Talk:HX-63

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Rotor wires, two selectable paths ?

"Moreover, each rotor wire could be selected from one of two paths."

This does not correspond to reality, but was often assumed in the past. The twelve 41-contact-rotors of the machine, nine of which were selected and then installed in a chosen sequence (12!/3! = 79,833,600 alternatives), have ONE fixed internal wiring each (41!). It was not possible to switch between several internal wirings. However, all rotors and the input roller could be opened and then rewired, but this was difficult to do and probably NEVER happened (Basic Key).

The popular error ("two paths") occurred either because 15 outputs of the rotor bank with 41 contacts were fed back to the input (re-entry), or because the machine had a real switchover between encryption and decryption: in the first case the signals ran the rotor bank in one direction, in the second case in the opposite direction (non-involutory function!). Both the 26 inputs and the 15 re-entries could be permuted by two "plugboards", more accurate "thumbwheel controlled matrices" (26! and 15!, "Input-" and "Re-entry Modifiers") realised with knurled dials or rotary switches on the back of the machine. A third additional plugboard there (9!, "Rotor Drive Unit Stepping Modifiers") allowed the permuted irregular advancement of the rotors : each rotor could carry an active pin in up to 41 positions. These were read by microswitches and acted like the notches on the rotorrings of the Enigma-rotors, but in a different manner. The plugboard made it possible to select which rotor position advanced another rotor position. However, at least one of the nine rotors MUST always advance with each cipher step.

Three device models were offered: one with an input and re-enty modifier (41 rotary adjusters in parallel behind the nine rotors INSIDE THE DEVICE), another with a detachable modifier unit on the back of the device, including a modifier for the rotor motion, and a third with a hard-wired modifier dummy on the back. The second model had the highest cryptographic complexity, the first model was cryptographically weaker due to the lack of adjustability of the rotor advance (except for rotor selection, rotor sequence and pin patterns on the rotors), and the third model was the cryptographically weakest.

The 3-modifiers-unit could be completely removed from the back of the machine. If a second such unit was available, the plugboards for the next internal key used could be set in advance and exchanged for the previously used "3-modifiers-unit" if necessary.

The internal key includes the permutations of the three plug boards (26! * 15! * 9!), the selection and installation sequence of the nine key rotors (79,833,600), as well as the number of legal possible variations of activated pins on the nine rotors (2^369) and one of two available rotor motion alternatives (M or MM). The external key or message key, which must be selected and set anew for each new cipher, only affects the start position setting of the nine rotors (41^9, the same size as the period length, see below).

The more pins on the rotors, the more irregular the progression. As 41 is a prime number, the maximum period length of 41^9 = 327,381,934,393,961 is retained for every pin number from 1 to 40, with odometric rotormovement There was no "double stepping anomaly" with the HX63 as with Enigma and Typex, which could have shortened the period length. The rotors were moved individuelly by electromagnetical stepping motors. The movement or the HX63 rotors however was not odometric, but more irregular. Details are actually not known.

The separation of the two "plug boards" (realized with rotary dials) for the 26 characters and 15 re-entries is completely superfluous, and gives away 36 bits of key space (41! = 3,35*10^49, (26! * 15!) = 5,27*10^38). However, 41 rotary dials with 41 positions each were possibly perceived as too complex and expensive, and therefore were not used after all.

There were no ring positions on the HX63, invented by Willi Korn, chief engineer at ChiMaAG or H&R (Enigma), i.e. the pin pattern could not be adjusted cyclically relative to the internal rotor wiring. As a result, the machine gave away a further factor of 41^8 = 7,984,925,229,121, i.e. about 43 bits, at least with the specified pin arrangement. Each rotor selection and sequence as well as pin arrangement thus provided only a single key period instead of 41^8 different ones. Instead of simply turning a rotor ring, 41 pins always had to be reset for each rotor. Permissiveactionlink (talk) 14:36, 28 July 2025 (UTC)[reply]