Polynomial Lattices for the BIKE Cryptosystem
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912918821404672 |
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| author | Schaller, Michael |
| author_facet | Schaller, Michael |
| contents | In this paper we introduce a rank $2$ lattice over a polynomial ring arising from the public key of the BIKE cryptosystem. The secret key is a sparse vector in this lattice. We study properties of this lattice and generalize the recovery of weak keys from "Weak keys for the quasi-cyclic MDPC public key encryption scheme". In particular, we show that they implicitly solved a shortest vector problem in the lattice we constructed. Rather than finding only a shortest vector, we obtain a reduced basis of the lattice which makes it possible to check for more weak keys. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23641 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polynomial Lattices for the BIKE Cryptosystem Schaller, Michael Cryptography and Security 11T71, 11H71, 94A60, 94B15, 94B75 In this paper we introduce a rank $2$ lattice over a polynomial ring arising from the public key of the BIKE cryptosystem. The secret key is a sparse vector in this lattice. We study properties of this lattice and generalize the recovery of weak keys from "Weak keys for the quasi-cyclic MDPC public key encryption scheme". In particular, we show that they implicitly solved a shortest vector problem in the lattice we constructed. Rather than finding only a shortest vector, we obtain a reduced basis of the lattice which makes it possible to check for more weak keys. |
| title | Polynomial Lattices for the BIKE Cryptosystem |
| topic | Cryptography and Security 11T71, 11H71, 94A60, 94B15, 94B75 |
| url | https://arxiv.org/abs/2507.23641 |