报告名称：Generalized Low Rank Parity Check Codes
报告专家：李春雷
专家所在单位：挪威卑尔根大学
报告时间：2023年7月10日9:00-12:00
报告地点：湖北大学数学与统计学学院201
专家简介：李春雷，男，现为挪威卑尔根大学信息系- Selmer研究中心副教授，主要从事信息安全相关领域的研究，重点关注密码学,编码理论,区块链和安全可靠通信 方面的研究。近年来在国际知名期刊上发表高质量学术论文40余篇， 其中在计算机学会（CCF）建议的A类期刊IEEE Transaction on Information Theory上发表论文7篇。2011-2016年间，李春雷作为核心成员参与多个研究项目，项目来源包括挪威研究理事会-自然科学基金，挪威理事会-计算机通信技术基金以及欧盟灯塔计划；自2016年起，李春雷独立主持2项研究项目，总经费20万挪威克朗（约17万人民币），项目分别由挪威Plogen公司资 助和挪威西部高校联盟资助。自2020年7月起，李春雷独立主持挪威研究理事会-信息科技通信领域的研究项目-新一代无线通信中的序列设计，总经费870万挪威克朗。
报告摘要：The last four decades witnessed significant developments of rank metric codes and their increasing applications in cryptography. In cryptographic applications, rank metric codes allow for smaller key sizes for the same level of security when compared to codes in the Hamming metric, such as the Goppa codes in the McEliece cryptosystem. Moreover, the decoding of a random Fq-linear rank metric code can be reduced to the MinRank problem which is proven to be NP-complete. The hardness of the decoding problem and the advantage of smaller key sizes for rank metric codes laid a good foundation for rank-based cryptography. Motivated by recent developments of algebraic attacks on the decoding problem for Fqm-linear rank metric codes, it is of great importance to explore Fq-linear rank metric codes that have no significant algebraic structure while allow for efficient decoding.
In this talk we will introduce our recent work on the aforementioned subject. To resolve the research problem, we propose a bilinear product over Fqmassociated with a 3-tensor over Fq. We introduce a method to generalize LRPC codes with 3-tensors. The generalized LRPC codes are in general Fq-linear matrix codes, while a particular choice of the 3-tensor corresponds to the original Fqm-linear LRPC codes. We propose two probabilistic polynomial-time decoding algorithms for the generalized LRPC codes. Theoretical analysis and experimental results show that the proposed algorithms have a decoding failure rate similar to that of decoding original Fqm-linear LRPC codes.
