报告题目：Generalized Low Rank Parity Check Codes
报告时间：2023年7月18日上午9:00-10:00
报告地点：西南交通大学犀浦校区X7510
报告人：李春雷
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 Fqm associated 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-Rme 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.
报告人简介：李春雷，挪威卑尔根大学教授，研究领域包括代数编码、密码学及其在安全云存储中的应用。近年来与国内外专家合作密切，在国际知名期刊上发表高质量学术论文40余篇，其发表的论文近5年内的引用次数为500余次；过去几年其应邀参与多个国际会议的组委会和程序委员会。 作为核心成员曾参与多个研究项目，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，独立主持2项研究项目，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，李春雷将主持一个由挪威理事会-计算机通信技术基金支持的研究项目-《无线通信中的序列设计》。
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