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Blockwise Rank Decoding Problem and LRPC Codes: Cryptosystems with Smaller Sizes

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Title: Blockwise Rank Decoding Problem and LRPC Codes: Cryptosystems with Smaller Sizes
Authors: Song, Yongcheng, Zhang, Jiang, Huang, Xinyi, Wu, Wei
Publisher Information: Springer Science and Business Media Deutschland GmbH
Publication Year: 2023
Collection: The Hong Kong University of Science and Technology: HKUST Institutional Repository
Subject Terms: LRPC Codes, NIST PQC Candidates, Post-Quantum Cryptography, Rank Decoding Problem, Rank Metric Code-Based Cryptography
Description: In this paper, we initiate the study of the Rank Decoding (RD) problem and LRPC codes with blockwise structures in rank-based cryptosystems. First, we introduce the blockwise errors (ℓ -errors) where each error consists of ℓ blocks of coordinates with disjoint supports, and define the blockwise RD (ℓ -RD) problem as a natural generalization of the RD problem whose solutions are ℓ -errors (note that the standard RD problem is actually a special ℓ -RD problem with ℓ= 1 ). We adapt the typical attacks on the RD problem to the ℓ -RD problem, and find that the blockwise structures do not ease the problem too much: the ℓ -RD problem is still exponentially hard for appropriate choices of ℓ> 1. Second, we introduce blockwise LRPC (ℓ -LRPC) codes as generalizations of the standard LPRC codes whose parity-check matrices can be divided into ℓ sub-matrices with disjoint supports, i.e., the intersection of two subspaces generated by the entries of any two sub-matrices is a null space, and investigate the decoding algorithms for ℓ -errors. We find that the gain of using ℓ -errors in decoding capacity outweighs the complexity loss in solving the ℓ -RD problem, which makes it possible to design more efficient rank-based cryptosystems with flexible choices of parameters. As an application, we show that the two rank-based cryptosystems submitted to the NIST PQC competition, namely, RQC and ROLLO, can be greatly improved by using the ideal variants of the ℓ -RD problem and ℓ -LRPC codes. Concretely, for 128-bit security, our RQC has total public key and ciphertext sizes of 2.5 KB, which is not only about 50% more compact than the original RQC, but also smaller than the NIST Round 4 code-based submissions HQC, BIKE, and Classic McEliece.
Document Type: conference object
Language: English
Relation: http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=LinksAMR&SrcApp=PARTNER_APP&DestLinkType=FullRecord&DestApp=WOS&KeyUT=001157420100010
DOI: 10.1007/978-981-99-8739-9_10
Availability: http://repository.hkust.edu.hk/ir/Record/1783.1-136502
https://doi.org/10.1007/978-981-99-8739-9_10
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Accession Number: edsbas.51EA798
Database: BASE
Description
Abstract:In this paper, we initiate the study of the Rank Decoding (RD) problem and LRPC codes with blockwise structures in rank-based cryptosystems. First, we introduce the blockwise errors (ℓ -errors) where each error consists of ℓ blocks of coordinates with disjoint supports, and define the blockwise RD (ℓ -RD) problem as a natural generalization of the RD problem whose solutions are ℓ -errors (note that the standard RD problem is actually a special ℓ -RD problem with ℓ= 1 ). We adapt the typical attacks on the RD problem to the ℓ -RD problem, and find that the blockwise structures do not ease the problem too much: the ℓ -RD problem is still exponentially hard for appropriate choices of ℓ> 1. Second, we introduce blockwise LRPC (ℓ -LRPC) codes as generalizations of the standard LPRC codes whose parity-check matrices can be divided into ℓ sub-matrices with disjoint supports, i.e., the intersection of two subspaces generated by the entries of any two sub-matrices is a null space, and investigate the decoding algorithms for ℓ -errors. We find that the gain of using ℓ -errors in decoding capacity outweighs the complexity loss in solving the ℓ -RD problem, which makes it possible to design more efficient rank-based cryptosystems with flexible choices of parameters. As an application, we show that the two rank-based cryptosystems submitted to the NIST PQC competition, namely, RQC and ROLLO, can be greatly improved by using the ideal variants of the ℓ -RD problem and ℓ -LRPC codes. Concretely, for 128-bit security, our RQC has total public key and ciphertext sizes of 2.5 KB, which is not only about 50% more compact than the original RQC, but also smaller than the NIST Round 4 code-based submissions HQC, BIKE, and Classic McEliece.
DOI:10.1007/978-981-99-8739-9_10