Who wants to see a magic trick?

[madness]

For my first trick, you send me two lines from the tableau of a quagmire cipher, and I tell you
which it is: quagmire 1, 2, 3, or 4, or just random garbage. You can use keywords that are as
wacky as you like, so the keys look random.

If you can figure out how I do it, you win.

Who wants to play?

[The-Letter-Wriggler]

Do the two line have to be consecutive?
Do they have to be within the keyword segment of the marix?
Can you tell me which quagmire is the following?

KJIHGFEDCBAZYXWVUTSRQPONML
HGFEDCBAZYXWVUTSRQPONMLKJI

[madness]

@TLW,

1. They do not have to be consecutive.
2. I don’t understand your second question.
3. Quagmire 1. Your keyword was the alphabet written backwards.

[madness]

@TLW,
BTW, it may appear that it took a long time to figure it out, but it did not. My answer awaited moderation since Oct 23rd.
I wouldn’t want you to think that it wasn’t really magic.

[madness]

@TLW,
It’s also a Q2 and a Beaufort.

[madness]

TLW’s comment has led me down a rabbit hole, and here is what I found.
Did you know that there are 13 ciphers that are simultaneously quagmire 1 and quagmire 2 ciphers?
One is the Vigenere, which is trivially all sorts of quagmires. Another is the Beaufort, which
is created with the keyword ZYXWVUTSRQPONMLKJIHGFEDCBA. The other 11 have these “keywords”:

ADGJMPSVYBEHKNQTWZCFILORUX
AFKPUZEJOTYDINSXCHMRWBGLQV
AHOVCJQXELSZGNUBIPWDKRYFMT
AJSBKTCLUDMVENWFOXGPYHQZIR
ALWHSDOZKVGRCNYJUFQBMXITEP
APETIXMBQFUJYNCRGVKZODSHWL
ARIZQHYPGXOFWNEVMDULCTKBSJ
ATMFYRKDWPIBUNGZSLEXQJCVOH
AVQLGBWRMHCXSNIDYTOJEZUPKF
AXUROLIFCZWTQNKHEBYVSPMJGD

If you didn’t notice, then let me point out that they are the affine cipher keys.

Then today I learned that there are 13 Q3s that have all of the even-numbered rotations of the Vigenere
in their tableaux. They are created with these keywords:

ABCDEFGHIJKLMNOPQRSTUVWXYZ (trivially)
ADCFEHGJILKNMPORQTSVUXWZYB
AFCHEJGLINKPMROTQVSXUZWBYD
AHCJELGNIPKRMTOVQXSZUBWDYF
AJCLENGPIRKTMVOXQZSBUDWFYH
ALCNEPGRITKVMXOZQBSDUFWHYJ
ANCPERGTIVKXMZOBQDSFUHWJYL
APCRETGVIXKZMBODQFSHUJWLYN
ARCTEVGXIZKBMDOFQHSJULWNYP
ATCVEXGZIBKDMFOHQJSLUNWPYR
AVCXEZGBIDKFMHOJQLSNUPWRYT
AXCZEBGDIFKHMJOLQNSPURWTYV
AZCBEDGFIHKJMLONQPSRUTWVYX

Try generating a tableau and see what I mean.

And if that weren’t enough, there are (2^13)(13!)/26 (trillions) Q3 ciphers that have ROT13
as one of the lines in their tableaux. Here is an example keyword and tableau:

keyword: WVTZAQPLKRHBSJIGMNDCYXEUOF

tableau:
KGUEWZCIDNSBYXTHRJMPVQAFOL
GEAZLHWXFOCDVTRNMYUJKSBPQI
UASBGDKZLPVWRHNFOTQXMYCIJE
EZBHINLTPQWFKRMOUVAYGCDJSX
WLGIDXBPHRAZSJYTVQKOCUENMF
ZHDNXOIRJSLPGMUQAKBVEWFYCT
CWKLBIAFZTUEQPJXYOVNSMGHRD
IXZTPRFYOUDNWVKMGCESLBHQAJ
DFLPHJZOTVEXAQSYCUWMBGIRKN
NOPQRSTUVWXYZABCDEFGHIJKLM <- ROT13
SCVWALUDEXMGOFPIJNYHQRKZTB
BDWFZPENXYGIUOQJSMCRAKLTVH
YVRKSGQWAZOUPLIEXFTDJNMBHC
XTHRJMPVQAFOLKGUEWZCIDNSBY
TRNMYUJKSBPQIGEAZLHWXFOCDV
HNFOTQXMYCIJEUASBGDKZLPVWR
RMOUVAYGCDJSXEZBHINLTPQWFK
JYTVQKOCUENMFWLGIDXBPHRAZS
MUQAKBVEWFYCTZHDNXOIRJSLPG
PJXYOVNSMGHRDCWKLBIAFZTUEQ
VKMGCESLBHQAJIXZTPRFYOUDNW
QSYCUWMBGIRKNDFLPHJZOTVEXA
ABCDEFGHIJKLMNOPQRSTUVWXYZ <- identity is in every Q3 tableau
FPIJNYHQRKZTBSCVWALUDEXMGO
OQJSMCRAKLTVHBDWFZPENXYGIU
LIEXFTDJNMBHCYVRKSGQWAZOUP

Now, who will submit two lines from a tableau (but not one of my special ones) for me?
The magic trick is still on.

[The-Letter-Wriggler]

@madness
The two lines from the tableau that I gave you were from a Quagmire III
The keyword was not written backwards but the plaintext alphabet was.

15 KJIHGFEDCBAZYXWVUTSRQPONML <– The two lines
17 IHGFEDCBAZYXWVUTSRQPONMLKJ
18 HGFEDCBAZYXWVUTSRQPONMLKJI <– I gave you

I checked out your submits for Q1 and Q2+Beaufort

As a Quagmire I
08 IJKLMNOPQRSTUVWXYZABCDEFGH <– reversed
09 JKLMNOPQRSTUVWXYZABCDEFGHI
10 KLMNOPQRSTUVWXYZABCDEFGHIJ
11 LMNOPQRSTUVWXYZABCDEFGHIJK <– reversed

As a Quagmire II with Beaufort coding gives the same tableau.
15 KJIHGFEDCBAZYXWVUTSRQPONML <– The two lines
17 IHGFEDCBAZYXWVUTSRQPONMLKJ
18 HGFEDCBAZYXWVUTSRQPONMLKJI <– I gave you

[madness]

I think there is one more thing that needs to be clear: Even though you may use a scrambled
plaintext alphabet, on the tableau an unscrambled alphabet is written across the top. Columns
are rearranged accordingly. I’m going to put an example of each quagmire here, so we can all
agree on how it’s done.

Q1, keyword = FLYINGSAUCER

abcdefghijklmnopqrstuvwxyz
AFCGDTYHWIJUKXLMNEZOBPQRVS
BGDHEUZIXJKVLYMNOFAPCQRSWT
CHEIFVAJYKLWMZNOPGBQDRSTXU
DIFJGWBKZLMXNAOPQHCRESTUYV
EJGKHXCLAMNYOBPQRIDSFTUVZW
FKHLIYDMBNOZPCQRSJETGUVWAX
GLIMJZENCOPAQDRSTKFUHVWXBY
HMJNKAFODPQBRESTULGVIWXYCZ
INKOLBGPEQRCSFTUVMHWJXYZDA
JOLPMCHQFRSDTGUVWNIXKYZAEB
KPMQNDIRGSTEUHVWXOJYLZABFC
LQNROEJSHTUFVIWXYPKZMABCGD
MROSPFKTIUVGWJXYZQLANBCDHE
NSPTQGLUJVWHXKYZARMBOCDEIF
OTQURHMVKWXIYLZABSNCPDEFJG
PURVSINWLXYJZMABCTODQEFGKH
QVSWTJOXMYZKANBCDUPERFGHLI
RWTXUKPYNZALBOCDEVQFSGHIMJ
SXUYVLQZOABMCPDEFWRGTHIJNK
TYVZWMRAPBCNDQEFGXSHUIJKOL
UZWAXNSBQCDOERFGHYTIVJKLPM
VAXBYOTCRDEPFSGHIZUJWKLMQN
WBYCZPUDSEFQGTHIJAVKXLMNRO
XCZDAQVETFGRHUIJKBWLYMNOSP
YDAEBRWFUGHSIVJKLCXMZNOPTQ
ZEBFCSXGVHITJWKLMDYNAOPQUR

Q2, keyword = FLYINGSAUCER (this is the easy one to figure out)

abcdefghijklmnopqrstuvwxyz
AUCERBDHJKMOPQTVWXZFLYINGS
BDHJKMOPQTVWXZFLYINGSAUCER
CERBDHJKMOPQTVWXZFLYINGSAU
DHJKMOPQTVWXZFLYINGSAUCERB
ERBDHJKMOPQTVWXZFLYINGSAUC
FLYINGSAUCERBDHJKMOPQTVWXZ
GSAUCERBDHJKMOPQTVWXZFLYIN
HJKMOPQTVWXZFLYINGSAUCERBD
INGSAUCERBDHJKMOPQTVWXZFLY
JKMOPQTVWXZFLYINGSAUCERBDH
KMOPQTVWXZFLYINGSAUCERBDHJ
LYINGSAUCERBDHJKMOPQTVWXZF
MOPQTVWXZFLYINGSAUCERBDHJK
NGSAUCERBDHJKMOPQTVWXZFLYI
OPQTVWXZFLYINGSAUCERBDHJKM
PQTVWXZFLYINGSAUCERBDHJKMO
QTVWXZFLYINGSAUCERBDHJKMOP
RBDHJKMOPQTVWXZFLYINGSAUCE
SAUCERBDHJKMOPQTVWXZFLYING
TVWXZFLYINGSAUCERBDHJKMOPQ
UCERBDHJKMOPQTVWXZFLYINGSA
VWXZFLYINGSAUCERBDHJKMOPQT
WXZFLYINGSAUCERBDHJKMOPQTV
XZFLYINGSAUCERBDHJKMOPQTVW
YINGSAUCERBDHJKMOPQTVWXZFL
ZFLYINGSAUCERBDHJKMOPQTVWX

Q3, keyword = FLYINGSAUCER

abcdefghijklmnopqrstuvwxyz
HPKQMABTEVWUXRZFLODYJINGCS
PXTZVBMFJLYDIKNGSWOAQUCEHR
KTOVPCHWBXZEFDLYIQJNMGSARU
QZVFWDOLKYIHNMGSAXPUTCERJB
MVPWQEJXDZFRLHYINTKGOSAUBC
ABCDEFGHIJKLMNOPQRSTUVWXYZ
BMHOJGEPUQTSVCWXZKRFDLYIAN
TFWLXHPYMINJGOSAUZQCVERBKD
EJBKDIUMSOPNQATVWHCXRZFLGY
VLXYZJQIONGKSPAUCFTEWRBDMH
WYZIFKTNPGSMAQUCELVRXBDHOJ
UDEHRLSJNKMYOGPQTBAVCWXZIF
XIFNLMVGQSAOUTCERYWBZDHJPK
RKDMHNCOAPQGTUVWXJEZBFLYSI
ZNLGYOWSTAUPCVERBIXDFHJKQM
FGYSIPXAVUCQEWRBDNZHLJKMTO
LSIANQZUWCETRXBDHGFJYKMOVP
OWQXTRKZHFLBYJINGVMSPAUCDE
DOJPKSRQCTVAWEXZFMBLHYINUG
YANUGTFCXERVBZDHJSLKIMOPWQ
JQMTOUDVRWXCZBFLYPHIKNGSEA
IUGCSVLEZRBWDFHJKAYMNOPQXT
NCSEAWYRFBDXHLJKMUIOGPQTZV
GEARUXIBLDHZJYKMOCNPSQTVFW
CHRJBYAKGMOIPSQTVDUWEXZFNL
SRUBCZNDYHJFKIMOPEGQATVWLX

Q4, keywords = SPACEGIRL FLYINGSAUCER

abcdefghijklmnopqrstuvwxyz
CKEMROBPDQTJVWXUZHAFLYINGS
HTJVKWMXOZFQLYIDNPBGSAUCER
ROBPDQHTJVWMXZFELKCYINGSAU
JVKWMXOZPFLTYINHGQDSAUCERB
BPDQHTJVKWXOZFLRYMEINGSAUC
YCIENRGBSDHUJKMLOAFPQTVWXZ
AHUJCKEMROPDQTVSWBGXZFLYIN
KWMXOZPFQLYVINGJSTHAUCERBD
GBSDAHUJCKMROPQNTEIVWXZFLY
MXOZPFQLTYIWNGSKAVJUCERBDH
OZPFQLTYVINXGSAMUWKCERBDHJ
IENRGBSDAHJCKMOYPULQTVWXZF
PFQLTYVIWNGZSAUOCXMERBDHJK
SDAHUJCKEMOBPQTGVRNWXZFLYI
QLTYVIWNXGSFAUCPEZORBDHJKM
TYVIWNXGZSALUCEQRFPBDHJKMO
VIWNXGZSFAUYCERTBLQDHJKMOP
DQHTJVKWMXZPFLYBIORNGSAUCE
UJCKEMROBPQHTVWAXDSZFLYING
WNXGZSFALUCIERBVDYTHJKMOPQ
EMROBPDQHTVKWXZCFJULYINGSA
XGZSFALUYCENRBDWHIVJKMOPQT
ZSFALUYCIERGBDHXJNWKMOPQTV
FALUYCIENRBSDHJZKGXMOPQTVW
NRGBSDAHUJKEMOPIQCYTVWXZFL
LUYCIENRGBDAHJKFMSZOPQTVWX

[madness]

The trick only works if we agree on definitions.
Q1: only plaintext alphabet is mixed
Q2: only ciphertext alphabet is mixed
Q3: both alphabets are mixed in the same way
Q4: both alphabets are mixed differently

[madness]

@TLW, if you only change the plaintext alphabet, then it’s not a Q3 but is a Q1.

Q1 with keyword ZYXWVUTSRQPONMLKJIHGFEDCBA:

8 HGFEDCBAZYXWVUTSRQPONMLKJI <- your two …
9 IHGFEDCBAZYXWVUTSRQPONMLKJ
10 JIHGFEDCBAZYXWVUTSRQPONMLK
11 KJIHGFEDCBAZYXWVUTSRQPONML <- … given lines

Q2 with keyword ZYXWVUTSRQPONMLKJIHGFEDCBA is exactly the same tableau.

I humbly suggest that you check your Q1 script.

[The-Letter-Wriggler]

@madness
My code conforms to the statements you gave in post #87220
You use the word -keyword- and I’m not sure what you mean by that.

There are three fields in quagmires:
[ 1] Plaintext Keyword (above tableau for column reference)
[ 2] Ciphertext Keyword (first line of tableau – zero shift)
[ 3] Keyword (also known as Indicator – the shifts/alphabets used)
also
[ 4] Offset (the letter that the plaintext key starts with)

Please decode the following that my code produced.

Q1 The keys are: Plaintext alphabet: rainbow, Keyword (indicator): DOROTHY
XAAOCJRGTIDUOHSQFXFMOMRWEUBSMODTZRZDTNXTBKMOSQWLDJMWJJIWHX
Q3 Keys As Q1
IPEONKPGFPTUSCXCKKWPKPDOUUWQPOHFRVZDFVKTWFPOACXMNKNORFJVHK

Do they give the correct plaintexts?

I do not understand your tableau are they what your code generates?
All the tableau that you have given are not what I get or use.

I use the ‘Text Book’ tableau both in code and printout, hence I do not
think I can give you two tableau lines to work your magic.

Here are printouts from my application for each quagmire I through IV.
Note: The lowercase alphabets will not line up in the forum post.

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Quagmire I
Plaintext:
Here is a printout from my application after a quagmire

Ciphertext:
OVMY PH W IXYJLVPO ZXEI FD QLISYZTZYKG HWOYX Q USHRIBXV

TYPE : Quagmire I
CODE : Standard
KEYS : quagbcdefhijklmnoprstvwxyz, A-Z, FOUR, q
[ 1] : quagbcdefhijklmnoprstvwxyz
[ 2] : ABCDEFGHIJKLMNOPQRSTUVWXYZ
[ 3] : FOUR (Length of 4)
[ 4] : q (Start [ 1] with this letter)
[ 5] : Text was taken as a whole (carriage returns ignored)
IKey : *Auto Key Not Used*
—————————–
Key to above:
TYPE : The Cipher Type
CODE : Standard, Beaufort or Variant Beaufort
KEYS : Actual Keywords Used
[ 1] : Plaintext Alpha
[ 2] : 00 Matrix Alpha
[ 3] : Keyword
[ 4] : Plaintext Shift
[ 5] : The whole, or line by line, text is taken
IKey : Intermediate Key (Auto PT/CT)
——————————-
Key Tableau Used(4 Shifts)
-> quagbcdefhijklmnoprstvwxyz
05 FGHIJKLMNOPQRSTUVWXYZABCDE
14 OPQRSTUVWXYZABCDEFGHIJKLMN
17 RSTUVWXYZABCDEFGHIJKLMNOPQ
20 UVWXYZABCDEFGHIJKLMNOPQRST
——————————-
The Full Tableau:
-> quagbcdefhijklmnoprstvwxyz
00 ABCDEFGHIJKLMNOPQRSTUVWXYZ
01 BCDEFGHIJKLMNOPQRSTUVWXYZA
02 CDEFGHIJKLMNOPQRSTUVWXYZAB
03 DEFGHIJKLMNOPQRSTUVWXYZABC
04 EFGHIJKLMNOPQRSTUVWXYZABCD
05 FGHIJKLMNOPQRSTUVWXYZABCDE
06 GHIJKLMNOPQRSTUVWXYZABCDEF
07 HIJKLMNOPQRSTUVWXYZABCDEFG
08 IJKLMNOPQRSTUVWXYZABCDEFGH
09 JKLMNOPQRSTUVWXYZABCDEFGHI
10 KLMNOPQRSTUVWXYZABCDEFGHIJ
11 LMNOPQRSTUVWXYZABCDEFGHIJK
12 MNOPQRSTUVWXYZABCDEFGHIJKL
13 NOPQRSTUVWXYZABCDEFGHIJKLM
14 OPQRSTUVWXYZABCDEFGHIJKLMN
15 PQRSTUVWXYZABCDEFGHIJKLMNO
16 QRSTUVWXYZABCDEFGHIJKLMNOP
17 RSTUVWXYZABCDEFGHIJKLMNOPQ
18 STUVWXYZABCDEFGHIJKLMNOPQR
19 TUVWXYZABCDEFGHIJKLMNOPQRS
20 UVWXYZABCDEFGHIJKLMNOPQRST
21 VWXYZABCDEFGHIJKLMNOPQRSTU
22 WXYZABCDEFGHIJKLMNOPQRSTUV
23 XYZABCDEFGHIJKLMNOPQRSTUVW
24 YZABCDEFGHIJKLMNOPQRSTUVWX
25 ZABCDEFGHIJKLMNOPQRSTUVWXY

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Quagmire II
Plaintext:
Here is a printout from my application after a quagmire

Ciphertext:
OTJC PD U QZXDVWGL DZEC NC OGQTXWRIXFO FULCZ O HWFVCHZT

TYPE : Quagmire II
CODE : Standard
KEYS : a-z, MIREABCDFGHJKLNOPQSTUVWXYZ, FOUR, a
[ 1] : abcdefghijklmnopqrstuvwxyz
[ 2] : MIREABCDFGHJKLNOPQSTUVWXYZ
[ 3] : FOUR (Length of 4)
[ 4] : a (Start [ 1] with this letter)
[ 5] : Text was taken as a whole (carriage returns ignored)
IKey : *Auto Key Not Used*
—————————–
Key to above:
TYPE : The Cipher Type
CODE : Standard, Beaufort or Variant Beaufort
KEYS : Actual Keywords Used
[ 1] : Plaintext Alpha
[ 2] : 00 Matrix Alpha
[ 3] : Keyword
[ 4] : Plaintext Shift
[ 5] : The whole, or line by line, text is taken
IKey : Intermediate Key (Auto PT/CT)
——————————-
Key Tableau Used(4 Shifts)
-> abcdefghijklmnopqrstuvwxyz
02 REABCDFGHJKLNOPQSTUVWXYZMI
08 FGHJKLNOPQSTUVWXYZMIREABCD
15 OPQSTUVWXYZMIREABCDFGHJKLN
20 UVWXYZMIREABCDFGHJKLNOPQST
——————————-
The Full Tableau:
-> abcdefghijklmnopqrstuvwxyz
00 MIREABCDFGHJKLNOPQSTUVWXYZ
01 IREABCDFGHJKLNOPQSTUVWXYZM
02 REABCDFGHJKLNOPQSTUVWXYZMI
03 EABCDFGHJKLNOPQSTUVWXYZMIR
04 ABCDFGHJKLNOPQSTUVWXYZMIRE
05 BCDFGHJKLNOPQSTUVWXYZMIREA
06 CDFGHJKLNOPQSTUVWXYZMIREAB
07 DFGHJKLNOPQSTUVWXYZMIREABC
08 FGHJKLNOPQSTUVWXYZMIREABCD
09 GHJKLNOPQSTUVWXYZMIREABCDF
10 HJKLNOPQSTUVWXYZMIREABCDFG
11 JKLNOPQSTUVWXYZMIREABCDFGH
12 KLNOPQSTUVWXYZMIREABCDFGHJ
13 LNOPQSTUVWXYZMIREABCDFGHJK
14 NOPQSTUVWXYZMIREABCDFGHJKL
15 OPQSTUVWXYZMIREABCDFGHJKLN
16 PQSTUVWXYZMIREABCDFGHJKLNO
17 QSTUVWXYZMIREABCDFGHJKLNOP
18 STUVWXYZMIREABCDFGHJKLNOPQ
19 TUVWXYZMIREABCDFGHJKLNOPQS
20 UVWXYZMIREABCDFGHJKLNOPQST
21 VWXYZMIREABCDFGHJKLNOPQSTU
22 WXYZMIREABCDFGHJKLNOPQSTUV
23 XYZMIREABCDFGHJKLNOPQSTUVW
24 YZMIREABCDFGHJKLNOPQSTUVWX
25 ZMIREABCDFGHJKLNOPQSTUVWXY

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Quagmire III
Plaintext:
Here is a printout from my application after a quagmire

Ciphertext:
PXSZ RH G HQQOKYPV QQDN DD RRHVQDTAQPE IYVZQ R USISNAQX

TYPE : Quagmire III
CODE : Standard
KEYS : quagbcdefhijklmnoprstvwxyz, A-Z, FOUR, q
[ 1] : quagbcdefhijklmnoprstvwxyz
[ 2] : QUAGBCDEFHIJKLMNOPRSTVWXYZ
[ 3] : FOUR (Length of 4)
[ 4] : q (Start [ 1] with this letter)
[ 5] : Text was taken as a whole (carriage returns ignored)
IKey : *Auto Key Not Used*
—————————–
Key to above:
TYPE : The Cipher Type
CODE : Standard, Beaufort or Variant Beaufort
KEYS : Actual Keywords Used
[ 1] : Plaintext Alpha
[ 2] : 00 Matrix Alpha
[ 3] : Keyword
[ 4] : Plaintext Shift
[ 5] : The whole, or line by line, text is taken
IKey : Intermediate Key (Auto PT/CT)
——————————-
Key Tableau Used(4 Shifts)
-> quagbcdefhijklmnoprstvwxyz
01 UAGBCDEFHIJKLMNOPRSTVWXYZQ
08 FHIJKLMNOPRSTVWXYZQUAGBCDE
16 OPRSTVWXYZQUAGBCDEFHIJKLMN
18 RSTVWXYZQUAGBCDEFHIJKLMNOP
——————————-
The Full Tableau:
-> quagbcdefhijklmnoprstvwxyz
00 QUAGBCDEFHIJKLMNOPRSTVWXYZ
01 UAGBCDEFHIJKLMNOPRSTVWXYZQ
02 AGBCDEFHIJKLMNOPRSTVWXYZQU
03 GBCDEFHIJKLMNOPRSTVWXYZQUA
04 BCDEFHIJKLMNOPRSTVWXYZQUAG
05 CDEFHIJKLMNOPRSTVWXYZQUAGB
06 DEFHIJKLMNOPRSTVWXYZQUAGBC
07 EFHIJKLMNOPRSTVWXYZQUAGBCD
08 FHIJKLMNOPRSTVWXYZQUAGBCDE
09 HIJKLMNOPRSTVWXYZQUAGBCDEF
10 IJKLMNOPRSTVWXYZQUAGBCDEFH
11 JKLMNOPRSTVWXYZQUAGBCDEFHI
12 KLMNOPRSTVWXYZQUAGBCDEFHIJ
13 LMNOPRSTVWXYZQUAGBCDEFHIJK
14 MNOPRSTVWXYZQUAGBCDEFHIJKL
15 NOPRSTVWXYZQUAGBCDEFHIJKLM
16 OPRSTVWXYZQUAGBCDEFHIJKLMN
17 PRSTVWXYZQUAGBCDEFHIJKLMNO
18 RSTVWXYZQUAGBCDEFHIJKLMNOP
19 STVWXYZQUAGBCDEFHIJKLMNOPR
20 TVWXYZQUAGBCDEFHIJKLMNOPRS
21 VWXYZQUAGBCDEFHIJKLMNOPRST
22 WXYZQUAGBCDEFHIJKLMNOPRSTV
23 XYZQUAGBCDEFHIJKLMNOPRSTVW
24 YZQUAGBCDEFHIJKLMNOPRSTVWX
25 ZQUAGBCDEFHIJKLMNOPRSTVWXY

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Quagmire IV
Plaintext:
Here is a printout from my application after a quagmire

Ciphertext:
QWKG SF W TMZGWYPN HMBF PC QJTVZZARZHQ HXNGM Q UEHSFKMW

TYPE : Quagmire IV
CODE : Standard
KEYS : quag, MIRE, FOUR, q
[ 1] : quagbcdefhijklmnoprstvwxyz
[ 2] : MIREABCDFGHJKLNOPQSTUVWXYZ
[ 3] : FOUR (Length of 4)
[ 4] : q (Start [ 1] with this letter)
[ 5] : Text was taken as a whole (carriage returns ignored)
IKey : *Auto Key Not Used*
—————————–
Key to above:
TYPE : The Cipher Type
CODE : Standard, Beaufort or Variant Beaufort
KEYS : Actual Keywords Used
[ 1] : Plaintext Alpha
[ 2] : 00 Matrix Alpha
[ 3] : Keyword
[ 4] : Plaintext Shift
[ 5] : The whole, or line by line, text is taken
IKey : Intermediate Key (Auto PT/CT)
——————————-
Key Tableau Used(4 Shifts)
-> quagbcdefhijklmnoprstvwxyz
02 REABCDFGHJKLNOPQSTUVWXYZMI
08 FGHJKLNOPQSTUVWXYZMIREABCD
15 OPQSTUVWXYZMIREABCDFGHJKLN
20 UVWXYZMIREABCDFGHJKLNOPQST
——————————-
The Full Tableau:
-> quagbcdefhijklmnoprstvwxyz
00 MIREABCDFGHJKLNOPQSTUVWXYZ
01 IREABCDFGHJKLNOPQSTUVWXYZM
02 REABCDFGHJKLNOPQSTUVWXYZMI
03 EABCDFGHJKLNOPQSTUVWXYZMIR
04 ABCDFGHJKLNOPQSTUVWXYZMIRE
05 BCDFGHJKLNOPQSTUVWXYZMIREA
06 CDFGHJKLNOPQSTUVWXYZMIREAB
07 DFGHJKLNOPQSTUVWXYZMIREABC
08 FGHJKLNOPQSTUVWXYZMIREABCD
09 GHJKLNOPQSTUVWXYZMIREABCDF
10 HJKLNOPQSTUVWXYZMIREABCDFG
11 JKLNOPQSTUVWXYZMIREABCDFGH
12 KLNOPQSTUVWXYZMIREABCDFGHJ
13 LNOPQSTUVWXYZMIREABCDFGHJK
14 NOPQSTUVWXYZMIREABCDFGHJKL
15 OPQSTUVWXYZMIREABCDFGHJKLN
16 PQSTUVWXYZMIREABCDFGHJKLNO
17 QSTUVWXYZMIREABCDFGHJKLNOP
18 STUVWXYZMIREABCDFGHJKLNOPQ
19 TUVWXYZMIREABCDFGHJKLNOPQS
20 UVWXYZMIREABCDFGHJKLNOPQST
21 VWXYZMIREABCDFGHJKLNOPQSTU
22 WXYZMIREABCDFGHJKLNOPQSTUV
23 XYZMIREABCDFGHJKLNOPQSTUVW
24 YZMIREABCDFGHJKLNOPQSTUVWX
25 ZMIREABCDFGHJKLNOPQSTUVWXY

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

[madness]

The way you are writing your tableaux is a handy way for encrypting and decrypting, where you can
see the keywords. But I think of quagmires as periodic substitution ciphers. Each substitution
has a key that is a scrambled alphabet, and it takes the straight alphabet as its input.

If you don’t try to think of it this way, you are going to miss out on some beautiful math(s).

[madness]

quagmire1.py dec dorothy rainbow XAAOCJRGTIDUOHSQFXFMOMRWEUBSMODTZRZDTNXTBKMOSQWLDJMWJJIWHX
ujfafntbwqmidfmnlfjwpfbwpiuufajwcgiawxfaujfainbowczwvpizof

quagmire1.py dec epspuiz rainbow XAAOCJRGTIDUOHSQFXFMOMRWEUBSMODTZRZDTNXTBKMOSQWLDJMWJJIWHX
thereisnoplacelikehomenomatterhowfarovertherainbowyoumaybe

quagmire3.py dec dorothy rainbow IPEONKPGFPTUSCXCKKWPKPDOUUWQPOHFRVZDFVKTWFPOACXMNKNORFJVHK
thereisnoplacelikehomenomatterhowfarovertherainbowyoumaybe

What text book are you using?

I conform to these:

https://www.cryptogram.org/downloads/aca.info/ciphers/QuagmireI.pdf
https://www.cryptogram.org/downloads/aca.info/ciphers/QuagmireII.pdf
https://www.cryptogram.org/downloads/aca.info/ciphers/QuagmireIII.pdf
https://www.cryptogram.org/downloads/aca.info/ciphers/QuagmireIV.pdf

What the ACA and I are doing differently from you is to put the shift key under A.
This should not affect the magic trick. What does affect it is that you should straighten
out the plaintext alphabet, so that the rows of the tableau are scrambled.

Using QUAG as the alphabet key and FOUR as the shift key, I get these rows of the Q1 tableau:
FHIJKLGMNOPQRSTUDVWXEYZABC
OQRSTUPVWXYZABCDMEFGNHIJKL
UWXYZAVBCDEFGHIJSKLMTNOPQR
RTUVWXSYZABCDEFGPHIJQKLMNO

Similarly, for Q3 you should straighten out the plaintext alphabet, so that the tableau lines
get scrambled even more, like these, for QUAG and FOUR:
IKLMNOJPRSTVWXYZFQUAHGBCDE
RTVWXYSZQUAGBCDEOFHIPJKLMN
GCDEFHBIJKLMNOPRUSTVAWXYZQ
TWXYZQVUAGBCDEFHRIJKSLMNOP

(It wouldn’t be much of a trick if I could just see that you have QUAGBCDEFHI… rotated on each line.)

Same for Q4, where I get these for FOUR and QUAG and MIRE:
HKLNOPJQSTUVWXYZFMIRGEABCD
QTUVWXSYZMIREABCODFGPHJKLN
WYZMIRXEABCDFGHJUKLNVOPQST
ACDFGHBJKLNOPQSTRUVWEXYZMI

[madness]

Here’s a reimagining of the trick:
Choose your alphabet keywords and cipher.
Choose one letter as your shift key and encrypt the alphabet ABCDEFGHIJKLMNOPQRSTUVWXYZ.
Choose a different letter as shift key and encrypt the alphabet again.
Post the two outputs.
From them, I can almost always determine the cipher and keywords.

Example:

quagmire3.py enc x flyingsaucer ABCDEFGHIJKLMNOPQRSTUVWXYZ
GEARUXIBLDHZJYKMOCNPSQTVFW
quagmire3.py enc j flyingsaucer ABCDEFGHIJKLMNOPQRSTUVWXYZ
VLXYZJQIONGKSPAUCFTEWRBDMH

Post
GEARUXIBLDHZJYKMOCNPSQTVFW
VLXYZJQIONGKSPAUCFTEWRBDMH

[Author]

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