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多变量密码和纠错编码密码作为后量子密码中的两个候选方案,因其都具备较高的效率和抗量子攻击的特性,成为密码学研究的新热点.然而,在对多变量密码的研究当中,核心映射的构造一直是研究的重点和难点,因此利用新方法构造核心映射是一个热门方向.另一方面,因为纠错编码密码在编码上具备数据压缩传输的优势,且与多变量密码在形式上的相似——矩阵运算,给构造多变量密码核心映射提供了新思路.本文针对多变量核心映射构造和数据压缩加密的问题,结合LRPC(Low Rank Parity Check)码和Cubic Simple Matrix加密方案的特点,利用秩矩阵码密钥量小的优势,设计了一种新的核心映射构造方法,由此提出了一个结合纠错编码的多变量签密方案.通过分析,表明方案具备了多变量密码和纠错编码密码的特点,在不明显增加密钥量和降低安全性的前提下,降低了原方案的密文扩展率,同时实现了加密和签名,使得用户和数据中心在传递数据时具备编码密码的优势.另外,在随机预言机模型下证明了方案具备IND-CCA2安全和EUF-CMA安全.
Multivariate cryptography and error-correcting coding cryptography as two candidate solutions in post-quantum cryptography have become new hot points in cryptography due to their high efficiency and resistance to quantum attacks.However, In the research, the construction of core mapping has always been the focus and difficulty of the research, so it is a hot topic to construct the core mapping using the new method.On the other hand, because the error correction coding has the advantages of encoding and compressing the data, The similarity of the codes in the form of matrix operation provides a new way to construct the multivariate cryptographic core mapping.In this paper, we discuss the construction of multivariate kernel mapping and data compression and encryption, combined with Low Rank Parity Check (LRPC) code and Cubic Simple Matrix The characteristics of the encryption scheme and the advantage of small key code of the rank matrix code, a new construction method of kernel mapping is proposed, and a multivariate signcryption scheme combining error correction coding is proposed.Through the analysis, it shows that the scheme has Multivariate password and error correction coding the characteristics of the password, without significantly increasing the amount of keys and reduce security under the premise of reducing the original program ciphertext Exhibition rate, while achieving encryption and signature, and data centers that have the advantage of user passwords encoded when transmitting data. Further, in the demonstrated embodiment includes a random oracle model IND-CCA2 security and safety EUF-CMA.