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Reliable probabilistic primality tests are fundamental in public-keycryptography. In adversarial scenarios, a composite with a high probability ofpassing a specific primality test could be chosen. In such cases, we needworst-case error estimates for the test. However, in many scenarios the numbersare randomly chosen and thus have significantly smaller error probability.Therefore, we are interested in average case error estimates. In this paper, weestablish such bounds for the strong Lucas primality test, as only worst-case,but no average case error bounds, are currently available. This allows us touse this test with more confidence. We examine an algorithm that draws odd$k$-bit integers uniformly and independently, runs $t$ independent iterationsof the strong Lucas test with randomly chosen parameters, and outputs the firstnumber that passes all $t$ consecutive rounds. We attain numerical upper boundson the probability on returing a composite. Furthermore, we consider a modifiedversion of this algorithm that excludes integers divisible by small primes,resulting in improved bounds. Additionally, we classify the numbers thatcontribute most to our estimate.

Average Case Error Estimates of the Strong Lucas Test