Although numerous papyri from ancient Egypt have been collected and preserved over the centuries, the recipe used to prepare black inks was only reported in manuscripts from the late Greco-Roman period. Black inks were mostly obtained after mixing carbon black with a binder agent and water. In previous studies performed on black inks apposed on papyri from ancient Egypt, additional chemical elements such as lead, iron, or copper were also identified, and the resulting chemical contrast with the papyrus support was used to virtually decrypt highly degraded or rolled papyri. Combining a series of synchrotron-based techniques with Raman spectroscopy and scanning electron microscopy, we investigated 10 papyri fragments from J.-F. Champollion's private collection. For each fragment, the carbon-black pigment found in the ink is identified as flame carbon (lampblack or soot). Using X-ray diffraction computed tomography, we show that the diffraction signal of the carbon-based pigment itself can be isolated. As a result, a contrast with the papyrus support is obtained, even in the absence of a specific chemical element in the ink. This is opening up new opportunities to decipher words written millennia ago, as part of our Cultural Heritage.