Codebusters - K2 Patristocrat

A K2 Patristocrat is a monoalphabetic substitution cipher. Every plaintext letter always turns into the same ciphertext letter, and the key is a 26-letter cipher alphabet built from a keyword. It is usually the harder form of the K2 family because the spaces are gone: the message is written in groups of five letters, and the word boundaries that usually start a crack are missing. The skill is recovering the key from letter patterns alone.

What the rules cover

Under the 2027 rules, the K2 Patristocrat is a Division C cipher. Division C item 3.e.i.(2) allows Patristocrats in one form: word spaces removed, letters printed in blocks of five, and a K1 or K2 alphabet.

Several other 2027 rules shape how a K2 Patristocrat plays out:

• No self-decryption (3.g). No letter may stand for itself in Aristocrats, Patristocrats or Xenocrypts.
• Not the timed question (3.h). The timed first question is always an Aristocrat with spaces, never a Patristocrat.
• Not a special bonus question (3.i). Up to three special bonus questions are marked on the exam, but they must be cipher types other than Aristocrats, Patristocrats and Xenocrypts. In 2027 at least one of them uses the new Homophonic cipher. A Patristocrat earns only its own points.
• Hints are unmarked. Item 3.e.i allows Patristocrats with or without a hint, and the crib-placement rule (3.j) lists only the cryptanalysis ciphers, not the Patristocrat. So a hint may be a word whose position in the ciphertext is not shown. Place it by pattern before any frequency work.
• Plaintext answers. The option to answer with the keyword instead of the decoded text (3.e.ii) is written for Aristocrats only. A Patristocrat asks for the plaintext, graded by the usual error count.

Event format

Codebusters is a written (or computer-based) exam for teams of up to 3, lasting about 50 minutes. Under the 2027 rules teams bring only writing utensils: no notes, no binder and no calculator of any class. The only aid is the resource sheet the Event Supervisor hands each team member. In Division C it carries the Morse code table, English and Spanish letter frequencies, the Porta table and the Baconian mappings, as needed for that exam. For a Patristocrat the frequency table is the part that matters.

The packet is printed single-sided so the team can pull it apart. Pages may be split up and questions answered in any order, alone or together (3.d).

How the cipher works

The cipher uses two rows of letters. The plain row is A to Z in order. The keyed row is a rearranged copy of the alphabet, and it is the key. To build the keyed row:

1. Write the keyword, keeping only the first copy of each letter.
2. Write the letters of A to Z that the keyword did not use, in alphabetical order, after the keyword. The result has 26 letters.
3. Align the rows. Each plain letter has one keyed letter directly beneath it.
4. The keyed row may be rotated (shifted) so the keyword starts under any plain letter, wrapping around from Z to A. Test writers choose a shift that leaves no letter mapped to itself.

Encryption and decryption use the same table in opposite directions.

Encryption, step by step

1. Remove spaces and punctuation and write the plaintext in capitals.
2. Find each plain letter in the plain row and note its position, with A = 1 through Z = 26.
3. Write the keyed letter at that same position.
4. Group the output in fives. The grouping is presentation only, so decoders ignore it.

Decryption, step by step

1. Remove the group spaces to get one continuous string.
2. Find each cipher letter in the keyed row and note its position.
3. Write the plain-row letter at that position.
4. Read the result and insert word breaks. The output has no spaces, so segmenting it is part of the job.

For the worked examples below, use the keyword ZEBRA. Its keyed row is:

plain  A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
keyed  Z E B R A C D F G H I J K L M N O P Q S T U V W X Y

Encrypting step by step

Encrypt the phrase "We are on the hill at dawn". Removing spaces gives WEAREONTHEHILLATDAWN, which is 20 letters, or four groups of five. For each plain letter, the keyed letter is the one at the same position in the keyed row.

Grouped ciphertext: VAZPA MLSFA FGJJZ SRZVL.

Plain A appears three times (rows 3, 15, 18) and always becomes Z; plain E (rows 2, 5, 10) always becomes A. That consistency is what makes the cipher solvable.

Decrypting step by step

Decrypt VAZPA MLSFA FGJJZ SRZVL. Remove the spaces, then look up each cipher letter in the keyed row. Its position in the keyed row gives the position in the plain row, and the plain-row letter at that position is the plaintext.

Reading the plain row gives WEAREONTHEHILLATDAWN, and inserting word breaks returns "We are on the hill at dawn". The round trip is the best check: re-encrypt your decoded text and confirm it reproduces the ciphertext exactly.

Checking a keyed alphabet against the rules

Rule 3.g forbids a letter from decrypting to itself, so a valid keyed row has no position where the keyed letter equals the plain letter. In the ZEBRA row, compare position by position: Z against A, E against B, B against C, and so on. No position matches, so the alphabet is valid.

Now try the keyword SCIENCE. Its keyed row is S C I E N A B D F G H J K L M O P Q R T U V W X Y Z. Position 20 holds T in both rows, and so do positions 21 to 26 (U through Z). This alignment is invalid, so a test using SCIENCE would shift the row. A keyed row as it actually appears on a valid question never has a fixed point, so if your reconstruction produces one, one of your guesses is wrong.

Placing a hint

When a question gives a hint word, use its letter pattern. Write the hint as a pattern of repeats, then slide it along the ciphertext looking for the same pattern.

Solving without spaces or a crib

Because a Patristocrat may have no hint and has no word boundaries, the work is a search. These steps work in order.

1. Tally the cipher letters. Count how often each letter appears. Compare the tally with the English letter frequencies on your resource sheet, and treat the first few matches as hypotheses. A short message does not follow the frequency table closely.
2. Look for repeated patterns. A doubled cipher letter often hides a doubled plain letter such as LL, EE or SS. A repeated three-letter string is a candidate for a common English word or ending such as THE, AND or ING.
3. Keep a two-column working table. Write each guess as plain letter to cipher letter. Each cipher letter may have only one plain letter, and each plain letter only one cipher letter. A guess that breaks this rule is wrong.
4. Exploit the K2 structure. After the keyword's letters, the rest of the keyed row runs through the alphabet in order. So for plain letters past the keyword, the cipher letters run in alphabetical order, cyclically (they may wrap from Z to A), so recover the run and then find where the keyword sits and the shift. In the unshifted ZEBRA row, the run C D F G H I J K L M N O P Q S T U V W X Y climbs steadily from plain F onward. If you know plain H is F and plain L is J, then plain I, J and K must be the cipher letters between F and J, in order: G, H, I.
5. Use the no-self rule to cut candidates. If a cipher letter is X, then plain X cannot be paired with it. Any guess that would map a letter to itself is eliminated before you test it against the text.
6. Fill the keyed row and verify. Once most of the row is known, complete the rest by elimination, decode, and re-encrypt the result to check.

Scoring and what the rules allow

Each Patristocrat is scored on the number of errors in its decoded plaintext (4.d). Two or fewer errors earn full credit. Each further error costs 100 points, never below zero: a 400-point question with five errors earns 100 points, and with seven errors earns 0.

The final score is the exam score plus the timing bonus plus the special bonus (4.b). The timing bonus, 2 × (600 − seconds), is earned only on the timed Aristocrat (4.f), and the special bonus (4.g) is reserved for the marked questions of other cipher types. A Patristocrat is worth exactly its printed points, so skip one that is not moving and come back to it.

Common pitfalls

Practice ciphertexts

Try these before reading the answers. The first gives the keyword. The other two do not.

References and further reading

• Science Olympiad, 2027 rules manual, Codebusters B and Codebusters C, and event pages: soinc.org
• American Cryptogram Association, for the definitions of keyed alphabets K1, K2 and K3: cryptogram.org
• SciOly Wiki, Codebusters page (linked, not copied): wiki.scioly.org
• Wikipedia, "Substitution cipher": en.wikipedia.org/wiki/Substitution_cipher
• Wikipedia, "Frequency analysis": en.wikipedia.org/wiki/Frequency_analysis