報告題目：Generalized Low Rank Parity Check Codes

報告時間：2023年7月18日上午9:00-10:00

報告地點(diǎn)：kaiyun開云官方網(wǎng)站犀浦校區(qū)X7510

報告人：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.

報告人簡介：李春雷，挪威卑爾根大學(xué)教授，研究領(lǐng)域包括代數(shù)編碼、密碼學(xué)及其在安全云存儲中的應(yīng)用。近年來與國內(nèi)外專家合作密切，在國際知名期刊上發(fā)表高質(zhì)量學(xué)術(shù)論文40余篇，其發(fā)表的論文近5年內(nèi)的引用次數(shù)為500余次；過去幾年其應(yīng)邀參與多個國際會議的組委會和程序委員會。 作為核心成員曾參與多個研究項目，項目來源包括挪威研究理事會-自然科學(xué)基金，挪威理事會-計算機(jī)通信技術(shù)基金以及歐盟燈塔計劃；自2016年起，獨(dú)立主持2項研究項目，項目分別由挪威 Plogen 公司資助和挪威西部高校聯(lián)盟資助；自2020年7月起，李春雷將主持一個由挪威理事會-計算機(jī)通信技術(shù)基金支持的研究項目-《無線通信中的序列設(shè)計》。

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