### Ciphertext-Only Attacks Against Compact-LWE Submitted to NIST PQC Project

LI Haoyu1,2,3, LIU Renzhang4, LIU Zhen1,3, PAN Yanbin1, XIE Tianyuan1,3

1. 1. Key Laboratory of Mathematics Mechanization, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; 2. State Key Laboratory of Cryptology, Beijing 100878, China; 3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China; 4. Westone Cryptologic Research Center, Westone Information Industry INC., Beijing 100070, China
• Received:2020-03-11 Revised:2020-08-18 Published:2022-06-20

LI Haoyu, LIU Renzhang, LIU Zhen, PAN Yanbin, XIE Tianyuan. Ciphertext-Only Attacks Against Compact-LWE Submitted to NIST PQC Project[J]. Journal of Systems Science and Complexity, 2022, 35(3): 1173-1190.

As a candidate of the standard of post-quantum cryptography for NIST, Liu, et al. submitted a new public-key encryption scheme Compact-LWE, whose structure is similar to LWE, but with different distribution of errors. They thought that the special error distribution would protect Compact-LWE from known lattice-based attacks. Furthermore, they recommended a set of small parameters to improve the efficiency of Compact-LWE and claimed it can offer 192-bit security. However, in this paper, the authors show that Compact-LWE is not secure under recommended parameters by presenting two ciphertext-only attacks. First, the authors show that the message can be recovered efficiently from the ciphertext. Then the authors go further to recover an equivalent private key efficiently from the public key by exploiting the special structure of Compact-LWE.
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