A recuperative bayonet reactor design for the high-temperature sulfuric acid decomposition step in sulfur-based thermochemical hydrogen cycles was evaluated using pinch analysis in conjunction with statistical methods. The objective was to establish the minimum energy requirement. Taking hydrogen production via alkaline electrolysis with nuclear power as the benchmark, the acid decomposition step can consume no more than 450 kJ/(mol of SO2) for sulfur cycles to be competitive. The lowest value of the minimum heating target, 320.9 kJ/(mol of SO2), was found at the highest pressure (90 bar) and peak process temperature (900 degrees C) considered, and at a feed concentration of 42.5 mol % H2SO4. This should be low enough for a practical water-splitting process, even including the additional energy required to concentrate the acid feed. Lower temperatures consistently gave higher minimum heating targets. The lowest peak process temperature that could meet the benchmark of 450 kJ/(mol of SO2) was 7.50 degrees C. If the decomposition reactor were to be heated indirectly by an advanced gas-cooled reactor heat source (50 degrees C temperature difference between the primary and secondary coolants, 25 degrees C minimum temperature difference between the secondary coolant and the process), then sulfur cycles using this concept could be: competitive with alkaline electrolysis provided that the primary heat source temperature is at least 825 degrees C. The bayonet design will not be practical if the (primary heat source) reactor outlet temperature is below 825 degrees C.