Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Lecture notes in computer science

Properties of Lattice Isomorphism as a Cryptographic Group Action

Benjamin Benčina, Alessandro Budroni, Jesús-Javier Chi-Domínguez, Mukul Kulkarni

Published Jan 1, 2024• 12 citations
Publisher
DOI
10.1007/978-3-031-62743-9_6

Related papers

Post-quantum Anonymous Signatures from the Lattice Isomorphism Group Action

Chris van Noorden, Paola de Perthuis

Lecture notes in computer science•Sep 26, 2026•0 citations

Cryptographic Group Actions and Applications

Navid Alamati, Luca De Feo, Hart William Montgomery +1 more

Lecture notes in computer science•Jan 1, 2020•125 citations

On Structure-Preserving Cryptography and Lattices

Dennis Hofheinz, Kristina Hostáková, Roman Langrehr +1 more

Lecture notes in computer science•Jan 1, 2024•0 citations

Don't Use It Twice: Reloaded! On the Lattice Isomorphism Group Action

Alessandro Budroni, Jesús-Javier Chi-Domínguez, Ermes Franch

Group actions have emerged as a powerful framework in post-quantum cryptography, serving as the foundation for various cryptographic primitives. The Lattice Isomorphism Problem (LIP) has recently gained attention as a promising hardness assumption for designing quantum-resistant protocols. Its formulation as a group action has opened the door to new cryptographic applications, including a commitment scheme and a linkable ring signature. In this work, we analyze the security properties of the LIP group action and present new findings. Specifically, we demonstrate that it fails to satisfy the weak unpredictability and weak pseudorandomness properties when the adversary has access to as few as three and two instances with the same secret, respectively. This significantly improves upon prior analysis by Budroni et al. (PQCrypto 2024). As a direct consequence of our findings, we reveal a vulnerability in the linkable ring signature scheme proposed by Khuc et al. (SPACE 2024), demonstrating that the hardness assumption underlying the linkable anonymity property does not hold.

IACR Communications in Cryptology•Jul 7, 2025•2 citations

Lattice-Based Cryptographic Constructions

S Zaky Mohamed

•Jul 26, 2026•0 citations

Graph States Under the Action of Local Clifford Group in Non-Binary Case

Mohsen Bahramgiri, Salman Beigi

Graph states are well-entangled quantum states that are defined based on a graph. Of course, if two graphs are isomorphic their associated states are the same. Also, we know local operations do not change the entanglement of quantum states. Therefore, graph states that are either isomorphic or equivalent under the local Clifford group have the same properties. In this paper, we first establish a bound on the number of graph states which are neither isomorphic nor equivalent under the action of local Clifford group. Also, we study graph states in non-binary case. We translate the action of local Clifford group, as well as measurement of Pauli operators, into transformations on their associated graphs. Finally, we present an efficient algorithm to verify whether two graph states, in non-binary case, are locally equivalent or not.

arXiv:quant-ph/0610267•Oct 31, 2006•27 citations
Group actions have emerged as a powerful framework in post-quantum cryptography, serving as the foundation for various cryptographic primitives. The Lattice Isomorphism Problem (LIP) has recently gained attention as a promising hardness assumption for designing quantum-resistant protocols. Its formulation as a group action has opened the door to new cryptographic applications, including a commitment scheme and a linkable ring signature. In this work, we analyze the security properties of the LIP group action and present new findings. Specifically, we demonstrate that it fails to satisfy the weak unpredictability and weak pseudorandomness properties when the adversary has access to as few as three and two instances with the same secret, respectively. This significantly improves upon prior analysis by Budroni et al. (PQCrypto 2024). As a direct consequence of our findings, we reveal a vulnerability in the linkable ring signature scheme proposed by Khuc et al. (SPACE 2024), demonstrating that the hardness assumption underlying the linkable anonymity property does not hold.
Graph states are well-entangled quantum states that are defined based on a graph. Of course, if two graphs are isomorphic their associated states are the same. Also, we know local operations do not change the entanglement of quantum states. Therefore, graph states that are either isomorphic or equivalent under the local Clifford group have the same properties. In this paper, we first establish a bound on the number of graph states which are neither isomorphic nor equivalent under the action of local Clifford group. Also, we study graph states in non-binary case. We translate the action of local Clifford group, as well as measurement of Pauli operators, into transformations on their associated graphs. Finally, we present an efficient algorithm to verify whether two graph states, in non-binary case, are locally equivalent or not.