Babbage-Vane Cipher

The Babbage-Vane Cipher is a two-stage substitution routine maintained in the Cryptographic Annex of Floor -17, Annex Theta, and is the sole authorised instrument for generating the two-character checksum appended to a Sovereign Sigil. It is not a cipher in the ordinary sense: it conceals nothing. Its entire function is to render a sigil's authenticity verifiable at a glance by a clerk who has not read the underlying instrument. The Cipher is counted among the three "working algorithms" of Annex Theta, alongside Cipher Theta and the Vex Cipher, though its keepers have always insisted on its precedence over both.

Structure and operation

The routine proceeds in two movements, each attributed to one of its namesakes. The first, the Babbage movement, reduces the sigil's registration string to a single ordinal by summing the positions of its consonants in the issuing docket's alphabet — a procedure set out in full at Registry Theta-7, Annex 2. The second, the Vane movement, is a fixed rotation of that ordinal through a table of forty-one columns, after which the resulting index is transcribed as two characters drawn from the checksum syllabary. The syllabary omits the letters I and O and the numerals 0 and 1, on the ground that a checksum which can be misread is not a checksum.

Working cryptographers refer to the two movements informally as "the walk" and "the turn." The Babbage-Vane Cipher is the only algorithm in the Annex whose intermediate values are required to be preserved in draft; all others are burned. Drafts are held for nine cycles and then pulped, and the pulp is weighed before disposal.

Origin and the attribution dispute

The Cipher entered general use in Cycle 31, shortly after Librarian-Superior Vane issued the Vane Directives to streamline the classification of paradox-adjacent subjects. The Directives require, at clause 12, that every sigil issued under their provisions carry "a close of two characters, computed by the method of Annex Theta, and by no other method." The phrasing has been litigated for six hundred cycles.

The dispute concerns which Vane. The Vane Directives are signed by the Librarian-Superior, but the rotation table in the second movement is demonstrably the work of a hand — the columns are ruled at a slight lean, a habit recorded of Undersecretary-Grade 7 Elara Vane in the survey returns of the Avian Liaison Office. The office of the Chief Librarian, Floor 12,104, holds that the Cipher is the Librarian-Superior's throughout and that the lean is a copying artefact. Arbella Cipher has argued the contrary in print, noting that the rotation table's forty-first column is blank and that the Librarian-Superior was on record as preferring tables of forty.

"Where a table carries a column it does not use, the table is not finished; and where a table is not finished, it was not the work of a Superior."

— Arbella Cipher, Recensions of the Annex, Folio 212

Relationship to the Vex and Theta algorithms

The Cipher is frequently confused with the Vex Cipher, which measures instability matrices for the detection of recursive paradoxes, and with the Cipher Theta, which generates adjudication records and resolution protocols within Spiral Theta. The confusion is understandable and is not corrected at the door. The three algorithms share a scribal hand, a room, and — in the early cycles — a single inkpot, and the first folio of the Annex register lists them without separation.

Functionally they are distinct. The Vex Cipher produces a measure; the Cipher Theta produces a record; the Babbage-Vane produces two characters and stops. A note appended to the Annex register by an unrecorded hand observes that "the Cipher is the only one of the three that a porter could operate," which is offered neither as praise nor as criticism.

The Cipher Recension and the disputed reading

The authoritative commentary on the Cipher's first movement is the Cipher Recension, Arbella Cipher's reconstruction of the Alphonse-Vance Disputation drawn from Alphonse the Calibrator's working notes. The Recension establishes that the Babbage movement was originally computed over all letters of the registration string, vowels included, and that the exclusion of vowels was introduced later as a correction for strings containing the letter A repeated three or more times.

There is no agreement on when the correction was made. The Third Concordance fixes the change at Cycle 29, Annex 4, and cites the Recension itself as its authority — a circularity that the Concordance's own annotators have flagged without resolving. A rival reading places the correction in Cycle 34, after the affair of the Sigil of the Ninth Landing, when three separate offices issued checksums that agreed with one another and disagreed with the sigils they closed. The affair is recorded in the Annex register as "the error at the landing," and no further particulars are given.

Maintenance and access

The rotation table is re-ruled every eleven cycles by two clerks working in the same room but not on the same day, so that neither can attest to the other's columns. Visitors to the Annex are asked to leave their seals at the door; the Cipher does not require them, and the keepers have found that seals left on the table get mixed up with the working drafts. The Petitioner Identification desk on the floor above maintains a separate and unrelated checksum for petitioners, and the two are not interchangeable, though they have been.

The Annex keeps a standing correction in a frame by the door, in the hand of the seventeenth keeper: "The turn is not reversible. Do not attempt to recover the string from the characters." Beneath it, in a later hand, someone has written that this is a pity.