Paper 2016/851

A New Algorithm for the Unbalanced Meet-in-the-Middle Problem

Ivica Nikolic and Yu Sasaki

Abstract

A collision search for a pair of $n$-bit unbalanced functions (one is $R$ times more expensive than the other) is an instance of the meet-in-the-middle problem, solved with the familiar standard algorithm that follows the tradeoff $TM=N$, where $T$ and $M$ are time and memory complexities and $N=2^n$. By combining two ideas, unbalanced interleaving and Oorschot-Wiener parallel collision search, we construct an alternative algorithm that follows $T^2 M = R^2 N$, where $M\le R$. Among others, the algorithm solves the well-known open problem: how to reduce the memory of unbalanced collision search.