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Abstract
The Tensor Isomorphism Problem (TIP) has been shown equivalent to the matrix code equivalence problem, making it an interesting candidate on which to build post-quantum cryptographic primitives. These hard problems have already been used in protocol development. One of these, MEDS, is currently in Round 1 of NIST’s call for additional post-quantum digital signatures.
In this work, we consider the TIP restricted to the orbits of a special class of tensors. The hardness of the decisional version of this problem is the foundation of a commitment scheme proposed by D’Alconzo, Flamini, and Gangemi (Asiacrypt 2023). We present polynomial-time algorithms for the decisional and computational versions of TIP for special orbits, which implies that the commitment scheme is not secure. The key observations of these algorithms are that these special tensors contain some low-rank points, and their stabilizer groups are not trivial.
With these new developments in the security of TIP in mind, we give a new commitment scheme based on the general TIP that is non-interactive, post-quantum, and statistically binding, making no new assumptions. Such a commitment scheme does not currently exist in the literature.
In this work, we consider the TIP restricted to the orbits of a special class of tensors. The hardness of the decisional version of this problem is the foundation of a commitment scheme proposed by D’Alconzo, Flamini, and Gangemi (Asiacrypt 2023). We present polynomial-time algorithms for the decisional and computational versions of TIP for special orbits, which implies that the commitment scheme is not secure. The key observations of these algorithms are that these special tensors contain some low-rank points, and their stabilizer groups are not trivial.
With these new developments in the security of TIP in mind, we give a new commitment scheme based on the general TIP that is non-interactive, post-quantum, and statistically binding, making no new assumptions. Such a commitment scheme does not currently exist in the literature.
Original language | English |
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Title of host publication | Advances in Cryptology – CRYPTO 2024 |
Subtitle of host publication | 44th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 18–22, 2024, Proceedings, Part I |
Editors | Leonid Reyzin, Douglas Stebila |
Publisher | Springer |
Pages | 141-173 |
Number of pages | 32 |
ISBN (Electronic) | 9783031683763 |
ISBN (Print) | 9783031683756 |
DOIs | |
Publication status | Published - 16 Aug 2024 |
Event | CRYPTO 2024 - Duration: 18 Aug 2024 → 22 Aug 2024 |
Publication series
Name | Lecture Notes in Computer Science |
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Publisher | Springer |
Volume | 14920 |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Conference
Conference | CRYPTO 2024 |
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Period | 18/08/24 → 22/08/24 |
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Post-Quantum Cryptography: a Cryptanalysis Approach
Petit, C. (Principal Investigator)
Engineering & Physical Science Research Council
1/10/21 → 30/09/26
Project: Research Councils