners and a center mark, formed by any letter. - Among 1,272,384 separator placements that divide the text into two alternating groups of 46 letters, 650 also form a rectangle: about 1 in 1,958. - Inside the rectangle: 46 letters besides the W’s. Outside (with AR): 46. This follows from the grid; it is not an independent fact. - W is the only letter of K4 forming such a rectangle at any width from 3 to 48. ### W as stops (hypothesis) - The reported K4 plaintext has 97 characters, as many as the ciphertext. The stop hypothesis keeps all 97 positions, including the five W cells. - Reading: I read the W’s as possible stops, such as X or ?, as in K2 and K3. The plaintext would then consist of six stretches of 20, 15, 11, 9, 15 and 22 letters. - A repeating key can contain the same letter in several places. The five W’s alone do not rule out encrypted stops. - Lead: K4’s lag-7 regularity weakens when the W’s are removed; the width-7 doublet alignment and repeated width-21 pairs disappear. Removing five random letters weakens the first two about as often; only the disappearance of the width-21 pairs is less common (2.6% of trials). This does not establish when the W’s entered the text. ### Up-down fold - Row 1 on row 5 (a shift of 76 positions), row 2 on row 4 (a shift of 38); row 3 is the hinge. - All five W’s respect it. Both cribs keep reading left to right. - Column 9: plaintext R over R, cipher P over P (one confirmation). ### The two cribs - EASTNORTHEAST: row 2, columns 3-15, starting right after a W. BERLINCLOCK: row 4, columns 7-17, ending right before a W. - Together they span exactly the 15 columns between the W’s. - Lead: Mirror reading (cipher + plain): J L J O D E G K U K K K L and O C G G B G O K T R U. Only 12 distinct values in 24; K five times, G four, O three. ### Group A - Segments 1, 3, 5: 46 letters. Contains BERLINCLOCK. - Same frequency shape as Group B: one letter five times, two four times, four three times, six twice, nine once. - 44 letters pair with Group B under the half-turn; ZZ at positions 47 and 48 have no partner in the other group. ### Group B - Segments 2, 4, 6: 46 letters. Contains EASTNORTHEAST. - Among all groupings of the six segments, the alternating one is the only one with identical frequency shapes. - 44 letters pair with Group A under the half-turn; AR at positions 96 and 97 remains outside the grid. ### Doubled letters - Six doublets: BB, QQ, SS, SS, ZZ, TT. - Lead: Where the plaintext is known, QQ comes from N, O and SS from S, T: neighbours in the alphabet. TT comes from I, N. - Two of the five W’s follow a doublet (BBW, ZZW), about a 1% event, noticed after the fact. ### Self-maps - S stays S (position 33) and K stays K (position 74). - Any system that can never leave a letter unchanged is excluded: Playfair and its variants, Porta, Enigma-type reciprocal machines. ### Center Z Z W A - Position 48 (Z) is the center cell of the 95-cell grid; position 49 (W) is the middle of the 97-letter line. Two centers, one cell apart: the difference is half the AR tail. ## Notes on single letters - **Position 19** (B; row 1, column 19): With position 20 it forms the doubled BB that comes right before the first W. ZZ does the same before the central W. - **Position 20** (B; row 2, column 1): Second B of the BB doublet, right before the first W. The run wraps here from row 1 into row 2. - **Position 21** (W; row 2, column 2): W, top-left mark: one cell in from the corner. Half-turn: lands on the W of position 75 (21 + 75 = 96). Up-down fold: lands on the W of position 59. - **Position 22** (F, plaintext E; row 2, column 3): First letter of EASTNORTHEAST, in the cell right after a W. In the half-turn it lies on the last letter of BERLINCLOCK (position 74). - **Position 23** (L, plaintext A; row 2, column 4): Lead: First A gives L (shift +11), one of the three large shifts of this crib. The second A (position 32) gives K. - **Position 24** (R, plaintext S; row 2, column 5): Lead: First S gives R. The second S (position 33) stays S. - **Position 25** (V, plaintext T; row 2, column 6): Lead: First T gives V. The later T’s give R (position 29) and S (position 34). Half-turn: T lies on L here and again at 29 / 67, with different cipher pairs (V over Z, then R over V). This rules out any fixed pair substitution on the fold. - **Position 26** (Q, plaintext N; row 2, column 7): Lead: QQ: two neighbouring plaintext letters (N, O) give the same cipher letter. - **Position 27** (Q, plaintext O; row 2, column 8): Lead: QQ: two neighbouring plaintext letters (N, O) give the same cipher letter. - **Position 28** (P, plaintext R; row 2, column 9): R gives P here and again at position 66: same column (9), two rows down. It is the one column where the up-down fold stacks equal plaintext letters, and the cipher letters are equal too. - **Position 29** (R, plaintext T; row 2, column 10): Lead: Second T: mirror key K (cipher + plain = K), like every second use in this crib. - **Position 30** (N, plaintext H; row 2, column 11): Lead: H gives N (shift +6), one of the three large shifts of this crib. - **Position 31** (G, plaintext E; row 2, column 12): Lead: Second E: mirror key K. The first E gave F, this one gives G. Half-turn: this E lies on the E of position 65, and the two are enciphered G and Y. This rules out one alphabet per fold column. - **Position 32** (K, plaintext A; row 2, column 13): Lead: Second A: mirror key K. The first A gave L, this one gives K. - **Position 33** (S, plaintext S; row 2, column 14): Self-map: S stays S. This excludes Playfair-type and Porta-type systems. Lead: Second S: mirror key K. - **Position 34** (S, plaintext T; row 2, column 15): Lead: Third T: mirror key L (K + 1). Lead: SS: the neighbours S, T give the same cipher letter. Last known letter of this crib. Positions 35-36 complete the segment and are unknown. - **Position 35** (O; row 2, column 16): Unknown plaintext. Knowing 35-36 would complete segment 2 and test the ‘second use’ lead directly. - **Position 36** (T; row 2, column 17): Unknown plaintext. Knowing 35-36 would complete segment 2 and test the ‘second use’ lead directly. T W T: the W of position 37 stands between two T’s. - **Position 37** (W; row 2, column 18): W, top-right mark: one cell in from the corner. Half-turn: lands on the W of position 59 (37 + 59 = 96). Up-down fold: lands on the W of position 75. - **Position 38** (T; row 2, column 19): T W T: the W of position 37 stands between two T’s. This T is the last cell of row 2 and the first letter of segment 3. - **Position 43** (S; row 3, column 5): SS doublet (positions 43-44), plaintext unknown. - **Position 44** (S; row 3, column 6): SS doublet (positions 43-44), plaintext unknown. - **Position 47** (Z; row 3, column 9): In the half-turn this Z lies on the central W. Positions 47 and 49 pair around the center cell, as the corner W’s do (21 + 75 = 37 + 59 = 47 + 49 = 96). - **Position 48** (Z; row 3, column 10): Center cell of the grid (row 3, column 10). Under the half-turn, position p lands on position 96 − p. With position 47 it forms the ZZ doublet. ZZ and AR are the four letters without a half-turn partner in the other group. - **Position 49** (W; row 3, column 11): Exact middle of the 97 letters and the median W: two W’s and 46 letters on each side. One cell right of the grid center. It respects the up-down symmetry only; the four corner W’s respect all three. - **Position 50** (A; row 3, column 12): First letter after the central W. - **Position 59** (W; row 4, column 2): W, bottom-left mark: one cell in from the corner. Half-turn: lands on the W of position 37. Up-down fold: lands on the W of position 21. - **Position 60** (I; row 4, column 3): Unknown plaintext. Positions 60-63, between the W and BERLIN, are the only unknown letters of segment 5. - **Position 61** (N; row 4, column 4): Unknown plaintext. Positions 60-63, between the W and BERLIN, are the only unknown letters of segment 5. - **Position 62** (F; row 4, column 5): Unknown plaintext. Positions 60-63, between the W and BERLIN, are the only unknown letters of segment 5. - **Position 63** (B; row 4, column 6): Unknown plaintext. Positions 60-63, between the W and BERLIN, are the only unknown letters of segment 5. - **Position 64** (N, plaintext B; row 4, column 7): First letter of BERLINCLOCK. - **Position 65** (Y, plaintext E; row 4, column 8): Half-turn: this E lies on the E of position 31, and the two are enciphered Y and G. This rules out one alphabet per fold column. - **Position 66** (P, plaintext R; row 4, column 9): R gives P, exactly as at position 28 (same column, two rows up). - **Position 67** (V, plaintext L; row 4, column 10): Lead: First L gives V. The second L (position 71) gives Z: +4 over 4 cells. - **Position 68** (T, plaintext I; row 4, column 11): TT doublet: plaintext I, N (not neighbours in the alphabet, unlike QQ and SS above). - **Position 69** (T, plaintext N; row 4, column 12): TT doublet: plaintext I, N (not neighbours in the alphabet, unlike QQ and SS above). - **Position 70** (M, plaintext C; row 4, column 13): Lead: First C gives M. The second C (position 73) gives P: +3 over 3 cells. - **Position 71** (Z, plaintext L; row 4, column 14): Lead: Second L gives Z: the step equals the distance (+4 over 4 cells). - **Position 73** (P, plaintext C; row 4, column 16): Lead: Second C gives P: the step equals the distance (+3 over 3 cells). - **Position 74** (K, plaintext K; row 4, column 17): Self-map: K stays K. Last letter of BERLINCLOCK, in the cell right before a W. In the half-turn it lies on the first letter of EASTNORTHEAST (position 22). - **Position 75** (W; row 4, column 18): W, bottom-right mark: one cell in from the corner. Half-turn: lands on the W of position 21. Up-down fold: lands on the W of position 37. - **Position 96** (A; left over): Outside the 95-cell grid, with no partner under its half-turn. K4 has 97 letters, so AR must still be accounted for. Reading: I have no explanation for AR. Treating it as filler or an end marker remains an assumption. - **Position 97** (R; left over): Outside the 95-cell grid, with no partner under its half-turn. K4 has 97 letters, so AR must still be accounted for. Reading: I have no explanation for AR. Treating it as filler or an end marker remains an assumption.