View source for Generalised ISISf

The Generalised ISIS<sub>f</sub> assumption (GenISIS<sub>f</sub>) was introduced by Dubois, Klooß, Lai, and Woo in 2025.<ref>Dubois, A., Klooß, M., Lai, R.W. and Woo, I.K. [https://eprint.iacr.org/2025/356.pdf Lattice-based proof-friendly signatures from vanishing short integer solutions]. ''IACR International Conference on Public-Key Cryptography.'' Cham: Springer Nature Switzerland, 2025.</ref> As the name suggests, it is a generalisation of the ISISf assumption introduced in 2023.<ref name=":0">Bootle, J., Lyubashevsky, V., Nguyen, N.K. and Sorniotti, A. [https://eprint.iacr.org/2023/560.pdf A framework for practical anonymous credentials from lattices]. ''Annual International Cryptology Conference''. Cham: Springer Nature Switzerland, 2023.</ref> It removes two restrictions imposed by ISIS<sub>f</sub>, which enables reducing to GenISIS<sub>f</sub>. Furthermore, GenISIS<sub>f</sub> inherits the ISIS<sub>f</sub> framework to generically generate constructions for several primitives. 

== Formal Definition ==

=== GenISIS<sub>f</sub> ===
TODO

=== Interactive GenISISf ===
TODO

== Hardness of GenISIS<sub>f</sub> and its interactive version ==
TODO

== Constructions based on GenISIS<sub>f</sub> ==
Bootle et al.<ref name=":0" /> provide a framework to generically build the following constructions from any ''interactive'' ISIS<sub>f</sub> instance. As any ISIS<sub>f</sub> instance is also a GenISIS<sub>f</sub> instance, GenISIS<sub>f</sub> inherits this framework.

* Signatures<ref name=":0" />
* Group signatures<ref name=":0" />
* Blind signatures<ref name=":0" /><ref name=":1">Lyubashevsky, Vadim, Gregor Seiler, and Patrick Steuer. [https://eprint.iacr.org/2024/1846.pdf The LaZer library: Lattice-based zero knowledge and succinct proofs for quantum-safe privacy]. ''Proceedings of the 2024 on ACM SIGSAC Conference on Computer and Communications Security''. 2024.</ref>
* Anonymous credentials<ref name=":0" /><ref name=":1" />

== Related Assumptions ==

* [[ISISf|ISIS<sub>f</sub>]]
* [[One-More-ISIS]]
* [[Randomised One-More-ISIS]]

== References ==
<references />