Orthogonalized lattice enumeration for solving SVP

Abstract

The orthogonalized integer representation was independently proposed by Ding et al. using genetic algorithm and Fukase et al. using sampling technique to solve shortest vector problem (SVP). Their results are promising. In this paper, we consider sparse orthogonalized integer representations for shortest vectors and propose a new enumeration method, called orthognalized enumeration, by integrating such a representation. Furthermore, we present a mixed BKZ method, called MBKZ, by alternately applying orthognalized enumeration and other existing enumeration methods. Compared to the existing ones, our methods have greater efficiency and achieve exponential speedups both in theory and in practice for solving SVP. Implementations of our algorithms have been tested to be effective in solving challenging lattice problems.

Partially known information attack on SM2 key exchange protocol

“…When l and l ′ are set to be 179 and 80 separately such that the number of http://engine.scichina.com/doi/10.1007/s11432-018-9515-9 known bits is 259, our experiments show that the attack can succeed with overwholeming probability over 40 samples. Additionally, note that our algorithm may perform better by further optimizations invoking new techniques from [23][24][25].…”

“…The most practical and widely-used algorithm by now is BKZ 2.0 proposed by Chen and Nguyen in 2011 [21], which is improved from the Schnorr-Euchner's BKZ [22]. In recent years, some variants of BKZ which perform better in practice have been investigated [23][24][25].…”

A Parallel Evolutionary Search for Shortest Vector Problem

“…) can be increased up to after each round by (lines 24,25). The rounds of this step continue the evolutionary search (a Genetic Algorithm) until the termination criteria (line 10) be satisfied and break the loop of the generations.…”

“…These two papers introduce promising test results. In [24], it is proposed a new enumeration by integrating sparse orthogonalized integer representations for shortest vectors, also proposed a mixed BKZ method by alternately applying orthognalized enumeration and other existing enumeration methods. This methods [24] have exponential speedups both in theory and in practice for solving SVP.…”

“…In [24], it is proposed a new enumeration by integrating sparse orthogonalized integer representations for shortest vectors, also proposed a mixed BKZ method by alternately applying orthognalized enumeration and other existing enumeration methods. This methods [24] have exponential speedups both in theory and in practice for solving SVP. Although the results of using orthogonalized integer representation in solving SVP is so hopeful, but our approach in this paper is to use the plain representation of lattice vectors.…”