**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.

**Category / Keywords: **meet-in-the-middle, tradeoff, collision search

**Original Publication**** (in the same form): **IACR-ASIACRYPT-2016

**Date: **received 4 Sep 2016, last revised 7 Sep 2016

**Contact author: **inikolic at ntu edu sg, sasaki yu@lab ntt co jp, cube444@gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20160907:141912 (All versions of this report)

**Short URL: **ia.cr/2016/851

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