Accurate Parameter Estimates for Punctured Key Recovery Linear Attacks

At EUROCRYPT 2024, Flórez-Gutiérrez and Todo introduced the puncturing technique for linear key recovery attacks. Puncturing works by modifying the map which evaluates the linear approximation as a function of the plaintext, ciphertext and key, by setting carefully chosen coordinates of its Fourier transform to zero. These modifications are intended to reduce the time complexity of the attack at the cost of an increase in data complexity. In this note, we revisit the model which is used to estimate the data complexity, clarify some of its underlying assumptions, and improve its accuracy. This leads to a revision of the cost estimates for several applications of puncturing in the literature, most notably for attacks whose data complexity is close to the full codebook.