node/test/pummel/test-crypto-timing-safe-equal-benchmarks.js

'use strict';
const common = require('../common');
if (!common.hasCrypto)
  common.skip('missing crypto');

if (!common.enoughTestMem)
  common.skip('memory-intensive test');

const assert = require('assert');
const crypto = require('crypto');

function runOneBenchmark(compareFunc, firstBufFill, secondBufFill, bufSize) {
  return eval(`
      const firstBuffer = Buffer.alloc(bufSize, firstBufFill);
      const secondBuffer = Buffer.alloc(bufSize, secondBufFill);

      const startTime = process.hrtime();
      const result = compareFunc(firstBuffer, secondBuffer);
      const endTime = process.hrtime(startTime);

      // Ensure that the result of the function call gets used, so it doesn't
      // get discarded due to engine optimizations.
      assert.strictEqual(result, firstBufFill === secondBufFill);

      endTime[0] * 1e9 + endTime[1];
    `);
}

function getTValue(compareFunc) {
  const numTrials = 1e5;
  const bufSize = 10000;
  // Perform benchmarks to verify that timingSafeEqual is actually timing-safe.

  const rawEqualBenches = Array(numTrials);
  const rawUnequalBenches = Array(numTrials);

  for (let i = 0; i < numTrials; i++) {
    if (Math.random() < 0.5) {
      // First benchmark: comparing two equal buffers
      rawEqualBenches[i] = runOneBenchmark(compareFunc, 'A', 'A', bufSize);
      // Second benchmark: comparing two unequal buffers
      rawUnequalBenches[i] = runOneBenchmark(compareFunc, 'B', 'C', bufSize);
    } else {
      // Flip the order of the benchmarks half of the time.
      rawUnequalBenches[i] = runOneBenchmark(compareFunc, 'B', 'C', bufSize);
      rawEqualBenches[i] = runOneBenchmark(compareFunc, 'A', 'A', bufSize);
    }
  }

  const equalBenches = filterOutliers(rawEqualBenches);
  const unequalBenches = filterOutliers(rawUnequalBenches);

  // Use a two-sample t-test to determine whether the timing difference between
  // the benchmarks is statistically significant.
  // https://wikipedia.org/wiki/Student%27s_t-test#Independent_two-sample_t-test

  const equalMean = mean(equalBenches);
  const unequalMean = mean(unequalBenches);

  const equalLen = equalBenches.length;
  const unequalLen = unequalBenches.length;

  const combinedStd = combinedStandardDeviation(equalBenches, unequalBenches);
  const standardErr = combinedStd * Math.sqrt(1 / equalLen + 1 / unequalLen);

  return (equalMean - unequalMean) / standardErr;
}

// Returns the mean of an array
function mean(array) {
  return array.reduce((sum, val) => sum + val, 0) / array.length;
}

// Returns the sample standard deviation of an array
function standardDeviation(array) {
  const arrMean = mean(array);
  const total = array.reduce((sum, val) => sum + Math.pow(val - arrMean, 2), 0);
  return Math.sqrt(total / (array.length - 1));
}

// Returns the common standard deviation of two arrays
function combinedStandardDeviation(array1, array2) {
  const sum1 = Math.pow(standardDeviation(array1), 2) * (array1.length - 1);
  const sum2 = Math.pow(standardDeviation(array2), 2) * (array2.length - 1);
  return Math.sqrt((sum1 + sum2) / (array1.length + array2.length - 2));
}

// Filter large outliers from an array. A 'large outlier' is a value that is at
// least 50 times larger than the mean. This prevents the tests from failing
// due to the standard deviation increase when a function unexpectedly takes
// a very long time to execute.
function filterOutliers(array) {
  const arrMean = mean(array);
  return array.filter((value) => value / arrMean < 50);
}

// t_(0.99995, ∞)
// i.e. If a given comparison function is indeed timing-safe, the t-test result
// has a 99.99% chance to be below this threshold. Unfortunately, this means
// that this test will be a bit flakey and will fail 0.01% of the time even if
// crypto.timingSafeEqual is working properly.
// t-table ref: http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf
// Note that in reality there are roughly `2 * numTrials - 2` degrees of
// freedom, not ∞. However, assuming `numTrials` is large, this doesn't
// significantly affect the threshold.
const T_THRESHOLD = 3.892;

const t = getTValue(crypto.timingSafeEqual);
assert(
  Math.abs(t) < T_THRESHOLD,
  `timingSafeEqual should not leak information from its execution time (t=${t})`,
);

// As a coherence check to make sure the statistical tests are working, run the
// same benchmarks again, this time with an unsafe comparison function. In this
// case the t-value should be above the threshold.
const unsafeCompare = (bufA, bufB) => bufA.equals(bufB);
const t2 = getTValue(unsafeCompare);
assert(
  Math.abs(t2) > T_THRESHOLD,
  `Buffer#equals should leak information from its execution time (t=${t2})`,
);