REPEATS If you have a Vigenere composed with a Playfair, you get repeats when either - the keyword is of even length and the gap is a multiple of the length of the keyword - the keyword is of odd length and the gap is twice the length of the keyword the following repeats occur. NLAW [736, 752] actually part of a length 6 repeat NLAWON BPVP [112, 576, 872] The gaps have a common factor of 8, strongly suggesting a keyword of length 8. If so, the 1,3,5,7 letters of the keyword always fall in the first half of the digraph, and the 2,4,6,8 always fall in the second half of the digraph. DOUBLE LETTERS There are 1064 letters in the ciphertext, and we know that there are 1000 in the message, so there must have been 64 insertions caused by doublings. These Xs are all inserted AFTER the Vigenere has happened. Their image under Playfair will stick out a lot in the frequency pattern. Perhaps we can look at the counts and work out which 4 letters are in the same row as X, and will get translated into X quite often. The doubling will always take stage1 ciphertext aa bc .. to aX ab c. Counts for each component and the total 0: A 04 B 06 C 05 D 05 E 04 F 04 G 08 H 01 I 05 J 00 K 00 L 01 M 10 N 11 O 04 P 08 Q 03 R 04 S 11 T 03 U 05 V 10 W 06 X 06 Y 05 Z 04 1: A 08 B 02 C 02 D 02 E 04 F 05 G 04 H 07 I 04 J 00 K 00 L 06 M 08 N 05 O 08 P 12 Q 05 R 05 S 05 T 02 U 04 V 07 W 06 X 13 Y 07 Z 02 2: A 06 B 03 C 08 D 03 E 05 F 01 G 07 H 05 I 04 J 00 K 05 L 06 M 05 N 05 O 02 P 07 Q 07 R 03 S 06 T 04 U 06 V 08 W 08 X 08 Y 04 Z 07 3: A 05 B 05 C 02 D 02 E 03 F 06 G 05 H 01 I 05 J 00 K 03 L 05 M 06 N 08 O 08 P 11 Q 01 R 02 S 08 T 02 U 06 V 12 W 10 X 08 Y 06 Z 03 4: A 03 B 00 C 05 D 02 E 05 F 07 G 14 H 07 I 04 J 00 K 02 L 04 M 10 N 09 O 08 P 07 Q 05 R 05 S 03 T 03 U 02 V 07 W 05 X 05 Y 08 Z 03 5: A 07 B 03 C 04 D 05 E 05 F 06 G 03 H 02 I 04 J 00 K 03 L 01 M 08 N 13 O 06 P 05 Q 04 R 05 S 06 T 04 U 04 V 03 W 08 X 13 Y 07 Z 04 6: A 08 B 02 C 04 D 00 E 10 F 05 G 06 H 05 I 04 J 00 K 07 L 06 M 03 N 08 O 04 P 02 Q 06 R 08 S 03 T 05 U 04 V 11 W 04 X 10 Y 02 Z 06 7: A 03 B 03 C 02 D 01 E 06 F 07 G 05 H 06 I 03 J 00 K 05 L 04 M 08 N 06 O 05 P 05 Q 05 R 10 S 05 T 03 U 03 V 09 W 08 X 10 Y 07 Z 04 T: A 44 B 24 C 32 D 20 E 42 F 41 G 52 H 34 I 33 J 00 K 25 L 33 M 58 N 65 O 45 P 57 Q 36 R 42 S 47 T 26 U 34 V 67 W 55 X 73 Y 46 Z 33 These make it look as if bottom row of Playfair grid might include VWXY and possibly even VWXYZ, which makes sense if we have a keyword alphabet. That would imply that the patterns caused by doubling will very often have a VWYZ in the second letter, There are 103 counts for bigrams ending in one of these AW 3 BV 1 BW 2 CV 1 CZ 2 EV 1 EW 1 EY 5 EZ 1 FV 2 FW 1 GW 1 GY 4 GZ 2 HV 3 IV 2 IY 1 KV 2 KY 1 KZ 1 LV 2 MW 2 NV 3 NW 1 NZ 1 OY 1 PV 1 PZ 1 QV 3 QW 1 QY 2 QZ 1 RV 1 RW 4 SW 7 SY 1 TW 1 TY 1 UV 3 UW 1 UZ 2 VY 1 VZ 1 WV 1 WY 4 XV 5 XW 2 XY 3 XZ 1 YW 4 ZW 1 ZY 3 The final row says that the Vigenere encoded text must have been made from within VWXYZ and was ZX 1 ZY 1 VW 1 VX 4 WZ 5 WV 2 WX 3 WY 1 XV 4 YV 1 YW 3 (26 total) This is certainly possible for some Vigenere, but we have no real way of knowing whether it is right. In the penultimate row, SW sticks out, so we may guess that S is above X, with some letter before it translating to S, and X translating to W. .S VWXYZ If so, because the grid has to be full, S must be followed by TU ..STU VWXYZ In the top row, EY is frequent, so guess that E occurs above X ..E.. ..... ..... ..STU VWXYZ BIEAC DFG RW is frequent, which fits with QRSTU. ..E.. ..... ..... QRSTU VWXYZ N occurs with VWXZ but not Y, so probably it is above Y. If so, O is in the keyword, and P is after N ..E.. ..... ...NP QRSTU VWXYZ This is compatible with the possibility that keyword is OMEGA, which was mentioned in their writeup. Try this OMEGA BCDFH IKLNP QRSTU VWXYZ It doesn't produce enough Xs in positions that would cause doubles. So instead, lets try to place L. It occurs with VX not W, so maybe it is above the column with RW in it ..E.. (0 in keyword) ..... .LMNP QRSTU VWXYZ If so, M is placed too, because of alphabet order. Try to place I/J. It does not connect to Z, but does to V,X,Y, so probably belongs in last column of second row. If so, K is also placed. ..E.. (0 in keyword) ....I KLMNP QRSTU VWXYZ We have ABCD FGH 0 still to place. Let's try putting CDFG in second row, in that order. Not nice. ..E.. (0 in keyword) CDFGI KLMNP QRSTU VWXYZ Would prefer to place F in one of last two columns, ..E.. (0,G,H,A in keyword) BCDFI KLMNP QRSTU VWXYZ Try one OHEGA BCDFI KLMNP QRSTU VWXYZ No good. Suspect placement of I was no good. Try instead BI0 as start of keyword BI... ..... KLMNP QRSTU VWXYZ =============================================================== The following was a dead end Try assuming that S is above X (S has frequency 47, which is high). ..STU VWXYZ Other high ones are G=52, M=58 ,N=65, P=57. Can't accomodate P, but N could work, as below .MNOP QRSTU VWXYZ OK. It would nearly work to have the alphabet be the ordinary alphabet, ABCDE F.GHI LMNOP QRSTU VWXYZ which makes me think that the Playfair keyword might be AI and the square could be. AIBCD EFGHK LMNOP QRSTU VWXYZ This would make the output of Vigenere be stage1: SH VN MI EO TH ... stage2: TG XL RF HL YO ... and the corresponding counts come out as 0: A 03 B 05 C 02 D 08 E 02 F 05 G 03 H 03 I 05 J 00 K 06 L 06 M 08 N 10 O 08 P 00 Q 10 R 04 S 03 T 07 U 01 V 06 W 06 X 07 Y 05 Z 10 1: A 04 B 05 C 01 D 03 E 01 F 06 G 10 H 03 I 05 J 00 K 06 L 05 M 06 N 13 O 02 P 05 Q 08 R 04 S 07 T 03 U 05 V 04 W 10 X 08 Y 03 Z 06 2: A 03 B 09 C 03 D 05 E 06 F 05 G 04 H 05 I 07 J 00 K 01 L 04 M 05 N 06 O 06 P 05 Q 05 R 08 S 05 T 04 U 06 V 04 W 07 X 09 Y 03 Z 08 3: A 03 B 02 C 05 D 03 E 02 F 02 G 04 H 06 I 05 J 00 K 08 L 10 M 05 N 08 O 02 P 07 Q 10 R 05 S 04 T 02 U 02 V 08 W 09 X 10 Y 06 Z 05 4: A 03 B 06 C 00 D 05 E 07 F 06 G 06 H 05 I 04 J 00 K 08 L 05 M 10 N 11 O 07 P 05 Q 03 R 04 S 04 T 03 U 02 V 06 W 04 X 07 Y 05 Z 07 5: A 00 B 12 C 04 D 03 E 00 F 06 G 03 H 03 I 07 J 00 K 07 L 11 M 12 N 05 O 02 P 04 Q 04 R 03 S 07 T 08 U 02 V 07 W 10 X 08 Y 05 Z 00 6: A 05 B 07 C 04 D 02 E 08 F 04 G 06 H 05 I 05 J 00 K 06 L 05 M 12 N 03 O 03 P 02 Q 04 R 05 S 10 T 03 U 03 V 04 W 10 X 05 Y 07 Z 05 7: A 09 B 05 C 01 D 02 E 03 F 07 G 06 H 06 I 03 J 00 K 03 L 10 M 02 N 04 O 08 P 03 Q 10 R 05 S 05 T 04 U 05 V 07 W 08 X 11 Y 02 Z 04 T: A 30 B 51 C 20 D 31 E 29 F 41 G 42 H 36 I 41 J 00 K 45 L 56 M 60 N 60 O 38 P 31 Q 54 R 38 S 45 T 34 U 26 V 46 W 64 X 65 Y 36 Z 45 which do not look that promising as direct standard alphabets. Then I got stuck Maybe alphabet 0 is B, which would imply Z=A (10) D=E (8) M=N (8), N=O (10) Q=R (10), looks OK, kinda if we ignore S=T (3) T=U (7) We want alphabet 1 or alphabet 7 1: A 04 B 05 C 01 D 03 E 01 F 06 G 10 H 03 I 05 K 06 L 05 M 06 N 13 O 02 P 05 Q 08 R 04 S 07 T 03 U 05 V 04 W 10 X 08 Y 03 Z 06 w x y z a b c d e f g h i k l m n o p q r s t u v Don't like it much, but lets look at the hypothesis that 1 is the W alphabet. Clearly doesn't work 1: A 04 B 05 C 01 D 03 E 01 F 06 G 10 H 03 I 05 K 06 L 05 M 06 N 13 O 02 P 05 Q 08 R 04 S 07 T 03 U 05 V 04 W 10 X 08 Y 03 Z 06 u v w x x y z a b c d e f g h i NOGOOD e f g h i k l m n NOGOOD t u v w x y z a b c d e NOGOOD a b c d e f g h i k NOGOOD n o p q r s t u v w x y z a NOGOOD i k l m n o p q r s t No, no, no, can't be good. Maybe the assumption about the Playfair square needs a change. I'm pretty sure the conclusion about