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Proceeding of International Conference
Yuri Lucas Direbieski, Hiroki Tanioka, Kenji Matsuura, Hironori Takeuchi, Masahiko Sano, Tetsushi Ueta, Security Impact Analysis of Degree of Field Extension in Lattice Attacks on Ring-LWE Problem, IEEE Computer Society, COMPSAC 2023 Workshop: The 1st IEEE International Workshop on Data Science & Machine Learning for Cybersecurity, IoT & Digital Forensics (DSML), pp.366-377, Turin, June 2023.
Abstract: Modern information communications use cryptography to keep the contents of communications confidential. RSA (RivestShamirAdleman) cryptography and elliptic curve cryptography, which are public-key cryptosystems, are widely used cryptographic schemes. However, it is known that these cryptographic schemes can be deciphered in a very short time by Shors algorithm when a quantum computer is put into practical use. Therefore, several methods have been proposed for quantum computer-resistant cryptosystems that cannot be cracked even by a quantum computer. A simple implementation of LWE-based lattice cryptography based on the LWE (Learning With Errors) problem requires a key length of O(n2) to ensure the same level of security as existing public-key cryptography schemes such as RSA and elliptic curve cryptography. In this paper, we attacked the Ring-LWE (RLWE) scheme, which can be implemented with a short key length, with a modified LLL (Lenstra-Lenstra-Lova sz) basis reduction algorithm and investigated the trend in the degree of field extension required to generate a secure and small key. Results showed that the lattice-based cryptography may be strengthened by employing Cullen or Mersenne prime numbers as the degree of field extension.

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Contact address: ueta @