拓扑非对称密码体制中的拓扑认证技术
Topological Authentication Technique In Topologically Asymmetric Cryptosystem
摘要：
使拓扑认证从理论走向实际应用是一项重要而富有挑战性的任务。在量子计算、隐私数据保护、格和密码学等方面的研究越来越受到人们的关注。研究表明，通过图操作、各种矩阵、图着色和图标记进行拓扑认证的优点是：与两个或两个以上不同的数学领域相关，不是图像，有大量的着色和标记，植根于现代数学，非对称密码的多样性，简单方便，易于创建，不可逆性，计算安全性，可证明安全性，基于各种图同态、度序列同态、图集同态的拓扑认证。随机拓扑编码和拓扑认证基于汉字认证、随机加边去边运算、随机加叶算法、图随机增长技术、运算图格和动态网络模型及其生成树和最大叶生成树。拓扑认证的实现是一个重要的课题，我们研究了：基于着色图的数字串生成，特殊图（完全图，树，平面图），公钥生成的一些方法。拓扑非对称密码系统的一些技术有：W型匹配标记、双型标记、互反型标记、拓扑同态、索引着色、图格、度序列格、度序列的每零Cds矩阵群、每零图群、具有着色闭包性质的图格、自相似网络格。
英文摘要：
Making topological authentication from theory to practical application is an important and challenging task. More and more researchers pay attention on coming quantum computation, privacy data protection, lattices and cryptography. Research show the advantages of topological authentications through graph operations, various matrices, graph colorings and graph labelings are: related with two or more different mathematical areas, be not pictures, there are huge number of colorings and labelings, rooted on modern mathematics, diversity of asymmetric ciphers, simplicity and convenience, easily created, irreversibility, computational security, provable security, and so on. Topological authentications based on various graph homomorphisms, degree-sequence homomorphisms, graph-set homomorphisms. Randomly topological coding and topological authentications are based on Hanzi authentication, randomly adding-edge-removing operation, randomly leaf-adding algorithms, graph random increasing techniques, operation graphic lattice and dynamic networked models and their spanning trees and maximum leaf spanning trees. Realization of topological authentication is an important topic, we study: number-based strings generated from colored graphs, particular graphs (complete graphs, trees, planar graphs), some methods of generating public-keys. some techniques of topologically asymmetric cryptosystem are: W-type matching labelings, dual-type labelings, reciprocal-type labelings, topological homomorphisms, indexed colorings, graphic lattices, degree-sequence lattices, every-zero Cds-matrix groups of degree-sequences, every-zero graphic groups, graphic lattices having coloring closure property, self-similar networked lattices.
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。
