He is best known for his work Minchah Belulah, an accessible commentary on the Torah written in response to the 1553 burning of every edition of the Talmud in Italy - an event Rabbi Menachem witnessed first hand.
But his work on cryptography is also fascinating. He wrote about it in his booklet "Zafenat Pane’ah," named after Joseph's royal Egyptian name.
According to the article, Abraham Menahem spent two years preparing Zafenat Pane’ah, and it was published in 1555. It appears that he took the method of encryption published in 1553 by Giovan Battista Bellaso and applied it to Hebrew.
Here is the page of Zafenat Pane'ah to help one encrypt (and decrypt) text:
Note the similarity with Bellaso's 1553 table, including the shifting of the alphabets.
Here's how it works. The sender and receiver of the message both know a password or passphrase that is the key. Find the row with the first letter of the key and choose the corresponding letter for the first letter of the message, and the cipher letter is the one that corresponds to it (above or below.) Then for the second letter of the message, do the same with the second letter of the key, and so forth. When you run out of letters of the key, just start at the beginning again.
Just like today, a stronger password makes it much harder to decrypt.
The receiver of the message does this in reverse, taking the first letter of the key, and choosing the corresponding plaintext on the row that has that letter.
One other very interesting thing about Rabbi Abraham Menachem is his escutcheon, his seal. It includes two topless women!
Rabbi Abraham Menachem was definitely an erudite, interesting and well-read person.
(h/t YMedad)