## On the Subject of Ultimate Cycles

How much security does one word need?

This module consists of a screen, eight dials with red labels, and a QWERTY keyboard.

The labels on the dials, when decrypted and read from left to right, spell out an eight letter word.

The word has been encrypted through a series of ciphers, indicated by the direction each dial is pointing, from left to right.

Once deciphered, find the word in the table below, the word written below it is the word that should be entered.

Apply the same sequence of encryptions to the response word, and type out the encrypted response word using the keys.

The word is automatically submitted when eight keys are pressed.

The red button can be pressed at any time before the eighth key is pressed to cancel the input.

Inputting any of the eight letters incorrectly will cause a strike to be issued and reset the module.

Note: Unless stated otherwise, any reference to a letter’s alphabetic position starts at A = 1. Similarly, any reference to the position of a dial starts from the leftmost dial = 1.

#### Logic component

For each dial: if the number of 45° rotations, starting from north, is odd, then the bit given by the dial is 1. Otherwise, it is 0.

Form four pairs of bits by grouping the bits corresponding to adjacent pairs of dials from left to right.
Form another four pairs of bits by grouping the bits corresponding to adjacent pairs of dials in reading order.
Each of the eight pairs of bits correspond to each of the eight dials from left to right.

Using the operator corresponding to the position of the north pointing dial, find the truth values of each pair; the encrypted letter depends on whether each is true or false.

ANDORXORNANDNORXNOR
LetterABCDEFGHIJKLMNOPQRSTUVWXYZ
Truth
Value
TrueUFZWDBVCLSHIJMNQGXKYTEOPRA
FalseNVYPWAHOQCMUGFDIRLTXBSKZJE

#### Atbash component

Each letter in the word is swapped with the letter with the same alphabetic position in the reversed alphabet.
That is, a letter with alphabetic position X will become the letter with alphabetic position 27 - X.

If the LED below the north pointing dial is lit, the Atbash cipher is applied to the input of the Logic cipher.
Otherwise, the Atbash cipher is applied to the output of the Logic cipher.

#### NE: Caesar Cipher

Each letter in the word has been shifted forwards through the alphabet by the number of 45° clockwise rotations, starting from north, to the direction its corresponding dial is pointing.

If the LED corresponding to this dial is lit, each letter is then shifted further by the position of the dial corresponding to this cipher.
Otherwise, each letter is then shifted backwards through the alphabet by the position of the dial corresponding to this cipher.

#### E: Playfair Cipher

The indexing of the lists start at zero.
• If the last dial is pointing east, use the word corresponding to the number of 45° rotations, starting from north, of the first dial.
• Otherwise, the number of 45° rotations, starting from north, of the next dial corresponds to which of the words in the lists below is the keyword for this cipher.
• If there are less than three unique* ports on the bomb, use the keyword from List A.
• Otherwise, use the keyword from List B.
• The keyword gives the first ten letters/top two rows of the keysquare.
• If the LED corresponding to this cipher is unlit, the keyword is entered into the keysquare in reading order.
• Otherwise, the keyword is entered into the keysquare in reverse reading order.
• The remaining 15 letters fill the rest of the keysquare in alphabetical order, excluding X, which is never used.
• The word is split into four pairs of letters.
• Each pair of letters is altered:
• If both letters are the same, the encrypted pair is two of the letter diametrically opposite in the keysquare.
• Otherwise, if both letters belong to the same row of the keysquare, shift both letters one space to the right along the row.
• Otherwise, if both letters belong to the same column of the keysquare, shift both letters once space down the column.
• Otherwise, the letters lie on diagonally opposite corners of a rectangle, the encrypted pair consists of the letters in the horizontally opposite corners from the original pair.
*A port is unique if there is only one of its type on the bomb.

List A: ALGORITHMS, AUTHORIZED, BLUEPRINTS, DESPICABLY, FORMIDABLE, HYPERBOLIC, IMPORTANCE, LABYRINTHS

List B: WANDERLUST, VANQUISHED, ULTRASONIC, SCRAMBLING, PRECAUTION, OSTRACIZED, METHODICAL, MAGNITUDES

Important:
• If the pair of letters is XX, the pair is unchanged by the cipher.
• If the pair of letters is either X# or #X, where # is not X, the X is changed to the other letter, forming a double letter pair, and enciphered normally.
Then, the new letter is changed back to an X.

#### SE: Pigpen Cipher

Each letter is translated using one of the two pigpen ciphers below.
Starting from north, the pigpen characters are rotated to face the direction the dial is pointing.
The rotated pigpen characters are then translated back, as though they are still facing north, to produce the encrypted letter.

If the LED corresponding to this cipher is unlit, use cipher I. Otherwise, use cipher II.

## Cipher II

#### S: Chaocipher

The indexing of the lists start at 0. For this cipher, the leftmost dial has a position of 0.
• The two lists give the keywords for two 5×5 keysquares, the keyword from List A is used for the first keysquare and the keyword from List B is used for the second:
• If the numbers in the serial number add up to more than 9, the keyword in List A is given by the position of dial and the keyword in List B is given by the number of 45° rotations, starting from north, of the previous dial.
• Otherwise, the keyword in List B is given by the position of dial and the keyword in List A is given by the number of 45° rotations, starting from north, of the previous dial.
• If the first dial is pointing south, the ‘previous’ dial is the last dial.
• These keywords are used to construct two cipher alphabets where each keyword precedes the remaining sixteen letters.
• For each letter, from left to right, consider the status of the LED below the dial in its position:
• If the status of the LED of the south dial is the same, the second cipher alphabet is shifted to the left by the number of 45° rotations from north to where the dial is pointing.
• Otherwise, the first cipher alphabet is shifted to the left by the number of 45° rotations from north to where the dial is pointing.
• Find the unencrypted letter in the first cipher alphabet.
The encrypted letter is in the same position as this letter in the second cipher alphabet.

Note: The shifted alphabets are not reset after each letter is encrypted.

List A: AFTERSHOCK, DESTROYING, DUPLICATES, FARSIGHTED, GRACIOUSLY, INFAMOUSLY, NIGHTMARES, PALINDROME

List B: DOWNSTREAM, EMORDNILAP, FLASHPOINT, INTRODUCES, PATHFINDER, QUADRICEPS, TRAPEZOIDS, WAVERINGLY

#### SW: Monoalphabetic Substitution Cipher

The position of the dial corresponds to which of the eight words in the list below is the keyword for this cipher:

DOCUMENTARILY, FLAMETHROWING, FLOWCHARTINGS, HYDROMAGNETIC, METALWORKINGS, MULTIBRANCHED, TROUBLEMAKING, UNPREDICTABLY

If the LED is unlit,the remaining thirteen letters of the alphabet are left in alphabetical order.
Otherwise, the remaining thirteen letters are positioned in reverse alphabetical order.

• If there are an even number of batteries, the keyword precedes the remaining letters to construct a cipher alphabet.
• Otherwise, the keyword follows the remaining letters to construct a cipher alphabet.

Each letter of the alphabet is mapped onto the letter of the cipher alphabet with the same alphabetic position.
The letters in the word change accordingly with these mappings.

#### W: Hill Cipher

If there are more lit than unlit indicators, the keyword for this cipher belongs to list A.
Otherwise the keyword for this cipher belongs to list B.

The keyword used depends and the rotations of the dials adjacent to the one corresponding to this cipher:

The indexing of the lists start at zero.

• If the first dial is pointing west, use the keyword corresponding to six plus the number of 45° rotations, starting from north, of the second dial.
• If the last dial is pointing west, use the keyword corresponding to six plus the number of 45° rotations, starting from north, of the seventh dial.
• Otherwise, use the keyword corresponding to the sum of the numbers of 45° rotations, starting from north, of the two dials adjacent to this one.

List A: AEON, COPY, EACH, GOOD, IOTA, KILO, MARK, ONCE, QUIT, RIOT, SYNC, UNDO, WORK, YEAR, ZEAL

List B: BOMB, BUSY, DICE, FAUX, HUSK, JUKE, LIMA, LOCI, NAME, PUSH, RISE, TASK, VOID, XYST, ZOOM

The alphabetic positions of the letters in the keyword modulo 26 form the entries of a 2×2 square keymatrix in reading order.
If the LED corresponding to this cipher is lit, the matrix is then transposed, swapping its top-right and bottom-left entries.
The word to be enciphered is broken into four pairs of letters and their alphabetic positions modulo 26 form entries in 2×1 vectors.
The vectors are multiplied by the keymatrix and taken modulo 26 to obtain the alphabetic positions of the encrypted pairs of letters.
(Because Z has an alphabetic position of 26, its corresponding entry in the encrypted vector is zero.)

#### NW: Bitshift Cipher

Find the 3 digit binary representations the numbers of rotations, starting from north, of each of the dials.

If the LED corresponding to a dial is lit, swap the 0s for 1s and the 1s for 0s in its binary representation.

Combine all of the binary representations together, from left to right.
Prepend a 0 and append a 1 to the combined binary representations to produce a 26 bit string.

Separate the alphabet into two sets, depending on whether each letter’s alphabetic position in the string of bits is a 1 or a 0.
The letters in these sets remain in alphabetical order.

If the LED corresponding to the NW dial is lit, each letter in the word is shifted to the right by the position of the NW dial.
Otherwise, each letter is shifted to the left by the position of the NW dial.

### Keyword Table

YOKOZUNACOMMANDOGLOOMINGTRICKIERGATEWAYSINCOMINGZYGOMATAFORMULAE
CIPHEREDCIRCUITSCONNECTSCONQUERSCOMMANDOCOMPILERCOMPUTERCONTINUE
DECRYPTSDECEIVEDDECIMATEDIVISIONDISCOVERDISCRETEDISPATCHDISPOSAL
NANOBOTSQUINTICSZIGZAGGYMONOMIALULTERIORKNUCKLEDUNDERWAYULTRARED
ENCIPHERENCRYPTSENCODINGENTRANCEEQUALISEEQUATORSEQUATIONEQUIPPED
FINALISEFINISHEDFINDINGSFINNICKYFORMULAEFORTUNESFORTRESSFORWARDS
DISCRETEJUNCTIONKILOWATTROTATIONPOSITRONDISPATCHENCIPHERSTANDOUT
GARRISONGARNEREDGATEPOSTGATEWAYSGAUNTLETGAMBLINGGATHEREDGLOOMING
DISCOVERJUNCTURETOGETHERGARRISONWHATNOTSDIVISIONTOGGLINGYEASAYER
INCOMINGINDICATEINDIRECTINDIGOESILLUDINGILLUSIONILLUSORYILLUMINE
JIGSAWEDJIMMYINGJOURNEYSJOUSTINGJUNCTIONJUNCTUREJUNKYARDJUDGMENT
YEARNINGTRIGONALVOLITIONDECRYPTSLABELINGSTARTINGOCTUPLESROTATORS
KILOWATTKILOVOLTKILOBYTEKINETICSKNOCKINGKNOCKOUTKNOWABLEKNUCKLED
CONQUERSEQUATIONGATEPOSTILLUSIONQUIRKISHNUMERATESTANDARDPOSTSYNC
MONOGRAMMONOLITHMONOMIALMONOTONEMULTITONMULTIPLYMULCTINGMULLIGAN

### Keyword Table cont.

NANOBOTSNANOGRAMNANOWATTNANOTUBENUMBEREDNUMEROUSNUMERALSNUMERATE
ZIPPEREDSTOCCATAVENDETTALINGEREDFINNICKYJUDGMENTHUNDREDSILLUDING
OCTANGLEOCTUPLESORDERINGORDINALSOBSERVEDOBSCUREDOBSTRUCTOBSTACLE
KNOCKINGWINGDINGUNDERLIELINEARLYTRIGGERSPROJECTSALLOTYPEYIELDERS
PROGRESSPROJECTSPROPHASEPROPHECYPOSTSYNCPOSSIBLEPOSITRONPOSITIVE
JIGSAWEDKILOVOLTALLOTTEDRELATIVEPROPHASECOMPILERLIMITINGNANOWATT
YELLOWEDMULCTINGGATHEREDWEAKENEDWHATNESSHAZINESSREVOLVEDENTRANCE
REVERSEDREVOLVEDREVEALEDROTATIONROTATORSRELATIONRELATIVERELAYING
FORTRESSWHATSITSBULLHORNGARNEREDINDIGOESLANGUAGECIRCUITSVOLTAGES