top of page

Back in the time of Julius Caesar, if one of the soldiers had wanted to send to Rome the message “SEND MORE PEPPERONI,” without revealing to the enemy the troop's dire shortage of pizza toppings, he would have dispatched a courier with the message “VHQG PRUH SHSSHURQL.” This is not in Latin, but rather in a clever cipher, or code, the invention of which is credited to that most brilliant of Caesars (prior to Sid), Julius. All the letters in the plaintext (the actual message) have been shifted three ahead in the alphabet to create the ciphertext..

This ciphering system, as transparent as crystal to us (?), was completely baffling to the tribal hordes for hundreds of years; however, as the Romans were to learn, code makers need to stay well ahead of code breakers. Let's survey the improvements to cryptography that led to today's cryptogram puzzles and take them a few steps further.

In Number Theory with Computer Applications by Kumanduri and Romero, I see that one way to cloud the message a bit is to have a formula which changes the letters. If we assign the letter “A” to the number zero, “B” to the number one, and so on, we can use a formula to transpose the numbers of a message to new numbers. For example, the formula “triple, and add one” would move the letter C in position 2, over to H in the seventh position. Whenever the formula results in a number higher than twenty-five, we cycle back to the beginning, as in 26 equals A, 27 equals B, and so on. Any odd multiplier (except for 13) will match each letter with a unique code letter. Why do you think that even multipliers and 13 won't work?

Formulas are made for code breakers to, well, de-formulate, so other encryption devises came to be employed. A random substitution of each letter for another would yield many possible codes. As a matter of fact, the number of ways to reorder the alphabet exceeds the number that begins with a four and is followed by twenty-six zeros. In spite of this vast number of possible substitution schemes, this system also yields to analysis. Cryptogram solvers decode brief messages every day. They take advantage of knowing where the word breaks are, and they count the frequency of letter occurrences to eliminate billions of possible substitutions. For example, we would not expect many words to end with a “u”, but we would expect the letters “e” and “t” to be used often.

Unless an encoder can be cleverly communicative, using phrases like “lugubrious calyx” to great advantage, his or her message, especially if a long one, will generally follow expected letter frequencies. John Allen Paulos, in the following excerpt from Beyond Innumeracy, comments on a work that defies those frequencies. I've disguised the word breaks, grouping by six letters, but to be of some help, I've picked a passage of mostly ordinary words, used a formula to transpose the letters, and retained the punctuation. HINT: HYVVYL is LETTER. The passage begins: “Georges Perec's 300-page novel La Disparition,

TWYQR'V OWRVES REQSRI HYHYVV YL“Y”YPO YBV,WDO WALQY,D WLVNYD WALARD WLVARE VYSRQV EROYQS RNSQRE MY.VNSR CWDVNS Q: RW“VNY”, “ELY”, “KYL Y”, ”NY”, “QNY”, “VNYU”,RW LYFYRE R“YFYR.”S RERYQQ EUWRQA ONHSBW ILEMQ,K WLCQVN EVWMSV HYVVYL Q,BYLYO TYDYRT QVNYQE RSVUER TQYLSW AQRYQQ WDQAON ERARTY LVECSR I,ELIAS RIVNEV OWRQVL ESRVER TELVSD SOYELY VNYYRI SRYQVN EVNEFY TLSFYR RWVWRH UWAHSB SERQJA VEHQWM ERUMES RQVLYE MEAVNW LQ...VWBH AMJEHH WDHERI AEIY'QB WQQSJS HSVSYQ.”

â€‹

December 2005, October, 2021