Benchmarking and Group Operation Counting

In this document we discuss your options when it comes to benchmarking code written using Cryptimeleon libraries as well as group operation counting provided by Cryptimeleon Math.

Runtime Benchmarking

Lazy Eval

While useful for automatic optimization, the lazy evaluation features of Math can create some benchmarking problems if not handled correctly.

Let’s take for example a signature scheme. During setup for your verification benchmark, you will probably execute the signing algorithm. If evaluation is deferred until later, group operations done during signing will only be executed once the result is needed during verification of your signature. This will obviously falsify your results for the verification benchmark.

Therefore, you should make sure to compute all group operations via any of the methods that force a blocking evaluation of the LazyGroupElement instance, for example using computeSync().


If you care about accuracy, we recommend using a micro-benchmarking framework such as JMH. We also strongly recommend working through the JMH Samples to make sure you avoid any bad practices that could potentially invalidate your benchmarks.

Our own benchmarks use JMH. Since JMH is made to be used with Maven, you will probably want to add a Gradle task for executing your JMH tests (if you use Gradle).

task jmh(type: JavaExec) {
    description = "This task runs JMH benchmarks"
    // Run tests inside jmh source path
    classpath = sourceSets.jmh.runtimeClasspath
    // Need to run the JMH main class which collects and runs the tests
    main = "org.openjdk.jmh.Main" 

    def include ='include', '');
    def exclude ='exclude');
    def prof ='prof'); // allow adding a profiler
    def format ='format', 'json');
    def resultFile = file("build/reports/jmh/result.${format}")

    args include
    if (exclude) {
        args '-e', exclude
    if (prof) {
        args '-prof', prof
    args '-rf', format
    args '-rff', resultFile

Above is the script we use for our Cryptimeleon Benchmark project. It allows us to use certain JMH parameters in addition to just running all tests contained in the jmh source set.

Group Operation Counting

Cryptimeleon Math includes capabilities for group operation counting. Specifically, it allows for tracking group inversions, squarings, operations, as well as (multi-)exponentiations for a specific group.


The functionality of group operation counting is provided by using a special group, the DebugGroup.

Note: Keep in mind that DebugGroup uses \(\mathbb{Z}_n\) under the hood, and so is only to be used when testing and/or counting group operations, not for other performance benchmarks.

import org.cryptimeleon.math.structures.groups.debug.DebugGroup;

// instantiate the debug group with a name and its size
DebugGroup debugGroup = new DebugGroup("DG1", 1000000);

// Get a random non-neutral element and square it
GroupElement elem = debugGroup.getUniformlyRandomNonNeutral();

// Print number of squarings in group

As seen above, DebugGroup provides the same interfaces as any other group in Math does, just with some additional features.

Whenever a group operation is performed, DebugGroup tracks it internally. The user can access the data via a variety of methods. These methods for data access can be separated in two categories: Methods whose names end in Total and ones whose names end in NoExpMultiExp. The former includes all group operations, even the ones done in (multi-)exponentiation algorithms while NoExpMultiExp methods only retrieve operation counts of operations not done in (multi-)exponentiations. This is useful if you want to track (multi-)exponentiations only as a single unit and not the underlying group operations. That data can be accessed via the getNumExps() and getMultiExpTermNumbers() methods, where the latter returns an array containing the number of bases in each multi-exponentiation done.

Additionally, resetCounters() can be used to reset all operation counters, and formatCounterData() provides a printable string that summarizes all collected data.

DebugGroup debugGroup = new DebugGroup("DG1", 1000000);
GroupElement elem = debugGroup.getUniformlyRandomNonNeutral();
GroupElement elem2 = debugGroup.getUniformlyRandomNonNeutral();
GroupElement elem3 = debugGroup.getUniformlyRandomNonNeutral();
GroupElement elem4 = debugGroup.getUniformlyRandomNonNeutral();

// Perform a multi-exponentiation with 4 bases
// An exponentiation
// Squaring, group op and inversion

// Print summary of all data
------- Operation data for DebugGroup(Lazy DG1;Lazy DG1) -------
----- Total group operation data: -----
    Number of Group Operations: 34
    Number of Group Inversions: 1
    Number of Group Squarings: 9
----- Group operation data without operations done in (multi-)exp algorithms: -----
    Number of Group Operations: 1
    Number of Group Inversions: 1
    Number of Group Squarings: 1
----- Other data: -----
    Number of exponentiations: 1
    Number of terms in each multi-exponentiation: [4]
    Number of retrieved representations (via getRepresentation()): 0

As you can see, the “Total group operation data” block has much higher numbers than the block below it, due to counting operations done during the multi-exponentiation and exponentiation.

Lazy Evaluation

DebugGroup does use lazy evaluation, meaning that compute() calls are necessary before retrieving tracked operation data, else the operation might have not been executed yet. However, compute() has been changed to behave like computeSync() in that it blocks until the computation is done. This is because non-blocking computation can lead to race conditions when printing the result of tracking the group operations, i.e. the computation has not been performed yet when the data is printed. So make sure to always call compute() on every DebugGroupElement before accessing any counter data.

Serialization Tracking

DebugGroup not only allows for tracking group operations, it also counts how many calls of getRepresentation() have been called on elements of the group. This has the purpose of allowing you to track serializations. The count is accessible via getNumRetrievedRepresentations().


Cryptimeleon Math also provides a BilinearGroup implementation that can be used for counting, the DebugBilinearGroup class. It uses a simple (not secure) \(\mathbb{Z}_n\) pairing.

In addition to the usual group operation counting done by the three DebugGroup instances contained in the bilinear group, DebugBilinearGroup also allows you to track number of pairings performed.

DebugBilinearGroup bilGroup = new DebugBilinearGroup(100);
// Get G1 and G2 of the bilinear group
DebugGroup groupG1 = (DebugGroup) bilGroup.getG1();
DebugGroup groupG2 = (DebugGroup) bilGroup.getG2();

GroupElement elemG1 = groupG1.getUniformlyRandomNonNeutral();
GroupElement elemG2 = groupG2.getUniformlyRandomNonNeutral();

// Compute a paring
bilGroup.getBilinearMap().apply(elemG1, elemG2).compute();