WORDS AND THEIR NEGATIVES

MATH 195

In the Vigenère cipher, we take plain text and add a key word: E_{K}(α) = K + α; to decrypt, we subtract D_{K}(β) = β − K. The problem is therefore upon us: when are these two processes the same? When is the negative of a word also an English word?

We take the identification A = 0, B = 1, C = 2, ..., Z = 25, so e.g. −(AT) = AH.

Alex Gonzalez (gr8gonzo@uclink4.berkeley.edu) found the following list of words using an exhaustive computer search on 45,254 words:

ad  ax
ah  at
ail  asp
an  an
Ann Ann
Anna Anna
fan  van
gut ugh
had tax
hag tau
Hal tap
Han tan
hem two
Ian San
imp  sol
jail rasp
jaw Rae
lab  paz
lac  pay
lamps Paoli
Lao Pam
lap  pal
lax  pad
men own
mew owe
moan oman
nan nan

Pasquale di Paoli (1725–1807) was a Corsican patriot who led (from 1755) the struggle for independence from Genoa. Paoli is also a town in Oklahoma of population 542.

Material relevant to Math 195: Cryptography.