Fractionated Morse cipher

What the Fractionated Morse cipher is

To fractionate a cipher is to break each plaintext letter into smaller pieces before encrypting, so that one ciphertext letter no longer matches one plaintext letter. Here the pieces are Morse symbols. The message is written in Morse with an x between letters and a double x between words, the string is cut into triplets, and each triplet becomes a letter. A Morse letter is one to four symbols long, so a ciphertext letter may hold the end of one plaintext letter and the start of the next.

There are 27 triplets of dot, dash and x, and one of them, three x’s, never occurs because the separators never run that long, which leaves exactly 26, one for each letter. The table lists them in a fixed order, dot before dash before x, and the keyed alphabet runs alongside: the keyword’s letters with repeats removed, then the rest of the alphabet in order. Whoever knows the keyword can rebuild the table in a minute.

The cipher is one of the types in the American Cryptogram Association’s catalogue of pencil-and-paper ciphers, the source of most Codebusters conventions. Its appeal for a contest is that it joins two skills: the Morse reading, which is mechanical, and the recovery of the keyed table, which is logic.

Solving without the keyword starts from the crib. The crib’s Morse, with its separators, is written out and laid over the ciphertext letters where the crib falls; each covered letter is then known to stand for a particular triplet, and those entries go into the table. Because the keyed alphabet is a keyword followed by the remaining letters in order, a handful of known entries often reveals the keyword, and then the whole table. The common mistake is an x miscounted at a word boundary, which shifts every triplet after it.

How to solve a Fractionated Morse cipher

The message is first written in Morse with an x between letters and xx between words, then cut into groups of three symbols. There are 26 possible triplets of dot, dash and x (every mix except xxx), and each stands for one letter of an alphabet keyed by a word.

1. Write the 26 triplets in order, dot before dash before x: ... ..- ..x .-. .-- .-x .x. .x- .xx -.. and so on to xx-.
2. Under them write the keyed alphabet: the keyword’s letters with repeats dropped, then the rest of the alphabet in order.
3. Replace each ciphertext letter with its triplet and write the triplets as one unbroken line.
4. Split the line at each x into letters and at each xx into words, then read the Morse. An x or two at the very end is only padding to fill the last triplet.
5. Without the keyword, use the crib: its Morse, with the x’s, tells you which triplets the marked ciphertext letters stand for, and those fill part of the table.

A worked example

Decode OBBIF MCYCW P (keyword COMET)

Keyed alphabet: C O M E T A B D F G H I J K L N P Q R S U V W X Y Z
Against the triplets: C ...   O ..-   M ..x   E .-.   T .--   A .-x   B .x.   …   Y xx.

O ..-  B .x.  B .x.  I -.x  F .xx  M ..x  C ...  Y xx.  C ...  W x--  P -x-
In one line: ..-.x..x.-.x.xx..x...xx....x---x-
Split at x and xx: ..-. .. .-. . / .. ... / .... --- -

Plaintext: FIRE IS HOT

Fractionated Morse in Codebusters

Among the Science Olympiad rule sets OlyPrep has read, Fractionated Morse is on the Division B Codebusters list and not on the elementary lists. The Division B rules OlyPrep has read give a crib of at least four plaintext characters and show where it falls in the ciphertext. The Division B reference sheet OlyPrep has read carries a Morse table, so the Morse does not have to be memorised, though a student who knows it reads faster. Scoring follows the usual rule, with a decoded message of up to two wrong letters commonly counted as solved.

The question rewards order. Students who write the triplet table out first, mark the crib’s triplets into it, and only then decode, commonly finish ahead of those who decode piece by piece. The final Morse string is long, and writing it in one unbroken line, then marking the single and double x’s, keeps the letters and words straight.

The lab below draws a science sentence, picks a keyword from its own list, and prints the ciphertext in groups of five. The key line names the keyword and the start of the triplet table; a second line gives a crib word and the ciphertext letters that hold it, the way a Division B question places 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 Fractionated Morse cipher

The lab below is set to the Fractionated Morse 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 Fractionated Morse cipher is tested

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

• Science Olympiad Division B — on the Codebusters list, with a crib of at least four characters placed on the ciphertext

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