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Sum-clock (additive wheels)

From the Buttcrack Cipher Wiki — the free field guide to classical ciphers

Sum-clock (additive wheels) — Several short wheels added together modulo 26, so the effective key is the least common multiple of their periods.

Two or more short wheels summed mod 26 over a keyed alphabet. Solved by joint coordinate ascent over the wheels, not by columns.

A worked example§

Encrypting a sample with the cipher itself, at build time:

MEET ME BY THE OLD CLOCK TOWER AT DAWN

Key: periods=[10, 8], alphabet=kryptos

produces the ciphertext

KWHWKDWSGQXOPUYQUPHXRIBJRWOIQO

This example is generated by running the cipher when the page is built, and the round trip is checked, so it always matches what the solver does.

How it is broken§

Four wheels of 4, 5, 6 and 7 give a key of period 420 — longer than a 153-letter message — so no column repeats and column statistics have nothing to work with. Two wheels are solved exactly: fix the short one and what remains is a plain Vigenere of known period.

History and context§

The engine behind several Paradigm Kryptos CTF challenges. PK3's two wheels are literally the words ORDINATE and PENTIMENTO, which this solver recovers in about five seconds.

See also§

Vigenère · Beaufort · Variant Beaufort · Gronsfeld · Porta · Quagmire III (keyed alphabet)

Browse every cipher in the Polyalphabetic ciphers family, read the history of codebreaking, or return to the wiki main page.

Frequently asked questions§

How is the Sum-clock (additive wheels) broken?

Four wheels of 4, 5, 6 and 7 give a key of period 420 — longer than a 153-letter message — so no column repeats and column statistics have nothing to work with. Two wheels are solved exactly: fix the short one and what remains is a plain Vigenere of known period.

What key does the Sum-clock (additive wheels) use?

wheel periods + wheels. The keyspace is unbounded in practice.

How much ciphertext do I need?

At least 60 characters for this solver to attempt it; short messages can be readable and still not be proof.

Can I break a Sum-clock (additive wheels) on this page?

Not with the browser build, which targets the common puzzle families. The desktop version searches it: see the Windows app page.

Categories: Polyalphabetic ciphers | Full-version ciphers | Cipher wiki
The facts in this article are generated from buttcrack's cipher registry when the site is built, so they describe the implementation you can run on this page. Registry-generated content is checked against the code; the history is editorial.

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It tries: Caesar, Atbash, ROT13, affine, Trithemius, rail fence, single-byte XOR, periodic Vigenère-family ciphers, autokey, selected encoding layers (such as Base64, hex, binary, decimal ASCII, Morse, and reverse), and—only with 60+ A–Z letters—statistical substitution.

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