Performance bottleneck when using JCE provider with client sdk V5

We are doing RSA message signing operation SHA256WithRSA
Under concurrent load like 5 transactions per seconds, we are observing latency starts increasing into seconds and grows exponentially as the load increases. Any performance benchmarks for this library or any tips on tuning performance?

No source file, test, or entry point is named. Start by locating the Java sample's RSA SHA256WithRSA signing path and reproduce the reported latency under concurrent load. Done means identifying the bottleneck and documenting a benchmark or supported tuning guidance.

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