2023-08-09
Finding short integer solutions when the modulus Is small
Publication
Publication
Presented at the
43rd Annual International Cryptology Conference, CRYPTO 2023 (August 2023), Santa Barbara, CA, USA
We present cryptanalysis of the inhomogenous short integer solution (ISIS ) problem for anomalously small moduli q by exploiting the geometry of BKZ reduced bases of q-ary lattices. We apply this cryptanalysis to examples from the literature where taking such small moduli has been suggested. A recent work [Espitau–Tibouchi–Wallet–Yu, CRYPTO 2022] suggests small q versions of the lattice signature scheme Falcon and its variant Mitaka. For one small q parametrisation of Falcon we reduce the estimated security against signature forgery by approximately 26 bits. For one small q parametrisation of Mitaka we successfully forge a signature in 15 s.
| Additional Metadata | |
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| doi.org/10.1007/978-3-031-38548-3_6 | |
| Lecture Notes in Computer Science | |
| A Reduction Theory for Codes and Lattices in Cryptography | |
| 43rd Annual International Cryptology Conference, CRYPTO 2023 | |
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Ducas, L., Espitau, T., & Postlethwaite, E. W. (2023). Finding short integer solutions when the modulus Is small. In Advances in Cryptology (pp. 150–176). doi:10.1007/978-3-031-38548-3_6 |
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