TY - GEN
T1 - Dynamic Self-dual DeepBKZ Lattice Reduction with Free Dimensions
AU - Nakamura, Satoshi
AU - Ikematsu, Yasuhiko
AU - Yasuda, Masaya
N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Number 16H02830.
Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
PY - 2021
Y1 - 2021
N2 - Lattice basis reduction is a mandatory tool to solve lattice problems such as the shortest vector problem (SVP), whose hardness assures the security of lattice-based cryptography. The most famous reduction is the celebrated algorithm by Lenstra-Lenstra–Lovász (LLL), and the block Korkine–Zolotarev (BKZ) is its blockwise generalization. At present, BKZ and its variants such as BKZ 2.0 are a de facto standard reduction algorithm to estimate the security level of lattice-based cryptosystems. Recently, DeepBKZ was proposed as a mathematical improvement of BKZ, in which LLL with deep insertions (DeepLLL) is called as a subroutine alternative to LLL. In this paper, we develop a new self-dual variant of DeepBKZ to obtain a reduced basis. Different from conventional self-dual algorithms, we select suitable free dimensions to reduce primal and dual lattice bases in our variant. We also report experimental results to compare our self-dual DeepBKZ with primal BKZ and DeepBKZ for several random lattice bases.
AB - Lattice basis reduction is a mandatory tool to solve lattice problems such as the shortest vector problem (SVP), whose hardness assures the security of lattice-based cryptography. The most famous reduction is the celebrated algorithm by Lenstra-Lenstra–Lovász (LLL), and the block Korkine–Zolotarev (BKZ) is its blockwise generalization. At present, BKZ and its variants such as BKZ 2.0 are a de facto standard reduction algorithm to estimate the security level of lattice-based cryptosystems. Recently, DeepBKZ was proposed as a mathematical improvement of BKZ, in which LLL with deep insertions (DeepLLL) is called as a subroutine alternative to LLL. In this paper, we develop a new self-dual variant of DeepBKZ to obtain a reduced basis. Different from conventional self-dual algorithms, we select suitable free dimensions to reduce primal and dual lattice bases in our variant. We also report experimental results to compare our self-dual DeepBKZ with primal BKZ and DeepBKZ for several random lattice bases.
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U2 - 10.1007/978-981-15-8061-1_30
DO - 10.1007/978-981-15-8061-1_30
M3 - Conference contribution
AN - SCOPUS:85098141238
SN - 9789811580604
T3 - Advances in Intelligent Systems and Computing
SP - 377
EP - 391
BT - Proceedings of the Sixth International Conference on Mathematics and Computing - ICMC 2020
A2 - Giri, Debasis
A2 - Buyya, Rajkumar
A2 - Ponnusamy, S.
A2 - De, Debashis
A2 - Adamatzky, Andrew
A2 - Abawajy, Jemal H.
PB - Springer Science and Business Media Deutschland GmbH
T2 - 6th International Conference on Mathematics and Computing, ICMC 2020
Y2 - 23 September 2020 through 25 September 2020
ER -