A New Reduction from Search SVP to Optimization SVP

TL;DR

This paper introduces a novel, efficient reduction from search SVP to optimization SVP requiring only a single oracle call, significantly improving upon previous methods and also applying to CVP problems.

Contribution

A new rank-preserving reduction from search SVP to optimization SVP with only one oracle call, enhancing efficiency over classical approaches.

Findings

Reduces the number of oracle calls to one for search SVP

Extends the reduction technique to search CVP

Improves upon Kannan's classical reduction method

Abstract

It is well known that search SVP is equivalent to optimization SVP. However, the former reduction from search SVP to optimization SVP by Kannan needs polynomial times calls to the oracle that solves the optimization SVP. In this paper, a new rank-preserving reduction is presented with only one call to the optimization SVP oracle. It is obvious that the new reduction needs the least calls, and improves Kannan's classical result. What's more, the idea also leads a similar direct reduction from search CVP to optimization CVP with only one call to the oracle.