In a method for cogenerating a shared cryptographic material implemented within a first electronic device, which is connected to a second electronic cogeneration device and to a third electronic cogeneration device, a shared encryption material (pkx) is determined, as a function of a set of cogeneration parameters ECG. The shared encryption material (pkx) is transmitted, and corresponding shared encryption materials (pky, pkz) are received from the other devices. A shared seed (mx) is computed as a function of the shared encryption materials (pkx, pky, pkz) and the set of cogeneration parameters ECG. A masked form (Ox) of said shared seed (mx) is transmitted, and masked forms (Oy, Oz) of corresponding shared seeds (my, mz) are received. A final seed (ad) is computed as a function of the masked forms (Ox, Oy, Oz) of the shared seeds (mx, my, mz) and the set of cogeneration parameters ECG.