浙江大学学报（理学版）2026，Vol.53Issue(1)：47-56,62,11.DOI:10.3785/1008-9497.24025
探索整数格的拓扑图编码实现
Exploring the topological graph encoding implementation of integer grids
摘要
Abstract
In the post quantum era,lattice cryptography is featured as an interdisciplinary and diversified research method,and is most likely to become post quantum cryptography.The graphic lattice in topological coding is the product of interdisciplinary study.Graphs in graphic lattices are stored by matrices and run in the computer,the main theoretical technology of topological coding is originated from mathematical disciplines such as discrete mathematics,number theory and algebra.Because topological coding contains a lot of mathematical conjectures and NP-problems,the number-based strings generated by topological coding possess irreversibility and computational security.Some new labelings and colorings are defined in this paper,and the algorithms to realize these labelings and colorings are given,and the classes of graphs admitting these new labelings and colorings are determined.We establish graphic lattices based on graph operations and graphic lattice bases,for asymmetric cryptography,and show connections among caterpillar-graphic lattices,their complementary graphic lattices and integer lattices.The technical methods in this paper are shown by effective and feasible algorithms.关键词
格密码/拓扑编码/全标号/全着色/图格/着色图格同态/非对称拓扑加密Key words
lattice-based cryptography/topological coding/total labeling/total coloring/graphic lattice/colored-graphic homomorphism/asymmetric topology cryptography分类
数理科学引用本文复制引用
ZHANG Mingjun,ZHANG Yujing,ZHANG Xiaohui,YAO Bing..探索整数格的拓扑图编码实现[J].浙江大学学报（理学版）,2026,53(1):47-56,62,11.基金项目
国家自然科学基金项目(61662066) （61662066）
甘肃省自然科学基金项目(25JRRA232) （25JRRA232）
高校教师创新基金项目(2023A-075) （2023A-075）
兰州市哲学社会科学规划项目(23-B22). （23-B22）
