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Are there any words in the English language which, when encrypted using the Caesar Cipher with any key, result in another English word? How may one go about determining which Caesar shifts are weakest in this context?

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    $\begingroup$ I'm voting to close this question as off-topic because it's fundamentally trivia about the English lexicon and orthography, and not really about the Caesar cipher. $\endgroup$ – Luis Casillas Jul 5 '18 at 22:26
  • $\begingroup$ see answer below, there is some security content to the question, unless all classical crypto questions are off topic. $\endgroup$ – kodlu Jul 5 '18 at 22:43
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    $\begingroup$ zoo shh odd pee app. cubed melon. fusion layout. river arena. wet owl god. marry gulls. do it pa. sleep bunny. $\endgroup$ – yyyyyyy Jul 5 '18 at 23:57
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    $\begingroup$ @yyyyyyy How did you generate those? $\endgroup$ – Keith Matthews Jul 6 '18 at 0:17
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    $\begingroup$ I'm voting to leave this question open since the question asks for any words, not all words and for an explanation rather than a direct solution for a homework question. Note though that asking for an explanation was only made after the first edit of the question by kodlu, so the list of words do represent an answer to the original question. $\endgroup$ – Maarten Bodewes Mar 24 '19 at 10:51
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Actually, we have a four-way (that is, four words that will can be converted into any of the others with the right shift). These words are:

ax, by, he, if

Other two letter words are:

am <-> my
at <-> pi
do <-> it
hi <-> no

We also have

the <-> max

I didn't do a systematic search for words over two letters; there certainly do appear that they are moderately plentiful


I've done a more systematic search over longer words; ignoring extremely obscure words, the best I found were

abjurer <-> nowhere
inkier <-> purply
fusion <-> layout
manful <-> thumbs
primero <-> sulphur
steeds <-> tuffet

(OK, 'tuffet' missed by 'obscure' criteria; I still liked it).

So, yes, there certainly are words can be be encoded into other words

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The longest pairs

  • 1 (and 25):
    • Common: Steeds and Tuffet
    • Uncommon: Anteed and Bouffe (If you paid your ante, you anteed, bouffe is another word for bouffant, a type of hat)
  • 2 (and 24):
    • Common: Pyic and Rake
    • Uncommon: Pyrryl and Rattan (longer than Osmic and Quoke)
  • 3 (and 23):
    • Common: Dolt and Grow
    • Uncommon: Ordlix and Rugola (Works and is longer than Teloi and Whorl, primero is a Spanish word and doesn't count)
  • 4 (and 22):
    • Common: Pecan and Tiger
    • Uncommon: La Llan and Pepper
  • 5 (and 21):
    • Common: Fizzy and Kneed
    • Uncommon: Pihvin and Unmans, Pinzon and Unsets(added both)
  • 6 (and 20):
    • Common: Fusion and Layout (fusion layouts?)
    • Uncommon: Wiliwili and Corocoro
  • 7 (and 19):
    • Common:
      • Inkier and Purply
      • Manful and Thumbs
    • Uncommon: Unfiber and Bumpily
  • 8 (and 18):
    • Common: Talk and Bits
    • Uncommon: Caddaw and Killie (Longer than Setal and Ambit)
  • 9 (and 17):
    • Common:
      • Sleep and Bunny
      • River and Arena
    • Uncommon: Verity and Enarch
  • 10 (and 16):
    • Common: Cubed and Melon
    • Uncommon:
      • Muumuu and Weewee
      • Rubbed and Bellon
  • 11 (and 15):
    • Common:
      • Spits and Dated
      • Spots and Dazed
    • Uncommon: Splits and Dawted
  • 12 (and 14):
    • Common: Road and Damp
    • Uncommon: Foeish and Raquet(Works and longer than Torus and Fadge)
  • 13:
    • Common: Green and Terra
    • Uncommon: Nowhere and Abjurer

Rot13 pairs

  • Abba / Noon
  • Abjurer / Nowhere
  • Anan / Nana
  • Ancre / Naper
  • Anil / Navy
  • Arba / Neon
  • ARBTRN / Neogea
  • Arin / Neva
  • Arry / Neel
  • Arvin / Neiva
  • Arvy / Neil
  • Aryn / Nela
  • Balk / Onyx
  • Bare / Oner
  • Barf / Ones
  • Barny / Oneal
  • Batha / Ongun
  • Becuna / Orphan
  • Bore / Ober
  • Bork / Obex
  • Bornu / Obeah
  • Brava / OENIN
  • Byran / Olena
  • Cent / Prag
  • Centre / Prager
  • Char / Pune
  • Chat / Pung
  • Chechen / Purpura
  • Cheer / Purre
  • Cheery / Purrel
  • Cheryl / Purely
  • Clerk / Pyrex
  • Craal / Penny
  • Crag / Pent
  • Cran / Pena
  • Cratch / Pengpu
  • Creel / Perry
  • Cynar / Plane
  • Dhoon / Qubba
  • Ebbs / Roof
  • Elong / Rybat
  • Ent / Rag
  • Entre / Rager
  • Envy / Rail
  • Erava / Renin
  • Errs / Reef
  • Faber / Snore
  • Farrel / Sneery
  • Freen / Serra
  • Frere / Serer
  • Fret / Serg
  • FUBAR / Shone
  • Furby / Sheol
  • Glar / Tyne
  • Glen / Tyra
  • Gnat / Tang(Backwards too)
  • Grath / Tengu
  • Greely / Terryl
  • Green / Terra
  • Greene / Terrar
  • Greeny / TErral
  • Greer / Terre
  • Gunar / Thane
  • Gunja / Thawn
  • Hern / Urea
  • Iraq / Vend
  • Ivan / Vina(Anagrams too!)
  • Ivar / Vine
  • Jebat / Wrong
  • Junes / Wharf
  • Jung / What
  • Junger / Whatre
  • Jura / When
  • KRan / Xena

We have a 6-letter shift for every length now.

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  • $\begingroup$ If you want to maintain this, can you do it in a new question on, say, puzzling.se, or make a web site for it? It's not really on-topic for crypto.se. $\endgroup$ – Squeamish Ossifrage Mar 24 '19 at 2:50
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Let $p_c$ be the probability of letter $c$. The collision probability $$\sum_{c} p_c^2$$ (used to extract the right shift in substitution ciphers) of English is well known to be $$P_{coll}\approx 0.065.$$

I have computed the shifted collision probability $$\sum_{c} p_c p_{c+k}$$ for a Caesar shift of $k$ letters. This is maximized at $t=0,$ for all probability distributions of course.

At the Caesar shift of $k=3$ it is approximately $$P_{coll}(3)\approx 0.033235,$$ whose reciprocal is around 30. So a Caesar shift of 3 should give another english word of length $L$ in roughly a sample of $30^L$ letters in an English text. Since number of short words is limited this may require a biggish $L$ in practice.

Other structural properties of language depart from uniform i.i.d. and should intuitively help collisions.

Shifts of 11 and 15 are the best for the cryptanalyst with shifted collision probability roughly $ 0.44288.$

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Triplets and more of 5-letter with repeated letters farre sneer toffs, dolls groov jurry wheel, aneer boffs hully narre, cheer diffs jolly purre, fizzy kneed loffe,

Triplets and more of 5-letter without repeated letters ebola herod robyn, gnarl taney xeric

Triplets and more of 6-letter words alexir jungra whaten, cleely pyrryl rattan vexxer (As a bonus, the first one contains my name!)

7-letter shifts abjurer nowhere, bumpily unfiber, chechen purpura, fusions layouty, primero sulphur,

8-letter shifts corocoro wiliwili

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  • $\begingroup$ "groov" and "jurry" are not words. They are "groove" and "jury". "aneer" and "narre" are not words. "diffs" is not a word. "loffe" is not a word. "herod" is a name, not a word. "alexir", "jungra", and "whaten" are not words. "cleely" and "vexxer" are not words. "layouty" is not a word. $\endgroup$ – egg Mar 24 '19 at 16:40
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    $\begingroup$ Rather than commenting on the fact that they are not words, you can edit the answer to simply remove them. $\endgroup$ – Ella Rose Mar 25 '19 at 1:54

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