mirror of https://github.com/gchq/CyberChef.git
757 lines
28 KiB
JavaScript
757 lines
28 KiB
JavaScript
/**
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* Emulation of the Bombe machine.
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*
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* @author s2224834
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* @author The National Museum of Computing - Bombe Rebuild Project
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* @copyright Crown Copyright 2019
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* @license Apache-2.0
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*/
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import OperationError from "../errors/OperationError.mjs";
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import Utils from "../Utils.mjs";
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import {Rotor, Plugboard, a2i, i2a} from "./Enigma.mjs";
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/**
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* Convenience/optimisation subclass of Rotor
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*
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* This allows creating multiple Rotors which share backing maps, to avoid repeatedly parsing the
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* rotor spec strings and duplicating the maps in memory.
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*/
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class CopyRotor extends Rotor {
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/**
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* Return a copy of this Rotor.
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* @returns {Object}
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*/
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copy() {
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const clone = {
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map: this.map,
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revMap: this.revMap,
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pos: this.pos,
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step: this.step,
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transform: this.transform,
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revTransform: this.revTransform,
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};
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return clone;
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}
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}
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/**
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* Node in the menu graph
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*
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* A node represents a cipher/plaintext letter.
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*/
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class Node {
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/**
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* Node constructor.
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* @param {number} letter - The plain/ciphertext letter this node represents (as a number).
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*/
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constructor(letter) {
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this.letter = letter;
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this.edges = new Set();
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this.visited = false;
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}
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}
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/**
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* Edge in the menu graph
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*
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* An edge represents an Enigma machine transformation between two letters.
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*/
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class Edge {
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/**
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* Edge constructor - an Enigma machine mapping between letters
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* @param {number} pos - The rotor position, relative to the beginning of the crib, at this edge
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* @param {number} node1 - Letter at one end (as a number)
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* @param {number} node2 - Letter at the other end
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*/
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constructor(pos, node1, node2) {
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this.pos = pos;
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this.node1 = node1;
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this.node2 = node2;
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node1.edges.add(this);
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node2.edges.add(this);
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this.visited = false;
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}
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/**
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* Given the node at one end of this edge, return the other end.
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* @param node {number} - The node we have
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* @returns {number}
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*/
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getOther(node) {
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return this.node1 === node ? this.node2 : this.node1;
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}
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}
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/**
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* As all the Bombe's rotors move in step, at any given point the vast majority of the scramblers
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* in the machine share the majority of their state, which is hosted in this class.
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*/
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class SharedScrambler {
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/**
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* SharedScrambler constructor.
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* @param {Object[]} rotors - List of rotors in the shared state _only_.
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* @param {Object} reflector - The reflector in use.
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*/
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constructor(rotors, reflector) {
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this.lowerCache = new Array(26);
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this.higherCache = new Array(26);
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for (let i=0; i<26; i++) {
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this.higherCache[i] = new Array(26);
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}
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this.changeRotors(rotors, reflector);
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}
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/**
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* Replace the rotors and reflector in this SharedScrambler.
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* This takes care of flushing caches as well.
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* @param {Object[]} rotors - List of rotors in the shared state _only_.
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* @param {Object} reflector - The reflector in use.
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*/
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changeRotors(rotors, reflector) {
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this.reflector = reflector;
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this.rotors = rotors;
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this.rotorsRev = [].concat(rotors).reverse();
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this.cacheGen();
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}
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/**
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* Step the rotors forward.
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* @param {number} n - How many rotors to step. This includes the rotors which are not part of
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* the shared state, so should be 2 or more.
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*/
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step(n) {
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for (let i=0; i<n-1; i++) {
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this.rotors[i].step();
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}
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this.cacheGen();
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}
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/**
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* Optimisation: We pregenerate all routes through the machine with the top rotor removed,
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* as these rarely change. This saves a lot of lookups. This function generates this route
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* table.
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* We also just-in-time cache the full routes through the scramblers, because after stepping
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* the fast rotor some scramblers will be in states occupied by other scrambles on previous
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* iterations.
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*/
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cacheGen() {
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for (let i=0; i<26; i++) {
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this.lowerCache[i] = undefined;
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for (let j=0; j<26; j++) {
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this.higherCache[i][j] = undefined;
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}
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}
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for (let i=0; i<26; i++) {
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if (this.lowerCache[i] !== undefined) {
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continue;
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}
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let letter = i;
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for (const rotor of this.rotors) {
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letter = rotor.transform(letter);
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}
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letter = this.reflector.transform(letter);
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for (const rotor of this.rotorsRev) {
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letter = rotor.revTransform(letter);
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}
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// By symmetry
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this.lowerCache[i] = letter;
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this.lowerCache[letter] = i;
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}
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}
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/**
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* Map a letter through this (partial) scrambler.
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* @param {number} i - The letter
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* @returns {number}
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*/
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transform(i) {
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return this.lowerCache[i];
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}
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}
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/**
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* Scrambler.
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*
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* This is effectively just an Enigma machine, but it only operates on one character at a time and
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* the stepping mechanism is different.
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*/
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class Scrambler {
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/** Scrambler constructor.
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* @param {Object} base - The SharedScrambler whose state this scrambler uses
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* @param {Object} rotor - The non-shared fast rotor in this scrambler
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* @param {number} pos - Position offset from start of crib
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* @param {number} end1 - Letter in menu this scrambler is attached to
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* @param {number} end2 - Other letter in menu this scrambler is attached to
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*/
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constructor(base, rotor, pos, end1, end2) {
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this.baseScrambler = base;
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this.initialPos = pos;
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this.changeRotor(rotor);
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this.end1 = end1;
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this.end2 = end2;
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// For efficiency reasons, we pull the relevant shared cache from the baseScrambler into
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// this object - this saves us a few pointer dereferences
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this.cache = this.baseScrambler.higherCache[pos];
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}
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/**
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* Replace the rotor in this scrambler.
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* The position is reset automatically.
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* @param {Object} rotor - New rotor
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*/
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changeRotor(rotor) {
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this.rotor = rotor;
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this.rotor.pos += this.initialPos;
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}
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/**
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* Step the rotor forward.
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*
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* The base SharedScrambler needs to be instructed to step separately.
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*/
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step() {
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// The Bombe steps the slowest rotor on an actual Enigma fastest, for reasons.
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// ...but for optimisation reasons I'm going to cheat and not do that, as this vastly
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// simplifies caching the state of the majority of the scramblers. The results are the
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// same, just in a slightly different order.
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this.rotor.step();
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this.cache = this.baseScrambler.higherCache[this.rotor.pos];
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}
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/**
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* Run a letter through the scrambler.
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* @param {number} i - The letter to transform (as a number)
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* @returns {number}
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*/
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transform(i) {
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let letter = i;
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const cached = this.cache[i];
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if (cached !== undefined) {
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return cached;
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}
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letter = this.rotor.transform(letter);
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letter = this.baseScrambler.transform(letter);
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letter = this.rotor.revTransform(letter);
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this.cache[i] = letter;
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this.cache[letter] = i;
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return letter;
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}
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/**
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* Given one letter in the menu this scrambler maps to, return the other.
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* @param end {number} - The node we have
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* @returns {number}
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*/
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getOtherEnd(end) {
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return this.end1 === end ? this.end2 : this.end1;
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}
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/**
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* Read the position this scrambler is set to.
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* Note that because of Enigma's stepping, you need to set an actual Enigma to the previous
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* position in order to get it to make a certain set of electrical connections when a button
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* is pressed - this function *does* take this into account.
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* However, as with the rest of the Bombe, it does not take stepping into account - the middle
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* and slow rotors are treated as static.
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* @return {string}
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*/
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getPos() {
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let result = "";
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// Roll back the fast rotor by one step
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let pos = Utils.mod(this.rotor.pos - 1, 26);
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result += i2a(pos);
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for (let i=0; i<this.baseScrambler.rotors.length; i++) {
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pos = this.baseScrambler.rotors[i].pos;
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result += i2a(pos);
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}
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return result.split("").reverse().join("");
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}
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}
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/**
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* Bombe simulator class.
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*/
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export class BombeMachine {
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/**
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* Construct a Bombe.
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*
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* Note that there is no handling of offsets here: the crib specified must exactly match the
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* ciphertext. It will check that the crib is sane (length is vaguely sensible and there's no
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* matching characters between crib and ciphertext) but cannot check further - if it's wrong
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* your results will be wrong!
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*
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* There is also no handling of rotor stepping - if the target Enigma stepped in the middle of
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* your crib, you're out of luck. TODO: Allow specifying a step point - this is fairly easy to
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* configure on a real Bombe, but we're not clear on whether it was ever actually done for
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* real (there would almost certainly have been better ways of attacking in most situations
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* than attempting to exhaust options for the stepping point, but in some circumstances, e.g.
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* via Banburismus, the stepping point might have been known).
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*
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* @param {string[]} rotors - list of rotor spec strings (without step points!)
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* @param {Object} reflector - Reflector object
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* @param {string} ciphertext - The ciphertext to attack
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* @param {string} crib - Known plaintext for this ciphertext
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* @param {boolean} check - Whether to use the checking machine
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* @param {function} update - Function to call to send status updates (optional)
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*/
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constructor(rotors, reflector, ciphertext, crib, check, update=undefined) {
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if (ciphertext.length < crib.length) {
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throw new OperationError("Crib overruns supplied ciphertext");
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}
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if (crib.length < 2) {
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// This is the absolute bare minimum to be sane, and even then it's likely too short to
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// be useful
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throw new OperationError("Crib is too short");
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}
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if (crib.length > 25) {
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// A crib longer than this will definitely cause the middle rotor to step somewhere
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// A shorter crib is preferable to reduce this chance, of course
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throw new OperationError("Crib is too long");
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}
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for (let i=0; i<crib.length; i++) {
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if (ciphertext[i] === crib[i]) {
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throw new OperationError(`Invalid crib: character ${ciphertext[i]} at pos ${i} in both ciphertext and crib`);
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}
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}
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this.ciphertext = ciphertext;
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this.crib = crib;
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this.initRotors(rotors);
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this.check = check;
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this.updateFn = update;
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const [mostConnected, edges] = this.makeMenu();
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// This is the bundle of wires corresponding to the 26 letters within each of the 26
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// possible nodes in the menu
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this.wires = new Array(26*26);
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// These are the pseudo-Engima devices corresponding to each edge in the menu, and the
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// nodes in the menu they each connect to
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this.scramblers = new Array();
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for (let i=0; i<26; i++) {
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this.scramblers.push(new Array());
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}
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this.sharedScrambler = new SharedScrambler(this.baseRotors.slice(1), reflector);
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this.allScramblers = new Array();
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this.indicator = undefined;
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for (const edge of edges) {
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const cRotor = this.baseRotors[0].copy();
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const end1 = a2i(edge.node1.letter);
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const end2 = a2i(edge.node2.letter);
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const scrambler = new Scrambler(this.sharedScrambler, cRotor, edge.pos, end1, end2);
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if (edge.pos === 0) {
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this.indicator = scrambler;
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}
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this.scramblers[end1].push(scrambler);
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this.scramblers[end2].push(scrambler);
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this.allScramblers.push(scrambler);
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}
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// The Bombe uses a set of rotors to keep track of what settings it's testing. We cheat and
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// use one of the actual scramblers if there's one in the right position, but if not we'll
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// just create one.
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if (this.indicator === undefined) {
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this.indicator = new Scrambler(this.sharedScrambler, this.baseRotors[0].copy(), 0, undefined, undefined);
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this.allScramblers.push(this.indicator);
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}
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this.testRegister = a2i(mostConnected.letter);
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// This is an arbitrary letter other than the most connected letter
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for (const edge of mostConnected.edges) {
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this.testInput = [this.testRegister, a2i(edge.getOther(mostConnected).letter)];
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break;
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}
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}
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/**
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* Build Rotor objects from list of rotor wiring strings.
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* @param {string[]} rotors - List of rotor wiring strings
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*/
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initRotors(rotors) {
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// This is ordered from the Enigma fast rotor to the slow, so bottom to top for the Bombe
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this.baseRotors = [];
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for (const rstr of rotors) {
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const rotor = new CopyRotor(rstr, "", "A", "A");
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this.baseRotors.push(rotor);
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}
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}
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/**
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* Replace the rotors and reflector in all components of this Bombe.
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* @param {string[]} rotors - List of rotor wiring strings
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* @param {Object} reflector - Reflector object
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*/
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changeRotors(rotors, reflector) {
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// At the end of the run, the rotors are all back in the same position they started
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this.initRotors(rotors);
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this.sharedScrambler.changeRotors(this.baseRotors.slice(1), reflector);
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for (const scrambler of this.allScramblers) {
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scrambler.changeRotor(this.baseRotors[0].copy());
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}
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}
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/**
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* If we have a way of sending status messages, do so.
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* @param {...*} msg - Message to send.
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*/
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update(...msg) {
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if (this.updateFn !== undefined) {
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this.updateFn(...msg);
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}
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}
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/**
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* Recursive depth-first search on the menu graph.
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* This is used to a) isolate unconnected sub-graphs, and b) count the number of loops in each
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* of those graphs.
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* @param {Object} node - Node object to start the search from
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* @returns {[number, number, Object, number, Object[]} - loop count, node count, most connected
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* node, order of most connected node, list of edges in this sub-graph
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*/
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dfs(node) {
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let loops = 0;
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let nNodes = 1;
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let mostConnected = node;
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let nConnections = mostConnected.edges.size;
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let edges = new Set();
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node.visited = true;
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for (const edge of node.edges) {
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if (edge.visited) {
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// Already been here from the other end.
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continue;
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}
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edge.visited = true;
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edges.add(edge);
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const other = edge.getOther(node);
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if (other.visited) {
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// We have a loop, record that and continue
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loops += 1;
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continue;
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}
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// This is a newly visited node
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const [oLoops, oNNodes, oMostConnected, oNConnections, oEdges] = this.dfs(other);
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loops += oLoops;
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nNodes += oNNodes;
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edges = new Set([...edges, ...oEdges]);
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if (oNConnections > nConnections) {
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mostConnected = oMostConnected;
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nConnections = oNConnections;
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}
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}
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return [loops, nNodes, mostConnected, nConnections, edges];
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}
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/**
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* Build a menu from the ciphertext and crib.
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* A menu is just a graph where letters in either the ciphertext or crib (Enigma is symmetric,
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* so there's no difference mathematically) are nodes and states of the Enigma machine itself
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* are the edges.
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* Additionally, we want a single connected graph, and of the subgraphs available, we want the
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* one with the most loops (since these generate feedback cycles which efficiently close off
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* disallowed states).
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* Finally, we want to identify the most connected node in that graph (as it's the best choice
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* of measurement point).
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* @returns [Object, Object[]] - the most connected node, and the list of edges in the subgraph
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*/
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makeMenu() {
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// First, we make a graph of all of the mappings given by the crib
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// Make all nodes first
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const nodes = new Map();
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for (const c of this.ciphertext + this.crib) {
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if (!nodes.has(c)) {
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const node = new Node(c);
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nodes.set(c, node);
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}
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}
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// Then all edges
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for (let i=0; i<this.crib.length; i++) {
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const a = this.crib[i];
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const b = this.ciphertext[i];
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new Edge(i, nodes.get(a), nodes.get(b));
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}
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// list of [loop_count, node_count, most_connected_node, connections_on_most_connected, edges]
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const graphs = [];
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// Then, for each unconnected subgraph, we count the number of loops and nodes
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for (const start of nodes.keys()) {
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if (nodes.get(start).visited) {
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continue;
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}
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const subgraph = this.dfs(nodes.get(start));
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graphs.push(subgraph);
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}
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// Return the subgraph with the most loops (ties broken by node count)
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graphs.sort((a, b) => {
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let result = b[0] - a[0];
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if (result === 0) {
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result = b[1] - a[1];
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}
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return result;
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});
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this.nLoops = graphs[0][0];
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return [graphs[0][2], graphs[0][4]];
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}
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/**
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* Bombe electrical simulation. Energise a wire. For all connected wires (both via the diagonal
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* board and via the scramblers), energise them too, recursively.
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* @param {number} i - Bombe wire bundle
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* @param {number} j - Bombe stecker hypothesis wire within bundle
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*/
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|
energise(i, j) {
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const idx = 26*i + j;
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if (this.wires[idx]) {
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return;
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}
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this.wires[idx] = true;
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// Welchman's diagonal board: if A steckers to B, that implies B steckers to A. Handle
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// both.
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const idxPair = 26*j + i;
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this.wires[idxPair] = true;
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if (i === this.testRegister || j === this.testRegister) {
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this.energiseCount++;
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if (this.energiseCount === 26) {
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// no point continuing, bail out
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return;
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}
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}
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|
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for (let k=0; k<this.scramblers[i].length; k++) {
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const scrambler = this.scramblers[i][k];
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const out = scrambler.transform(j);
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const other = scrambler.getOtherEnd(i);
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// Lift the pre-check before the call, to save some function call overhead
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const otherIdx = 26*other + out;
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if (!this.wires[otherIdx]) {
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this.energise(other, out);
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if (this.energiseCount === 26) {
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|
return;
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|
}
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|
}
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|
}
|
|
if (i === j) {
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|
return;
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|
}
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|
for (let k=0; k<this.scramblers[j].length; k++) {
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|
const scrambler = this.scramblers[j][k];
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const out = scrambler.transform(i);
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const other = scrambler.getOtherEnd(j);
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|
const otherIdx = 26*other + out;
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if (!this.wires[otherIdx]) {
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this.energise(other, out);
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|
if (this.energiseCount === 26) {
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|
return;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Trial decryption at the current setting.
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|
* Used after we get a stop.
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|
* This applies the detected stecker pair if we have one. It does not handle the other
|
|
* steckering or stepping (which is why we limit it to 26 characters, since it's guaranteed to
|
|
* be wrong after that anyway).
|
|
* @param {string} stecker - Known stecker spec string.
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|
* @returns {string}
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|
*/
|
|
tryDecrypt(stecker) {
|
|
const fastRotor = this.indicator.rotor;
|
|
const initialPos = fastRotor.pos;
|
|
const res = [];
|
|
const plugboard = new Plugboard(stecker);
|
|
// The indicator scrambler starts in the right place for the beginning of the ciphertext.
|
|
for (let i=0; i<Math.min(26, this.ciphertext.length); i++) {
|
|
const t = this.indicator.transform(plugboard.transform(a2i(this.ciphertext[i])));
|
|
res.push(i2a(plugboard.transform(t)));
|
|
this.indicator.step(1);
|
|
}
|
|
fastRotor.pos = initialPos;
|
|
return res.join("");
|
|
}
|
|
|
|
/**
|
|
* Format a steckered pair, in sorted order to allow uniquing.
|
|
* @param {number} a - A letter
|
|
* @param {number} b - Its stecker pair
|
|
* @returns {string}
|
|
*/
|
|
formatPair(a, b) {
|
|
if (a < b) {
|
|
return `${i2a(a)}${i2a(b)}`;
|
|
}
|
|
return `${i2a(b)}${i2a(a)}`;
|
|
}
|
|
|
|
/**
|
|
* The checking machine was used to manually verify Bombe stops. Using a device which was
|
|
* effectively a non-stepping Enigma, the user would walk through each of the links in the
|
|
* menu at the rotor positions determined by the Bombe. By starting with the stecker pair the
|
|
* Bombe gives us, we find the stecker pair of each connected letter in the graph, and so on.
|
|
* If a contradiction is reached, the stop is invalid. If not, we have most (but not
|
|
* necessarily all) of the plugboard connections.
|
|
* You will notice that this procedure is exactly the same as what the Bombe itself does, only
|
|
* we start with an assumed good hypothesis and read out the stecker pair for every letter.
|
|
* On the real hardware that wasn't practical, but fortunately we're not the real hardware, so
|
|
* we don't need to implement the manual checking machine procedure.
|
|
* @param {number} pair - The stecker pair of the test register.
|
|
* @returns {string} - The empty string for invalid stops, or a plugboard configuration string
|
|
* containing all known pairs.
|
|
*/
|
|
checkingMachine(pair) {
|
|
if (pair !== this.testInput[1]) {
|
|
// We have a new hypothesis for this stop - apply the new one.
|
|
// De-energise the board
|
|
for (let i=0; i<this.wires.length; i++) {
|
|
this.wires[i] = false;
|
|
}
|
|
this.energiseCount = 0;
|
|
// Re-energise with the corrected hypothesis
|
|
this.energise(this.testRegister, pair);
|
|
}
|
|
|
|
const results = new Set();
|
|
results.add(this.formatPair(this.testRegister, pair));
|
|
for (let i=0; i<26; i++) {
|
|
let count = 0;
|
|
let other;
|
|
for (let j=0; j<26; j++) {
|
|
if (this.wires[i*26 + j]) {
|
|
count++;
|
|
other = j;
|
|
}
|
|
}
|
|
if (count > 1) {
|
|
// This is an invalid stop.
|
|
return "";
|
|
} else if (count === 0) {
|
|
// No information about steckering from this wire
|
|
continue;
|
|
}
|
|
results.add(this.formatPair(i, other));
|
|
}
|
|
return [...results].join(" ");
|
|
}
|
|
|
|
/**
|
|
* Check to see if the Bombe has stopped. If so, process the stop.
|
|
* @returns {(undefined|string[3])} - Undefined for no stop, or [rotor settings, plugboard settings, decryption preview]
|
|
*/
|
|
checkStop() {
|
|
// Count the energised outputs
|
|
const count = this.energiseCount;
|
|
if (count === 26) {
|
|
return undefined;
|
|
}
|
|
// If it's not all of them, we have a stop
|
|
let steckerPair;
|
|
// The Bombe tells us one stecker pair as well. The input wire and test register we
|
|
// started with are hypothesised to be a stecker pair.
|
|
if (count === 25) {
|
|
// Our steckering hypothesis is wrong. Correct value is the un-energised wire.
|
|
for (let j=0; j<26; j++) {
|
|
if (!this.wires[26*this.testRegister + j]) {
|
|
steckerPair = j;
|
|
break;
|
|
}
|
|
}
|
|
} else if (count === 1) {
|
|
// This means our hypothesis for the steckering is correct.
|
|
steckerPair = this.testInput[1];
|
|
} else {
|
|
// This was known as a "boxing stop" - we have a stop but not a single hypothesis.
|
|
// If this happens a lot it implies the menu isn't good enough.
|
|
// If we have the checking machine enabled, we're going to just check each wire in
|
|
// turn. If we get 0 or 1 hit, great.
|
|
// If we get multiple hits, or the checking machine is off, the user will just have to
|
|
// deal with it.
|
|
if (!this.check) {
|
|
// We can't draw any conclusions about the steckering (one could maybe suggest
|
|
// options in some cases, but too hard to present clearly).
|
|
return [this.indicator.getPos(), "??", this.tryDecrypt("")];
|
|
}
|
|
let stecker = undefined;
|
|
for (let i = 0; i < 26; i++) {
|
|
const newStecker = this.checkingMachine(i);
|
|
if (newStecker !== "") {
|
|
if (stecker !== undefined) {
|
|
// Multiple hypotheses can't be ruled out.
|
|
return [this.indicator.getPos(), "??", this.tryDecrypt("")];
|
|
}
|
|
stecker = newStecker;
|
|
}
|
|
}
|
|
if (stecker === undefined) {
|
|
// Checking machine ruled all possibilities out.
|
|
return undefined;
|
|
}
|
|
// If we got here, there was just one possibility allowed by the checking machine. Success.
|
|
return [this.indicator.getPos(), stecker, this.tryDecrypt(stecker)];
|
|
}
|
|
let stecker;
|
|
if (this.check) {
|
|
stecker = this.checkingMachine(steckerPair);
|
|
if (stecker === "") {
|
|
// Invalid stop - don't count it, don't return it
|
|
return undefined;
|
|
}
|
|
} else {
|
|
stecker = `${i2a(this.testRegister)}${i2a(steckerPair)}`;
|
|
}
|
|
const testDecrypt = this.tryDecrypt(stecker);
|
|
return [this.indicator.getPos(), stecker, testDecrypt];
|
|
}
|
|
|
|
/**
|
|
* Having set up the Bombe, do the actual attack run. This tries every possible rotor setting
|
|
* and attempts to logically invalidate them. If it can't, it's added to the list of candidate
|
|
* solutions.
|
|
* @returns {string[][3]} - list of 3-tuples of candidate rotor setting, plugboard settings, and decryption preview
|
|
*/
|
|
run() {
|
|
let stops = 0;
|
|
const result = [];
|
|
// For each possible rotor setting
|
|
const nChecks = Math.pow(26, this.baseRotors.length);
|
|
for (let i=1; i<=nChecks; i++) {
|
|
// Benchmarking suggests this is faster than using .fill()
|
|
for (let i=0; i<this.wires.length; i++) {
|
|
this.wires[i] = false;
|
|
}
|
|
this.energiseCount = 0;
|
|
// Energise the test input, follow the current through each scrambler
|
|
// (and the diagonal board)
|
|
this.energise(...this.testInput);
|
|
|
|
const stop = this.checkStop();
|
|
if (stop !== undefined) {
|
|
stops++;
|
|
result.push(stop);
|
|
}
|
|
// Step all the scramblers
|
|
// This loop counts how many rotors have reached their starting position (meaning the
|
|
// next one needs to step as well)
|
|
let n = 1;
|
|
for (let j=1; j<this.baseRotors.length; j++) {
|
|
if ((i % Math.pow(26, j)) === 0) {
|
|
n++;
|
|
} else {
|
|
break;
|
|
}
|
|
}
|
|
if (n > 1) {
|
|
this.sharedScrambler.step(n);
|
|
}
|
|
for (const scrambler of this.allScramblers) {
|
|
scrambler.step();
|
|
}
|
|
// Send status messages at what seems to be a reasonably sensible frequency
|
|
// (note this won't be triggered on 3-rotor runs - they run fast enough it doesn't seem necessary)
|
|
if (n > 3) {
|
|
this.update(this.nLoops, stops, i/nChecks);
|
|
}
|
|
}
|
|
return result;
|
|
}
|
|
}
|