43:null 44:["$","title",null,{"children":"BB84: Quantum Key Distribution | jmfbo | Observable"}] 4a:T159b,(() => { if(!document.getElementById('serif-fonts')){ const l=document.createElement('link'); l.id='serif-fonts'; l.rel='stylesheet'; l.href='https://fonts.googleapis.com/css2?family=Fraunces:opsz,wght@9..144,400;9..144,500;9..144,600&display=swap'; document.head.append(l); } const SERIF="'Fraunces', serif", SANS="-apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif"; const INK='#1a1714', PAPER='#faf8f3', MUTED='#8a8378', LIGHT='#e5e7eb', CORAL='#FB6247', TEAL='#52BEAC', GOLD='#ac9356', ICE='#6ad4ff'; const container = document.createElement('div'); container.style.cssText = 'font:13px/1.5 ' + SANS + '; max-width:880px;'; const ctrl = document.createElement('div'); ctrl.style.cssText = 'margin:8px 0;display:flex;gap:10px;align-items:center;'; const eveLab = document.createElement('label'); eveLab.style.cssText = 'display:flex;gap:5px;align-items:center;cursor:pointer;'; const eveCb = document.createElement('input'); eveCb.type = 'checkbox'; eveLab.append(eveCb, document.createTextNode('Eve eavesdrops')); const runBtn = document.createElement('button'); runBtn.textContent = 'Run'; runBtn.style.cssText = 'padding:6px 14px;cursor:pointer;background:none;border:1px solid #c9bfa8;color:' + INK + ';font-family:' + SANS + ';'; ctrl.append(eveLab, runBtn); container.append(ctrl); const readout = document.createElement('div'); readout.style.cssText = 'font-family:' + SERIF + ';font-size:14px;color:' + INK + ';min-height:20px;margin:2px 0 6px;'; container.append(readout); const svg = d3.create('svg').attr('viewBox', [0, 0, 880, 360]).style('width', '100%').style('max-width', '880px').style('height', 'auto').style('font-family', SANS); svg.append('rect').attr('width', 880).attr('height', 360).attr('fill', PAPER); container.append(svg.node()); const N = 16; const X0 = 62, STEP = 52; let ab = [], aa = [], bb = [], bm = []; function rnd(){ return Math.random() < 0.5 ? 0 : 1; } function run(){ aa = Array.from({length:N}, rnd); ab = Array.from({length:N}, rnd); bb = Array.from({length:N}, rnd); bm = []; for(let i=0;i 0.1; readout.innerHTML = 'Matched bases ' + siftedTotal + '/' + N + ' · error rate ' + Math.round(rate*100) + '% — ' + (eveDetected ? 'Eve is present — abort.' : 'No eavesdropper — key secure.'); } runBtn.addEventListener('click', run); eveCb.addEventListener('change', run); run(); return container; })()4b:Tfce,(() => { if(!document.getElementById('serif-fonts')){ const l=document.createElement('link'); l.id='serif-fonts'; l.rel='stylesheet'; l.href='https://fonts.googleapis.com/css2?family=Fraunces:opsz,wght@9..144,400;9..144,500;9..144,600&display=swap'; document.head.append(l); } const SERIF="'Fraunces', serif", SANS="-apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif"; const INK='#1a1714', PAPER='#faf8f3', MUTED='#8a8378', LIGHT='#e5e7eb', CORAL='#FB6247', TEAL='#52BEAC', GOLD='#ac9356', ICE='#6ad4ff'; const container = document.createElement('div'); container.style.cssText = 'font:13px/1.5 ' + SANS + '; max-width:760px;'; const ctrl = document.createElement('div'); ctrl.style.cssText = 'margin:8px 0;display:flex;gap:10px;align-items:center;font-size:12px;'; const lab = document.createElement('span'); lab.textContent = 'skew the basis'; lab.style.cssText = 'color:' + MUTED + ';'; const slider = document.createElement('input'); slider.type = 'range'; slider.min = 0; slider.max = 1; slider.value = 0.15; slider.step = 0.01; slider.style.cssText = 'flex:1;max-width:280px;'; ctrl.append(lab, slider); container.append(ctrl); const readout = document.createElement('div'); readout.style.cssText = 'font-family:' + SERIF + ';font-size:14px;color:' + INK + ';min-height:20px;margin:2px 0 6px;'; container.append(readout); const W = 720, H = 560, CX = 360, CY = 280; const svg = d3.create('svg').attr('viewBox', [0, 0, W, H]).style('width', '100%').style('max-width', '760px').style('height', 'auto'); svg.append('rect').attr('width', W).attr('height', H).attr('fill', PAPER); container.append(svg.node()); let target = [CX - 40, CY - 30]; function basis(){ const t = 0.15 + (+slider.value) * 1.35; const v1 = [1, 0], v2 = [Math.cos(t), Math.sin(t)]; return { v1, v2 }; } function render(){ const { v1, v2 } = basis(); const s = 30; const pts = []; const R = 12; for(let m=-R; m<=R; m++) for(let n=-R; n<=R; n++){ pts.push({ m, n, x: CX + s*(m*v1[0] + n*v2[0]), y: CY + s*(m*v1[1] + n*v2[1]) }); } svg.selectAll('g.lat').remove(); const g = svg.append('g').attr('class', 'lat'); const delaunay = d3.Delaunay.from(pts.map(p => [p.x, p.y])); const vor = delaunay.voronoi([0, 0, W, H]); g.append('g').selectAll('path').data([...vor.cellPolygons()]).join('path') .attr('d', d => 'M' + d.map(p => p[0] + ' ' + p[1]).join('L') + 'Z') .attr('fill', 'none').attr('stroke', LIGHT).attr('stroke-width', 0.7); g.selectAll('circle').data(pts).join('circle') .attr('cx', d => d.x).attr('cy', d => d.y).attr('r', 1.6).attr('fill', MUTED); g.append('line').attr('x1', CX).attr('y1', CY).attr('x2', CX + s*v1[0]).attr('y2', CY + s*v1[1]).attr('stroke', TEAL).attr('stroke-width', 2.5); g.append('line').attr('x1', CX).attr('y1', CY).attr('x2', CX + s*v2[0]).attr('y2', CY + s*v2[1]).attr('stroke', GOLD).attr('stroke-width', 2.5); let best = null, bd = Infinity; for(const p of pts){ const d = (p.x - target[0])**2 + (p.y - target[1])**2; if(d < bd){ bd = d; best = p; } } g.append('line').attr('x1', target[0]).attr('y1', target[1]).attr('x2', best.x).attr('y2', best.y).attr('stroke', CORAL).attr('stroke-width', 2).attr('stroke-dasharray', '4 3'); g.append('circle').attr('cx', best.x).attr('cy', best.y).attr('r', 5).attr('fill', 'none').attr('stroke', CORAL).attr('stroke-width', 2.5); g.append('circle').attr('cx', target[0]).attr('cy', target[1]).attr('r', 6).attr('fill', CORAL).style('cursor', 'grab'); svg.call(d3.drag().on('drag', (event) => { target = [event.x, event.y]; render(); })); const skew = +slider.value; readout.innerHTML = skew < 0.35 ? 'Basis nearly square — the nearest point is obvious, the problem is easy.' : 'Basis skewed — the fundamental cell is a sliver, the nearest point is hard to find.'; } slider.addEventListener('input', render); render(); return container; })()4c:[] 48:{"id":"9bc4d304908835b8","slug":"bb-84-quantum-key-distribution","title":"BB84: Quantum Key Distribution","thumbnail":"973b30d54ffebb7c87e5ccc2cbfbacd8f13750ed5a6c21bb3cb7ee3628d466e5","access_level":"public","create_time":"$D2026-10-20T13:38:27.988Z","update_time":"$D2026-10-20T21:52:17.734Z","view_time":null,"first_public_time":"$D2026-10-20T21:07:47.490Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"13e9f68b1ec1653b","login":"ssp2","name":"jmfbo","avatar_url":"https://avatars-next.observableusercontent.com/86da5640a4a538e054fc577d613a9d57f0da60f5d4a14a3da6b4e0fb3e5a5800","tier":"free_2026","bio":"founder and principal engineer at sindio.net","following":false},"version":36,"publish_version":36,"role":null,"authored":false,"authors":[{"type":"individual","id":"f18d27787b7a1d20","login":"ssp2","name":"jmfbo","avatar_url":"https://avatars-next.observableusercontent.com/86da5640a4a538e054fc577d613a9d57f0da60f5d4a14a3da6b4e0fb3e5a5800","tier":null,"bio":"founder and principal engineer at sindio.net","following":false}],"members":[{"type":"team","id":"13e9f68b1ec1653b","login":"ssp2","name":"jmfbo","avatar_url":"https://avatars-next.observableusercontent.com/86da5640a4a538e054fc577d613a9d57f0da60f5d4a14a3da6b4e0fb3e5a5800","tier":"free_2026","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"BB84: Quantum Key Distribution","cells":[{"id":1,"value":"# BB84: Quantum Key Distribution","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":3,"value":"BB84 is a method/protocol in Quantum Key Distribution that involves random bits being encoded, by one participant, in bases randomly chosen by that participant, and being sent to another participant. The receiving participant measures them in bases randomly chosen by the latter, and only the positions where both participants chose the same basis are retained to become the shared key. Any interception (like eavesdropping) disturbs the states and surfaces as an error rate. This contributes toward interception (eavesdropping) being detected, as opposed to it just being prevented.\n\n\nBelow, Alice encodes random bits in random bases, and sends them to Bob. Then Bob measures in his own random bases. Where their bases match, they retain the corresponding bit. All the bits retained become the shared key. Eavesdrop, and the error rate betrays you.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2,"value":"$4a","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"# The Lattice Problem: Post Quantum Cryptography","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":8,"value":"Among cryptography that is tough for quantum computers is the lattice problem with skewed basis. In fact, the lattice problem with skewed basis, is what post quantum cryptography rests on. The gist thereof, in a nutshell, is: Given a point, which lattice point is nearest? The response is simple when the basis is square, and extremely brutal when the basis is skewed.\n\nThe grey dots are the lattice points, the light grey lines are voronoi cells (each point's \"territory\"). The teal line is basis vector v1, and gold line is basis vector v2. The red dot is the target (drag it), and the red dashed line/ring is its nearest lattice point.\n\nIf, below, you drag the slider, you skew the basis, and the fundamental cells stretch.\n\n\nDrag the red dot and the red line snaps to the nearest point. You notice that it finds it simple to offer a response when the basis is square/nearly square, and finds it extremely brutal to offer a response when basis is skewed.\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"$4b","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W4c","stdlib":"2"}} 49:"$48:body"