Math Fingerprinting

Math fingerprinting exploits tiny precision differences in how JavaScript engines compute transcendental mathematical functions. These differences come from the CPU architecture, not the browser.

How it works

Neoprint computes 22 mathematical operations and stores the full-precision results:

const data = {
  acos: Math.acos(0.123456789),
  acosh: Math.acosh(1e10),
  asin: Math.asin(0.123456789),
  asinh: Math.asinh(1),
  atan: Math.atan(2),
  atanh: Math.atanh(0.5),
  atan2: Math.atan2(0.04, -0.04),
  cbrt: Math.cbrt(100),
  cos: Math.cos(21 * Math.LN2),
  cosh: Math.cosh(1),
  exp: Math.exp(1),
  expm1: Math.expm1(1),
  log: Math.log(10),
  log1p: Math.log1p(10),
  log2: Math.log2(7),
  log10: Math.log10(7),
  sin: Math.sin(1e300),
  sinh: Math.sinh(1),
  sqrt: Math.sqrt(2),
  tan: Math.tan(-1e300),
  tanh: Math.tanh(1),
  pow: Math.pow(Math.PI, -100),
}

Why results differ across devices

IEEE 754 floating-point standard allows implementations to differ in the last 1-2 bits of precision for transcendental functions. Different JS engines (V8, JavaScriptCore, SpiderMonkey) and CPU architectures (x86, ARM) produce slightly different results.

Example: Math.atan(2) might return:

• 1.1071487177940904 on Chrome/V8 (x86)
• 1.1071487177940906 on Safari/JSC (ARM)

Entropy and stability

Property	Value
Entropy	~6 bits
Stability	0.95
Typical duration	<1ms

Math is the most stable collector alongside WebGL. Values only change when the user switches CPU architecture or JS engine version.

Cross-browser normalization

For crossBrowserId, math values are rounded to 8 significant digits to absorb V8 vs JavaScriptCore last-digit differences while preserving architecture-level differences (x86 vs ARM).

Web Worker offloading

Math runs in a Web Worker by default since it requires no DOM access.

Usage

const fp = await neoprint.get({ collectors: ['math'] })
const math = fp.components.math.value

console.log(math.sin)  // 1e300 produces different results per platform
console.log(math.tan)  // -1e300 is another strong differentiator