Higher-order differences based research on comparison between type-1 generalized Feistel-SP network and Feistel-SPSP network

The powers against the higher-order differential cryptanalysis of the single-SP(substitution-permutation) model and the double-SP model are studied in the type-1 Feistel network by analyzing the growths of algebraic degrees. Combining the higher-order integral and the higher-order difference, a new method is exploited to estimate the upper bounds of algebraic degrees for the 4-line type-1 Feistel-SP scheme and the 4-line type-1 Feistel-SPSP scheme. Applying the new method, distinguishers of the two schemes are constructed with four common parameters. As a result, the dou-ble-SP model is weaker than the single-SP model against the higher-order differential attack under the 4-line type-1 Feis-tel structure.