Improving Linear Key Recovery Attacks Using Walsh Spectrum Puncturing

In some linear key recovery attacks, the function which determines the value of the linear approximation from the plaintext, ciphertext and key is replaced by a similar map in order to improve the time or memory complexity at the cost of a data complexity increase. We propose a general framework for key recovery map substitution, and introduce Walsh spectrum puncturing, which consists of removing carefully-chosen coefficients from the Walsh spectrum of this map. The capabilities of this technique are illustrated by describing improved attacks on reduced-round Serpent (including the first 12-round attack on the 192-bit key variant), GIFT-128 and Noekeon, as well as the full DES.