Multidimensional Extension of Matsui's Algorithm 2

Matsui’s one-dimensional Alg. 2 can be used for recovering bits of the last round key of a block cipher. In this paper a truly multidimensional extension of Alg. 2 based on established statistical theory is presented. Two possible methods, an optimal method based on the log-likelihood ratio and a χ2-based goodness-of-fit test are compared in theory and by practical experiments on reduced round Serpent. The theory of advantage by Selçuk is generalised in multiple dimensions and the advantages and data, time and memory complexities for both methods are derived.