Cryptoquip Construction
I was curious about whether the “hint” that you get with an official Cryptoquip makes any difference.
I was also curious about how hard it is to construct a decent Cryptoquip.
Deciphering Clear Text
I tried my program on a chunk of clear text with no hint:
Solved letters:
a b e g h l m o p r s t u y
a b e ? h l ? o ? r s t ? y
Solved Puzzle:
she sells seashells by the seashore rubber baby buggy bumpers
she sells seashells by the seashore r?bber baby b???y b???ers
Didn’t quite solve it. The ‘g’ in only one word, and the ‘u’ at index 1 of every word it’s in makes this unsolveable with my method. “buggy”, even when ‘b’ and ‘y’ clear letters are known, could match about 20 dictionary words without considering cross-word cipher letter commonalities, and about 5 words (“biddy”, “buddy”, “buffy”, buggy", “bunny”) if you consider common letters between words.
Considering cross-word letter combinations with “bumper” doesn’t help, either. As a cipher text word, “bumpers” matches “bumpers”, “bunkers”, “bickers” and “binders”, so the ‘u’ cipher letter could match ‘u’ or ‘i’ clear text letters.
Cryptoquips in general aren’t solveable without a leap of intuition. Cryptoquip writers probably have to avoid texts with one letter that only occurs once, or only at the same position in similar-length words. They may follow other heuristics, too. Of course I’m leaving out the aesthetics of a particular, witty, quip.
Does the hint make a difference
The 2022-09-07 Cryptoquip (Denver Post) looks like this:
a=y
fklo x izwm dlubclq x ulmldwzpa fkzml tyqp
x ukzmj z iylqq aby ubymj qxa qklq x cxtbw czobw
Solved letters:
a b c d f i j k l m o p q t u w x y z
y o m b w g d h e l n t s j c r a u i
Solved Puzzle:
fklo x izwm dlubclq x ulmldwzpa fkzml tyqp x ukzmj z iylqq aby ubymj qxa qklq
when a girl becomes a celebrity while just a child i guess you could say shes
x cxtbw czobw
a major minor
My program solves it in 4 cycles. Without the a=y hint, it does not solve it in any number of cycles.
The hint does make a difference.
| Hint | Cycles to solve | Frequency of cipher letter | Word freq of cipher letter |
|---|---|---|---|
| a=y | 4 | 3 | 3 |
| d=b | 4 | 2 | 2 |
| b=o | 5 | 5 | 5 |
| z=i | 5 | 6 | 6 |
| l=e | 5 | 8 | 6 |
| p=t | 5 | 2 | 2 |
| u=c | 5 | 4 | 4 |
| x=a | 5 | 6 | 6 |
| w=r | 6 | 4 | 4 |
| c=m | 6 | 3 | 3 |
| m=l | 6 | 5 | 5 |
| o=n | 6 | 2 | 2 |
| y=u | 7 | 4 | 4 |
| k=h | 7 | 4 | 4 |
| f=w | 8 | 2 | 2 |
| q=s | 8 | 7 | 5 |
| i=g | unsolved | 2 | 2 |
| j=d | unsolved | 2 | 2 |
| t=j | unsolved | 2 | 2 |
| none | unsolved |
Apparently not every hint is of equal value. Just as clearly, a good hint (fewer cycles) is a cipher letter that appears more often, in more cipher words. Looks like a hint with a vowel as a clear letter is more valuable. There are exceptions to all of these.
That means that adding a hint is an art, not a science.
Conclusion
I hereby conclude that good cryptoquips are more of an art than a science. Clearly heuristics exist for making them appropriately easy to solve. But just as clearly, the witty nature of many quips is beyond science.
Two (or more) solutions to the same puzzle
It’s possible to have a Cryptoquip with 2 solutions, just like it’s possible to have two files with the same CRC32 checksum.
Simple examples are easy:
qiiw hiio
The above could decipher to “boop look” or “book loop” or “cool hoop” or probably many others.
How hard is it to construct such a puzzle of reasonable length? I tried, but it seems hard.