The source-subtracted cosmic infrared background (CIB) fluctuations uncovered in deep Spitzer data cannot be explained by known galaxy populations and appear strongly coherent with unresolved cosmic X-ray background (CXB). This suggests that the source-subtracted CIB contains emissions from significantly abundant accreting black holes (BHs). We show that theoretically such populations would have the angular power spectrum which is largely independent of the epochs occupied by these sources, provided they are at z>~ 4, offering an important test of the origin of the new populations. Using the current measurements we reconstruct the underlying soft X-ray CXB from the new sources and show that its fluctuations, while consistent with a high-z origin, have an amplitude that cannot be reached in direct measurements with the foreseeable X-ray space missions. This necessitates application of the methods developed by the authors to future IR and X-ray datasets, which must cover large areas of the sky in order to measure the signal with high precision. The LIBRAE project within ESAs Euclid mission will probe source-subtracted CIB over ~1/2 the sky at three near-IR bands, and its cross-power with unresolved CXB can be measured then from the concurrent eROSITA mission covering the same areas of the sky. We discuss the required methodology for this measurement and evaluate its projected S/N to show the unique potential of this experimental configuration to accurately probe the CXB from the new BH sources and help identify their epochs.
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