Codebusters - Atbash

Atbash is the simplest cipher you will see on a Codebusters exam. It has no key and no arithmetic beyond one subtraction, so it is worth points quickly once you recognize it. The catch is that it is easy to recognize only if you check for it early.

What the rules cover

Atbash is a Division B code type only. In the 2027 rules it is item 3.e.ix of the Division B Regional list, named as the English form of the cipher (not the Hebrew original). It does not appear anywhere on the Division C lists.

The event format around it is the same at every level in 2027:

• Team and time. Teams of up to 3, about 50 minutes for the whole exam.
• What you bring. Writing utensils only. No notes, no reference sheets of your own and, new for 2027, no calculators of any kind: the only materials allowed are the ones the Event Supervisor hands out.
• The resource sheet. Each Division B team member gets a sheet (rules item 2.d) carrying the Morse Code Table, English and Spanish letter frequencies, the Porta Table, the Atbash Table and the Baconian mappings, as needed for that exam. The Division C sheet has no Atbash Table, which matches the cipher being absent from the C lists.
• The packet. It is printed single-sided so teammates can pull pages apart and work on different questions at once.

You do not need to memorize the Atbash Table, but you should be able to rebuild it in seconds from the rule behind it, so a misread row never costs you points.

What Atbash is

Atbash is a monoalphabetic substitution cipher with a fixed alphabet. Each plaintext letter is replaced by the letter at the mirror position of the alphabet: A becomes Z, B becomes Y, and so on, down to M becoming N. Spaces and punctuation are not changed.

Because the mapping is the same for every message, Atbash has no key. Every Atbash message uses the same 13 pairs:

Three properties follow directly from the mirror structure, and each one is useful on the exam:

1. The cipher is self-inverse. If A becomes Z, then Z becomes A. Encrypting a message and decrypting it use the same operation, so one table serves both directions.
2. No letter maps to itself. A letter would have to sit at its own mirror position, which is impossible in a 26-letter alphabet. If a decode ever seems to show a letter unchanged, you have made a copying error.
3. Each pair adds to the same total. With A = 0 through Z = 25, every pair of partners adds to 25. This gives a quick self-check: if two partners do not sum to 25, one of them is wrong.

Encrypting and decrypting step by step

Because Atbash is self-inverse, the procedure is identical for both directions. Use it for encryption and decryption alike.

1. Write the message in capital letters, keeping every space and punctuation mark in its original position.
2. For each letter, find it in the first column of the pair table, or in the second column if it appears there.
3. Replace the letter with its partner. Leave spaces and punctuation alone.
4. Check the output by decoding one word a second time. Each letter should return to the one you started with.

Worked example: encryption

Encrypt the phrase SCIENCE IS FUN.

Applying the same table to the other two words gives IS → RH and FUN → UFM. The ciphertext is:

HXRVMXV RH UFM

Notice that the two letters C in SCIENCE both became X. A monoalphabetic cipher always replaces a given plaintext letter with the same cipher letter, so repeated letters are a consistency check on your work.

Worked example: decryption

Decrypt the ciphertext GSRH RH Z HVXIVG. The steps are the same as in encryption:

Continue with the other words: RH → IS, Z → A, and HVXIVG → SECRET. The plaintext is:

THIS IS A SECRET

Re-encrypting THIS IS A SECRET returns GSRH RH Z HVXIVG, which confirms the decode.

Solving Atbash on exam conditions

Atbash problems are usually fast, but only if you identify them early. Use these checks in order.

1. Test the first word. The mirror of THE is GSV, of AND is ZMW, and of IS is RH. If the first two or three words of a ciphertext turn into readable English under the mirror, you have the whole cipher. If they turn into nonsense, it is probably not Atbash, so move on to another code type.
2. Use the short-word pairs. Common words map to recognizable ciphertext. THE becomes GSV, AND becomes ZMW, ARE becomes ZIV, THAT becomes GSZG, YOU becomes BLF, FOR becomes ULI, WITH becomes DRGS, IT becomes RG, IN becomes RM, OF becomes LU, and TO becomes GL. A two-letter ciphertext word such as RH is a strong candidate for IS.
3. Look at single letters. The only one-letter English words are A and I. So a lone cipher letter Z is probably A, and a lone cipher letter R is probably I.
4. Use the word breaks. Atbash keeps spaces, so word lengths are visible. A three-letter cipher word that starts with G is a good candidate for THE, because G is the partner of T. Test it first.
5. Check for consistency. After you decode a few words, each cipher letter should map to exactly one plaintext letter. If one cipher letter seems to stand for two different plaintext letters, one decode is wrong.
6. Do not build a substitution table. Because the mapping is fixed, you never need to work out a new alphabet. Once you know the rule, decode the rest of the message directly from the Atbash Table.

Frequency analysis is rarely needed for Atbash. Still, in a long ciphertext, the most common cipher letters are usually the mirrors of the most common English letters. E, T, A, O, I and N become V, G, Z, L, R and M. If V and G dominate your count, that is strong support for Atbash.

Telling Atbash apart from Caesar

Caesar is the other keyless-looking cipher on the 2027 Division B list, and the two are easy to confuse at a glance because both keep word breaks. One quick test separates them. In a Caesar cipher, every letter moves the same distance, so the gap between cipher and plain letters is constant. In Atbash, the gap changes from letter to letter while the sum stays at 25. If GSV decodes to THE, check: G (6) + T (19) = 25 and S (18) + H (7) = 25, so it is Atbash. A Caesar shift would need G→T and S→H to be the same shift, and they are not (13 forward versus 15 forward).

Timing and scoring

The whole Division B exam lasts about 50 minutes, so the goal is to finish an Atbash problem quickly and move on. Because each answer is scored by counting errors in the decoded plaintext, a final check is still worth the few seconds it takes.

• Error allowance (rules item 4.d). Two or fewer errors in the plaintext earn full credit. Each error beyond two costs 100 points, and a question never drops below 0. A 300-point Atbash with 4 errors scores 300 − 2 × 100 = 100 points; with 5 or more errors it scores 0.
• Timed question (3.h). The timed first question is always an Aristocrat with spaces, so Atbash never earns the timing bonus of 2 × (600 − seconds). Do not open the packet hunting for the Atbash while your team is on the clock for question 1.
• Special bonus (3.i and 4.g). Up to three questions that are not Aristocrats, Patristocrats or Xenocrypts can be marked as special bonus questions. Atbash is its own code type, so it can be one of them. In 2027 at least one bonus slot must go to the Homophonic cipher, which leaves at most two for every other type. A bonus question counts only if it is solved with no penalty points, which means two or fewer errors. One solved bonus question adds 150 points, two add 400 and three add 750.
• Tiebreakers (4.i). Ties are broken on questions the supervisor picks in advance, by score, then degree of correctness, then number attempted. A clean Atbash costs little time and can only help.

Common pitfalls

Practice

References and further reading

• The 2027 Division B Codebusters rules: resource sheet in 2.d, the code-type lists in 3.e (Atbash is 3.e.ix) and 3.f, the timed and bonus questions in 3.h and 3.i, and scoring in section 4. Check the official rules and any clarifications from Science Olympiad before competing.
• The American Cryptogram Association, cryptogram.org, for classical cipher resources and the standard descriptions of monoalphabetic ciphers.
• The Atbash entry on Wikipedia, en.wikipedia.org/wiki/Atbash, for the history of the cipher, including the Hebrew original that the rules do not use.