A fuel supply circuit for an aeronautical cryogenic turbomachine including: at least one cryogenic reservoir containing a liquid fuel topped with a boil-off gas and including a high-pressure liquid pump to supply at least one main propulsion device of the turbomachine with liquid fuel, an auxiliary turbomachine including an electric generator, a gas compressor to supply the auxiliary turbomachine with gaseous fuel, and a buffer gas reservoir connecting the gas compressor to the cryogenic reservoir to reinject gas into the cryogenic reservoir in order to maintain the pressure in the cryogenic reservoir above a predefined value, the electric generator supplying the high-pressure liquid pump and the gas compressor.