What is the crossover error rate?
The crossover error rate (CER) is the error rate at which a biometric system's false acceptance rate (FAR) equals its false rejection rate (FRR). It is also called the equal error rate (EER). Because FAR and FRR pull against each other, a figure for either one alone says little about accuracy; a vendor can advertise a tiny FAR by setting a very strict threshold and staying quiet about a large FRR. The CER sums up accuracy in one number that is fair to compare. The lower the CER, the better the system tells genuine users from impostors.
How the crossover point is found
Testers run genuine and impostor attempts at a range of threshold settings and record both error rates at each one. As the threshold tightens, FAR falls and FRR rises. Plotted on one chart, the two curves cross, and the error rate at that crossing is the CER. The figures below are illustrative, for a single fingerprint reader:
| Threshold | FAR | FRR |
|---|---|---|
| Loose | 4.0% | 0.3% |
| Medium | 1.1% | 1.1% |
| Strict | 0.05% | 5.2% |
The two rates meet at 1.1 percent, so that is this reader's CER.
Comparing systems with CER
Suppose reader A has a CER of 1.1 percent and reader B a CER of 3.5 percent. Reader A is the more accurate product, and it will generally make fewer errors of both kinds across the useful range of settings. Two cautions apply. CER figures are only comparable when they come from similar test conditions and similar groups of people, so independent test results count for more than a vendor's own data sheet. And CER measures matching accuracy against ordinary impostors, not resistance to fakes such as a molded fingerprint, which depends on liveness detection.
CER is a benchmark, not the setting you run
Few deployments operate exactly at the crossover. A vault or data center door is tuned to the strict side, accepting a higher FRR to keep FAR very low. A gym turnstile or a time clock may run on the loose side, because turning members away costs more than the occasional false match. The CER tells you which product to buy; the threshold you set decides which error you live with.
CER vs. FAR vs. FRR
- FAR: how often impostors are accepted, a security measure.
- FRR: how often legitimate users are rejected, a usability measure.
- CER: the rate where the two meet, one number for comparing systems.
Crossover error rate on the CompTIA Security+ exam
The CER is not on the SY0-801 acronym list; it is taught with biometric authentication under objective 4.5. A question that asks which metric to use when choosing between two biometric products, or which value shows the more accurate system, points to the lowest CER. Distractors are FAR or FRR on their own, since either can be made to look good by moving the threshold, and the claim that adjusting sensitivity lowers the CER, when it only moves the system along the two curves.