Modeling and application of AND gates’s correlation in linear cryptanalysis

Abstract With the increasingly widespread application scenarios of the Internet of Things, the demand for lightweight ciphers continues to grow. For some lightweight ciphers whose only nonlinear component is the AND gate, their resistance to linear cryptanalysis relies heavily on the properties of the AND operation, making the analysis of such AND gates crucial. In current linear cryptanalysis, two main methods exist: estimating the correlation of linear charactertics based on the number of active AND gates or constructing cipher-specific models that calculate the correlation among AND gates. The former method lacks precision, while the latter method lacks generality. Considering the correlation among AND gates allows for a more accurate assessment of a cipher’s resistance to linear cryptanalysis. However, there is currently no general model to systematically characterize the correlation between quadratic AND gates. This paper proposes a model to characterize the correlation between quadratic AND gates. We apply the model to TinyJAMBU and MiniMORUS. For the permutation $$P_l$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>l</mml:mi> </mml:msub> </mml:math> of TinyJAMBU, we improve the absolute of correlation of the 512-round linear charactertics from $$2^{-46}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>46</mml:mn> </mml:mrow> </mml:msup> </mml:math> to $$2^{-33}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>33</mml:mn> </mml:mrow> </mml:msup> </mml:math> . For 760-round, we identify a valid linear charactertics with absolute of correlation of $$2^{-63}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>63</mml:mn> </mml:mrow> </mml:msup> </mml:math> . For MiniMORUS-640 and MiniMORUS-1280, we find unique linear charactertics with absolute of correlations of $$2^{-8}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>8</mml:mn> </mml:mrow> </mml:msup> </mml:math> each.