[Resource Topic] 2023/447: Provable Lattice Reduction of $\mathbb Z^n$ with Blocksize $n/2$

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Provable Lattice Reduction of \mathbb Z^n with Blocksize n/2

Authors: Léo Ducas


The Lattice Isomorphism Problem (LIP) is the computational task of recovering, assuming it exists, a orthogonal linear transformation sending one lattice to another. For cryptographic purposes, the case of the trivial lattice \mathbb Z^n is of particular interest ($\mathbb Z$LIP). Heuristic analysis suggests that the BKZ algorithm with blocksize \beta = n/2 + o(n) solves such instances (Ducas, Postlethwaite, Pulles, van Woerden, ASIACRYPT 2022).

In this work, I propose a provable version of this statement, namely, that $\mathbb Z$LIP can indeed be solved by making polynomially many calls to a Shortest Vector Problem (SVP) oracle in dimension at most n/2 + 1.

ePrint: https://eprint.iacr.org/2023/447

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