# Slide Reduction, Revisited---Filling the Gaps in SVP Approximation

## TL;DR

This paper generalizes a lattice reduction algorithm to efficiently solve the approximate Shortest Vector Problem (SVP) for a wide range of approximation factors, significantly impacting cryptographic applications.

## Contribution

It extends Gama and Nguyen's slide reduction algorithm to cover all relevant approximation factors for cryptography, providing the fastest provably correct solutions.

## Key findings

- Developed a generalized slide reduction algorithm for approximate SVP
- Achieved the fastest provably correct algorithms for a broad range of approximation factors
- Focused on the approximation range most relevant for cryptography

## Abstract

We show how to generalize Gama and Nguyen's slide reduction algorithm [STOC '08] for solving the approximate Shortest Vector Problem over lattices (SVP). As a result, we show the fastest provably correct algorithm for $\delta$-approximate SVP for all approximation factors $n^{1/2+\varepsilon} \leq \delta \leq n^{O(1)}$. This is the range of approximation factors most relevant for cryptography.