Homophonic cipher

What the Homophonic cipher is

In a simple substitution, E is the commonest letter of the ciphertext because it is the commonest of the plaintext, and that is how such ciphers are broken. A homophonic substitution spreads the common letters across several symbols, called homophones, so that a solver counting symbols sees a flatter picture. The more homophones a letter has, the better it is hidden; historical versions commonly gave the commonest letters the most.

Homophonic ciphers are old. The earliest commonly cited are diplomatic ciphers of the Italian states of the fifteenth century, and the idea runs through the codebooks of the centuries after. They were an answer to frequency analysis, which was already understood. The version Codebusters uses is a tidy modern one, with a fixed structure that makes a pencil-and-paper solve possible in a contest.

In that version the numbers 01 to 100, with 100 written as 00, fall into four blocks of 25. The first block starts at the keyword’s first letter and counts on through the alphabet, wrapping from Z to A; the second starts at its second letter, and so on. A block has 25 numbers and the alphabet 26 letters, so each block skips one letter, the one just before its start, and most letters have four homophones, a few three. Decoding with the keyword is counting: find the block, subtract its first number, and count on from its starting letter.

Without the keyword, the crib does the work. Each crib number and the letter it stands for name the starting letter of that number’s block, by counting back, and three or four such starting letters usually suggest the word. The mistakes are the wrap from Z to A, which is easy to drop, the 00 that means 100, and the skipped letter, which makes a block one letter short and can make a careful count look wrong when it is right.

How to solve a Homophonic cipher

A substitution in which a letter can be written several ways, so the common letters hide among many symbols. The numbers 01 to 100, with 100 written 00, fall in four blocks of 25. Each block counts through the alphabet from one letter of a four-letter keyword.

1. Write the four blocks: 01–25, 26–50, 51–75 and 76–00. The first starts at the keyword’s first letter, the second at its second letter, and so on.
2. Within a block, count on through the alphabet, going from Z back to A. A block has 25 numbers, so it skips one letter: the one just before its start.
3. To decode a number, find its block, subtract the block’s first number, and count that many letters on from the block’s starting letter.
4. Without the keyword, use the crib: each crib number and its letter name the starting letter of that number’s block, by counting back. Three of the four usually suggest the word.
5. Check the keyword on a few numbers outside the crib before decoding the rest.

A worked example

Decode 14 49 57 83 38 71 88 22 31 63 91 39 (keyword FROG)

01 starts at F, 26 at R, 51 at O, 76 at G.

14 is in 01–25: 13 on from F → S
49 is in 26–50: 23 on from R → O
57 is in 51–75: 6 on from O → U
83 is in 76–00: 7 on from G → N
The same way: 38 → D   71 → I   88 → S   22 → A   31 → W   63 → A   91 → V   39 → E

Plaintext: SOUND IS A WAVE

Homophonic in Codebusters

Among the Science Olympiad rule sets OlyPrep has read, the Homophonic cipher is on the Division B Codebusters list and not on the elementary lists; it is the type the Division B list added most recently. The Division B rules OlyPrep has read use a keyword of at least four distinct letters and a crib that reveals at least three of them. Scoring follows the usual rule, with a decoded message of up to two wrong letters commonly counted as solved.

The same rules give the Homophonic a place among the special-bonus questions: a paper’s bonus questions, worth extra when solved with no errors, include at least one Homophonic. That makes it worth practising to a zero-error standard, not just to two errors, and the habit that gets there is checking the keyword on numbers outside the crib before decoding the rest.

The lab below draws a science sentence and a four-letter keyword of distinct letters, picks one of each letter’s homophones at random, and spreads the crib’s letters across at least three blocks, so the crib always fixes at least three key letters. The key line names the keyword and the block starts; a second line gives the crib and the numbers that hold it. Covering the key line turns the challenge into the crib solve. The easy setting uses a short sentence and the hard setting a long one. Check compares letters only, exactly; Reveal shows the plaintext.

Practice the Homophonic cipher

The lab below is set to the Homophonic cipher alone. Pick a difficulty, generate a challenge, decode it, then check your answer or reveal the solution. It runs in your browser, needs no account, and is unlimited on every OlyPrep plan.

Where the Homophonic cipher is tested

The Science Olympiad rule sets OlyPrep has read that name this cipher:

• Science Olympiad Division B — on the Codebusters list, and among the special-bonus questions

Cipher lists change with each season’s rules; a tournament’s own rulebook is the authority on what it tests.