不等式_解决_与_CVP - 针对CTF挑战的CVP “技巧”

项目说明

Inequality Solving with CVP

A special case of this problem has another algorithm : check the "Special Case" folder for details

A full writeup on this toolkit (in Korean) will hopefully be posted for SAMSUNG Software Membership blog.

How to use

The sol has four inputs, matrix `mat, lower/upper bounds lb, ub, and a weight.

Assume mat is an n x m integer matrix. This means there are n and m inequalities.

Each column of the mat represents a linear combination of the n .

Each entry of lb, ub denotes a lower/upper bound to that linear combination.

Of course, we require the length of lb, ub to be m.

weight is a that you do *NOT* have to initialize. It will be explained later.

result is the result of the CVP

applied_weights is the applied weights during the weighting process (see below)

fin is the actual value of the , recovered when n = m and are linearly independent

We also have a heuristic for number of solutions for the inequality. This is a good way to decide if this method is feasible. For some notes on this topic, check out Mystiz's writeup on Example Challenge 5.

The reasoning behind the algorithm

Warning : the stuff I say here are not mathematically precise. It's based on intuition

Basically what the algorithm does, is to build a lattice with the gi and find a closest (with Babai's algorithm) to (lb + vb) / 2. However, there is one more twist to the algorithm.

The reason we hope that CVP will solve our problem is basically as follows

However, there's a case where this reasoning fails.

To do this, we have to *scale* our inequalities so ub_i - lb_i becomes of similar size.

Further Comments

项目信息

开发语言：Sage

Star 数：149

技术要点

该项目属于CTF思路方向的开源资源，代码结构清晰，适合安全研究人员学习参考。项目围绕CVP "trick" for CTF challenges展开，提供了可运行的实现，对理解相关安全机制、工具原理与攻防技术具有较高的研究价值。

从技术实现角度看，此类项目的核心在于对底层原理的深入理解与工程化落地。开发者在研究过程中可以结合官方文档与社区讨论，梳理项目的初始化流程、核心模块职责与数据流转，逐步掌握其中的技术细节与设计思路。

使用与学习建议

1. 下载源码压缩包，解压到本地环境。

2. 根据项目类型准备对应的运行环境与依赖。

3. 按照 README 中的步骤完成配置与部署。

4. 在隔离的测试环境中运行验证，避免影响生产系统。

免责声明

本资源来源于开源社区，仅供安全研究、技术学习与合法授权范围内的攻防演练使用，请勿用于任何非法或侵害他人权益的用途。使用本项目产生的一切后果由使用者自行承担。