Improved polytopic differential neural distinguishers for SIMON, SIMECK, and SPECK block ciphers

Abstract In recent years, the application of deep learning in cryptanalysis has gained significant attention, particularly with the emergence of neural network-based distinguishers. At CRYPTO’19, Gohr demonstrated that neural networks could develop differential distinguishers capable of producing highly competitive attacks against existing methods. Building on this foundation, we propose multiple input polytopic differential neural distinguishers ( PDND s) for the lightweight block ciphers SIMON, SIMECK, and SPECK. Our approach incorporates a novel data generation method that utilizes two polytope differences, resulting in more precise training data and enhanced model accuracy. Through extensive experiments in single-key and related-key scenarios, we evaluate and validate the intrinsic performance of our neural distinguishers. Our results show that PDND s significantly outperform the baseline, polytopic, multiple, and mixture differential neural distinguishers, utilizing a single input difference, in accuracy across various cipher rounds. Notably, our PDND s achieved $$100\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>100</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> accuracy for up to 7 rounds of SIMON32 and SIMECK32, and $$99.39\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>99.39</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> accuracy for 5 rounds of SPECK32 in the single-key scenario. Additionally, for extended rounds, we achieved accuracy levels of up to 12 rounds for SIMON32, 13 for SIMECK32, and 8 for SPECK32 without requiring staged training. In the related-key scenario, our method further improved performance, introducing 13-round and 15-round RK-PDND s for SIMON32 and SIMECK32, respectively, underscoring the enhanced capabilities of our approach. Furthermore, we demonstrate the effectiveness of our neural distinguishers through a key recovery test, where they successfully distinguish between correct and incorrect keys, confirming the practical applicability of our approach in cryptanalysis.