Paper 2024/1578
Quantum Group Actions
Abstract
In quantum cryptography, there could be a new world, Microcrypt, where
cryptography is possible but one-way functions (OWFs) do not exist. Although many fundamental primitives and useful applications have been found in Microcrypt, they lack ``OWFs-free'' concrete hardness assumptions on which they are based. In classical cryptography, many hardness assumptions on concrete mathematical problems have been introduced, such as the discrete logarithm (DL) problems or the decisional Diffie-Hellman (DDH) problems on concrete group structures related to finite fields or elliptic curves. They are then abstracted to generic hardness assumptions such as the DL and DDH assumptions over group actions. Finally, based on these generic assumptions, primitives and applications are constructed. The goal of the present paper is to introduce several abstracted generic hardness assumptions in Microcrypt, which could connect the concrete mathematical hardness assumptions with applications. Our assumptions are based on a quantum analogue of group actions. A group action is a tuple
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- quantum cryptographygroup actionsmicrocrypt
- Contact author(s)
-
tomoyuki morimae @ yukawa kyoto-u ac jp
keita xagawa @ tii ae - History
- 2024-10-08: approved
- 2024-10-07: received
- See all versions
- Short URL
- https://ia.cr/2024/1578
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2024/1578, author = {Tomoyuki Morimae and Keita Xagawa}, title = {Quantum Group Actions}, howpublished = {Cryptology {ePrint} Archive, Paper 2024/1578}, year = {2024}, url = {https://eprint.iacr.org/2024/1578} }