| 研究実績の概要 |
In FY 2023, we proposed a new modification to the Blum-Kalai-Widgerson (BKW) algorithm, commonly used to solve Learning Parity with Noise (LPN) problems and Learning With Errors (LWE) lattice problems. LPN and LWE form the foundation of many post-quantum (PQ) cryptographic schemes, and the performance of the BKW algorithm helps determine the security parameters of these schemes. Our modification enhances the precision of the sample filtering sub-procedure in the LPN oracle, reducing the number of samples needed to solve LPN problems compared to the original BKW algorithm. This suggests that the security parameters of current PQ cryptographic schemes based on LPN and LWE may be insufficient, and larger parameters might be required to ensure practical security.
In another research area, we introduced a new computational problem based on the tensor rank problem and proved it to be NP-hard, meaning even quantum computers cannot solve it in the hardest cases. We also proposed a new zero-knowledge identification scheme based on this problem, ensuring security against quantum adversaries, assuming the average case of the problem remains hard for quantum computers.
Finally, we developed a new framework for constructing post-quantum multi-signatures, resulting in a two-round multi-signature scheme with nearly tight security under a decisional computational problem assumption. We implemented this framework using a standardized elliptic curve. The nearly tight security allows for more flexibility in key size selection in ensuring practical security.
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