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Add Bombe operation

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Still needs some work, but functional
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s2224834 2019-01-04 13:33:31 +00:00
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/**
* Emulation of the Bombe machine.
*
* @author s2224834
* @copyright Crown Copyright 2019
* @license Apache-2.0
*/
import OperationError from "../errors/OperationError";
import Utils from "../Utils";
import {Rotor, a2i, i2a} from "./Enigma";
/**
* Convenience/optimisation subclass of Rotor
*
* This allows creating multiple Rotors which share backing maps, to avoid repeatedly parsing the
* rotor spec strings and duplicating the maps in memory.
*/
class CopyRotor extends Rotor {
/**
* Return a copy of this Rotor.
*/
copy() {
const clone = {
map: this.map,
revMap: this.revMap,
pos: this.pos,
step: this.step,
transform: this.transform,
revTransform: this.revTransform,
};
return clone;
}
}
/**
* Node in the menu graph
*
* A node represents a cipher/plaintext letter.
*/
class Node {
/**
* Node constructor.
* @param {number} letter - The plain/ciphertext letter this node represents (as a number).
*/
constructor(letter) {
this.letter = letter;
this.edges = new Set();
this.visited = false;
}
}
/**
* Edge in the menu graph
*
* An edge represents an Enigma machine transformation between two letters.
*/
class Edge {
/**
* Edge constructor - an Enigma machine mapping between letters
* @param {number} pos - The rotor position, relative to the beginning of the crib, at this edge
* @param {number} node1 - Letter at one end (as a number)
* @param {number} node2 - Letter at the other end
*/
constructor(pos, node1, node2) {
this.pos = pos;
this.node1 = node1;
this.node2 = node2;
node1.edges.add(this);
node2.edges.add(this);
this.visited = false;
}
/**
* Given the node at one end of this edge, return the other end.
* @param node {number} - The node we have
* @returns {number}
*/
getOther(node) {
if (this.node1 === node) {
return this.node2;
}
return this.node1;
}
}
/**
* Scrambler.
*
* This is effectively just an Enigma machine, but it only operates on one character at a time and
* the stepping mechanism is different.
*/
class Scrambler {
/** Scrambler constructor.
* @param {Object[]} rotors - List of rotors in this scrambler
* @param {Object} reflector - This scrambler's reflector
* @param {number} pos - Position offset from start of crib
* @param {number} end1 - Letter in menu this scrambler is attached to
* @param {number} end2 - Other letter in menu this scrambler is attached to
*/
constructor(rotors, reflector, pos, end1, end2) {
this.reflector = reflector;
this.rotors = rotors;
this.rotorsRev = [].concat(rotors).reverse();
this.initialPos = pos;
this.rotors[0].pos += pos;
this.end1 = end1;
this.end2 = end2;
}
/**
* Step the rotors forward.
*
* All nodes in the Bombe step in sync.
* @param {number} n - How many rotors to step
*/
step(n) {
// The Bombe steps the slowest rotor on an actual Enigma first.
for (let i=this.rotors.length - 1; i>=this.rotors.length-n; i--) {
this.rotors[i].step();
}
}
/**
* Run a letter through the scrambler.
* @param {number} i - The letter to transform (as a number)
* @returns {number}
*/
transform(i) {
let letter = i;
for (const rotor of this.rotors) {
letter = rotor.transform(letter);
}
letter = this.reflector.transform(letter);
for (const rotor of this.rotorsRev) {
letter = rotor.revTransform(letter);
}
return letter;
}
/**
* Given one letter in the menu this scrambler maps to, return the other.
* @param end {number} - The node we have
* @returns {number}
*/
getOtherEnd(end) {
if (this.end1 === end) {
return this.end2;
}
return this.end1;
}
/**
* Read the position this scrambler is set to.
* Note that because of Enigma's stepping, you need to set an actual Enigma to the previous
* position in order to get it to make a certain set of electrical connections when a button
* is pressed - this function *does* take this into account.
* However, as with the rest of the Bombe, it does not take stepping into account - the middle
* and slow rotors are treated as static.
* @return {string}
*/
getPos() {
let result = "";
for (let i=0; i<this.rotors.length; i++) {
let pos = this.rotors[i].pos;
// Enigma steps *before* encrypting each character. This means we need to roll the fast
// rotor back by one before outputting it, to ensure the position is correct for the
// first character.
// As usual with the Bombe we do not take stepping of other rotors into account!
if (i === 0) {
pos = Utils.mod(pos - 1, 26);
}
result += i2a(pos);
}
return result.split("").reverse().join("");
}
}
/**
* Bombe simulator class.
*/
export class BombeMachine {
/**
* Construct a Bombe.
*
* Note that there is no handling of offsets here: the crib specified must exactly match the
* ciphertext. It will check that the crib is sane (length is vaguely sensible and there's no
* matching characters between crib and ciphertext) but cannot check further - if it's wrong
* your results will be wrong!
* @param {string[]} rotors - list of rotor spec strings (without step points!)
* @param {Object} reflector - Reflector object
* @param {string} ciphertext - The ciphertext to attack
* @param {string} crib - Known plaintext for this ciphertext
* @param {function} update - Function to call to send status updates (optional)
*/
constructor(rotors, reflector, ciphertext, crib, update=undefined) {
if (ciphertext.length !== crib.length) {
throw new OperationError("Ciphertext and crib length differ");
}
if (crib.length < 2) {
// This is the absolute bare minimum to be sane, and even then it's likely too short to
// be useful
throw new OperationError("Crib is too short");
}
if (crib.length > 25) {
// A crib longer than this will definitely cause the middle rotor to step somewhere
// A shorter crib is preferable to reduce this chance, of course
throw new OperationError("Crib is too long");
}
for (let i=0; i<ciphertext.length; i++) {
if (ciphertext[i] === crib[i]) {
throw new OperationError(`Invalid crib: character ${ciphertext[i]} at pos ${i} in both ciphertext and crib`);
}
}
this.ciphertext = ciphertext;
this.crib = crib;
// This is ordered from the Enigma fast rotor to the slow, so bottom to top for the Bombe
this.baseRotors = [];
for (const rstr of rotors) {
const rotor = new CopyRotor(rstr, "", "A", "A");
this.baseRotors.push(rotor);
}
this.updateFn = update;
const [mostConnected, edges] = this.makeMenu();
// This is the bundle of wires corresponding to the 26 letters within each of the 26
// possible nodes in the menu
this.wires = new Array(26*26).fill(false);
// These are the pseudo-Engima devices corresponding to each edge in the menu, and the
// nodes in the menu they each connect to
this.scramblers = new Array();
for (let i=0; i<26; i++) {
this.scramblers.push(new Array());
}
this.allScramblers = new Array();
this.indicator = undefined;
for (const edge of edges) {
const cRotors = [];
for (const r of this.baseRotors) {
cRotors.push(r.copy());
}
const end1 = a2i(edge.node1.letter);
const end2 = a2i(edge.node2.letter);
const scrambler = new Scrambler(cRotors, reflector, edge.pos, end1, end2);
if (edge.pos === 0) {
this.indicator = scrambler;
}
this.scramblers[end1].push(scrambler);
this.scramblers[end2].push(scrambler);
this.allScramblers.push(scrambler);
}
// The Bombe uses a set of rotors to keep track of what settings it's testing. We cheat and
// use one of the actual scramblers if there's one in the right position, but if not we'll
// just create one.
if (this.indicator === undefined) {
this.indicator = new Scrambler(this.baseRotors, reflector, 0, undefined);
this.allScramblers.push(this.indicator);
}
this.testRegister = a2i(mostConnected.letter);
// This is an arbitrary letter other than the most connected letter
for (const edge of mostConnected.edges) {
this.testInput = [this.testRegister, a2i(edge.getOther(mostConnected).letter)];
break;
}
}
/**
* If we have a way of sending status messages, do so.
* @param {string} msg - Message to send.
*/
update(msg) {
if (this.updateFn !== undefined) {
this.updateFn(msg);
}
}
/**
* Recursive depth-first search on the menu graph.
* This is used to a) isolate unconnected sub-graphs, and b) count the number of loops in each
* of those graphs.
* @param {Object} node - Node object to start the search from
* @returns {[number, number, Object, number, Object[]} - loop count, node count, most connected
* node, order of most connected node, list of edges in this sub-graph
*/
dfs(node) {
let loops = 0;
let nNodes = 1;
let mostConnected = node;
let nConnections = mostConnected.edges.size;
let edges = new Set();
node.visited = true;
for (const edge of node.edges) {
if (edge.visited) {
// Already been here from the other end.
continue;
}
edge.visited = true;
edges.add(edge);
const other = edge.getOther(node);
if (other.visited) {
// We have a loop, record that and continue
loops += 1;
continue;
}
// This is a newly visited node
const [oLoops, oNNodes, oMostConnected, oNConnections, oEdges] = this.dfs(other);
loops += oLoops;
nNodes += oNNodes;
edges = new Set([...edges, ...oEdges]);
if (oNConnections > nConnections) {
mostConnected = oMostConnected;
nConnections = oNConnections;
}
}
return [loops, nNodes, mostConnected, nConnections, edges];
}
/**
* Build a menu from the ciphertext and crib.
* A menu is just a graph where letters in either the ciphertext or crib (Enigma is symmetric,
* so there's no difference mathematically) are nodes and states of the Enigma machine itself
* are the edges.
* Additionally, we want a single connected graph, and of the subgraphs available, we want the
* one with the most loops (since these generate feedback cycles which efficiently close off
* disallowed states).
* Finally, we want to identify the most connected node in that graph (as it's the best choice
* of measurement point).
* @returns [Object, Object[]] - the most connected node, and the list of edges in the subgraph
*/
makeMenu() {
// First, we make a graph of all of the mappings given by the crib
// Make all nodes first
const nodes = new Map();
for (const c of this.ciphertext + this.crib) {
if (!nodes.has(c)) {
const node = new Node(c);
nodes.set(c, node);
}
}
// Then all edges
for (let i=0; i<this.crib.length; i++) {
const a = this.crib[i];
const b = this.ciphertext[i];
new Edge(i, nodes.get(a), nodes.get(b));
}
// list of [loop_count, node_count, most_connected_node, connections_on_most_connected, edges]
const graphs = [];
// Then, for each unconnected subgraph, we count the number of loops and nodes
for (const start of nodes.keys()) {
if (nodes.get(start).visited) {
continue;
}
const subgraph = this.dfs(nodes.get(start));
graphs.push(subgraph);
}
// Return the subgraph with the most loops (ties broken by node count)
graphs.sort((a, b) => {
let result = b[0] - a[0];
if (result === 0) {
result = b[1] - a[1];
}
return result;
});
this.nLoops = graphs[0][0];
return [graphs[0][2], graphs[0][4]];
}
/**
* Implement Welchman's diagonal board: If A steckers to B, that implies B steckers to A, and
* so forth. This function just gets the paired wire.
* @param {number[2]} i - Bombe state wire
* @returns {number[2]}
*/
getDiagonal(i) {
return [i[1], i[0]];
}
/**
* Bombe electrical simulation. Energise a wire. For all connected wires (both via the diagonal
* board and via the scramblers), energise them too, recursively.
* @param {number[2]} i - Bombe state wire
*/
energise(i) {
const idx = 26*i[0] + i[1];
if (this.wires[idx]) {
return;
}
this.energiseCount ++;
this.wires[idx] = true;
this.energise(this.getDiagonal(i));
for (const scrambler of this.scramblers[i[0]]) {
const out = scrambler.transform(i[1]);
const other = scrambler.getOtherEnd(i[0]);
this.energise([other, out]);
}
}
/**
* 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[][2]} - list of pairs of candidate rotor setting, and calculated stecker pair
*/
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++) {
this.wires.fill(false);
// Energise the test input, follow the current through each scrambler
// (and the diagonal board)
this.energiseCount = 0;
this.energise(this.testInput);
// Count the energised outputs
let count = 0;
for (let j=26*this.testRegister; j<26*(1+this.testRegister); j++) {
if (this.wires[j]) {
count++;
}
}
// If it's not all of them, we have a stop
if (count < 26) {
stops += 1;
let stecker;
// 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]) {
stecker = `${i2a(this.testRegister)} <-> ${i2a(j)}`;
break;
}
}
} else if (count === 1) {
// This means our hypothesis for the steckering is correct.
stecker = `${i2a(this.testRegister)} <-> ${i2a(this.testInput[1])}`;
} else {
// Unusual, probably indicative of a poor menu. I'm a little unclear on how
// this was really handled, but we'll return it for the moment.
stecker = `? (wire count: ${count})`;
}
result.push([this.indicator.getPos(), stecker]);
}
// 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;
}
}
for (const scrambler of this.allScramblers) {
scrambler.step(n);
}
// Send status messages at what seems to be a reasonably sensible frequency
if (n > 2) {
const msg = `Bombe run with ${this.nLoops} loops in menu (2+ desirable): ${stops} stops, ${Math.floor(100 * i / nChecks)}% done`;
this.update(msg);
}
}
return result;
}
}