NNRU，NTRU的非交换类似物

摘要：

NTRU公钥密码体制与Ajtai-Dwork、GGH体制一样，都是研究得比较深入的基于格的密码体制。NTRU是一个很难的数学问题，在一定的格中找到短向量。（Shamir 1997）提出了一种基于格的攻击，通过这种攻击，他可以找到原始秘密密钥或备用密钥。Shamir得出结论，如果设计一个NTRU的变体，其中加密和解密过程中涉及的计算是不可交换的，那么该系统将是安全的，以抵抗基于格的攻击。本文提出了一个新的密码系统，具有上述性质，我们已经证明了它是完全安全的，以抵抗基于格的攻击。它在非交换环M=M_kZ [X]/（X^n - I_{k*k}）中工作，其中M是R={Z}[X]/（X^n-1）中的k × k个多项式矩阵的矩阵环.此外，对于相同的信息位，我们的速度比NTRU提高了O（k^{1.624）倍。

英文摘要：

NTRU public key cryptosystem is well studied lattice-based Cryptosystem along with Ajtai-Dwork and GGH systems. Underlying NTRU is a hard mathematical problem of finding short vectors in a certain lattice. (Shamir 1997) presented a lattice-based attack by which he could find the original secret key or alternate key. Shamir concluded if one designs a variant of NTRU where the calculations involved during encryption and decryption are non-commutative then the system will be secure against Lattice based attack.This paper presents a new cryptosystem with above property and we have proved that it is completely secure against Lattice based attack. It operates in the non-commutative ring M=M_k Z[X]/(X^n - I_{k*k}, where M is a matrix ring of k*k matrices of polynomials in R={Z}[X]/(X^n-1). Moreover We have got speed improvement by a factor of O(k^{1.624) over NTRU for the same bit of information.

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。