基于NP-hard实例的背包密码系统
Knapsack cryptosystems built on NP-hard instance
摘要：
我们构造了三个公钥背包密码系统。标准的背包密码系统隐藏了背包问题的简单实例，并已被打破。本文中考虑的系统面临着这个问题：它们隐藏了背包问题的一个随机（可能是困难的）实例。我们提供了复杂度结果（密钥的大小，加密/解密所需的时间...）和实验结果。第二个密码系统（最快的一个和一个与最短的密钥）的安全性结果。概率多项式约简表明，找到私钥就像分解两个素数的乘积一样困难。我们还考虑启发式攻击。首先，密码系统的密度可以任意选择接近1，丢弃低密度攻击。最后，我们考虑了基于LLL算法的显式启发式攻击，并证明了对于这些攻击，公钥与随机密钥一样安全。
英文摘要：
We construct three public key knapsack cryptosystems. Standard knapsack cryptosystems hide easy instances of the knapsack problem and have been broken. The systems considered in the article face this problem: They hide a random (possibly hard) instance of the knapsack problem. We provide both complexity results (size of the key, time needed to encypher/decypher...) and experimental results. Security results are given for the second cryptosystem (the fastest one and the one with the shortest key). Probabilistic polynomial reductions show that finding the private key is as difficult as factorizing a product of two primes. We also consider heuristic attacks. First, the density of the cryptosystem can be chosen arbitrarily close to one, discarding low density attacks. Finally, we consider explicit heuristic attacks based on the LLL algorithm and we prove that with respect to these attacks, the public key is as secure as a random key.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
