Breaking and Improving a Lattice-Code-Based Cryptosystem by Li, Ling, Xing, and Yeo

Li, Ling, Xing, and Yeo (LLXY) have proposed a code-based encryption scheme based on factoring in finite fields. The security of the scheme relies on both the decoding problem for <inline-formula> <tex-math notation="LaTeX">(q-1) </tex-math></inline-formula>-ary cod...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 71; no. 9; pp. 6857 - 6869
Main Authors: Athukorala, Pabasara, Galbraith, Steven D.
Format: Journal Article
Language:English
Published: IEEE 01.09.2025
Subjects:
Code-based cryptography
Codes
Decoding
Encryption
Generators
lattice-based cryptography
Lattices
Linear codes
Niederreiter KEM
Public key
Vectors
Zinc
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:Li, Ling, Xing, and Yeo (LLXY) have proposed a code-based encryption scheme based on factoring in finite fields. The security of the scheme relies on both the decoding problem for <inline-formula> <tex-math notation="LaTeX">(q-1) </tex-math></inline-formula>-ary codes, and the Bounded Distance Decoding problem for the <inline-formula> <tex-math notation="LaTeX">\ell _{1} </tex-math></inline-formula>-norm in a family of lattices. On the negative side, we describe a Chosen Ciphertext Attack that breaks the claimed CCA protection proposed by LLXY. We also extend a previous cryptanalysis by Lapiha using decoding attacks, and argue that the May-Ozerov information set decoding attack is the most powerful decoding attack on the scheme. On the positive side, we streamline the description of the scheme and give simple algorithms to generate the public keys. We also give a Niederreiter version of the scheme that has smaller ciphertexts, and show how to correctly obtain a CCA secure Key Encapsulation Mechanism by using standard techniques.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2025.3573912