Cryptographic Group Actions and Applications

Alamati, Navid; Feo, Luca De; Montgomery, Hart; Patranabis, Sikhar

doi:10.1007/978-3-030-64834-3_14

Cited by 75 publications

(39 citation statements)

References 68 publications

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“…Observe that all the requirements in the previous definitions lead to an efficient (and then, effective) use of the action in a protocol. In order to use them in cryptography we need some computational assumptions, as defined in [3]. With P[A] we denote the probability of the event A.…”

Section: Cryptographic Assumptionsmentioning

confidence: 99%

“…In [3], they define concepts of one-way function and weakly unpredictable and weakly pseudorandom permutations. To ease the notation, we directly define these concepts in terms of group actions.…”

Section: Cryptographic Assumptionsmentioning

confidence: 99%

“…In many of these applications is required an abelian group, however in this work we consider the generic case. An overview is given in [3].…”

Section: Cryptographic Assumptionsmentioning

confidence: 99%

“…Group Actions. Cryptographic Group Actions (CGA) were introduced by Almati et al [3] in 2020 and, under the name of Hard Homogeneous Spaces by Couveignes [11] in 2006. They are a powerful tool to design cryptographic protocols.…”

Section: Introductionmentioning

confidence: 99%

“…This work. We introduce some worst-case problems modelling computational assumptions related to group actions from [3]: by their nature, these assumptions cover the average-case view of these problems. We show that, if such problems are NP-hard, then some widely believed complexity assumptions fall.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Note on the Hardness of Problems from Cryptographic Group Actions

D'Alconzo¹

2022

Preprint

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Given a cryptographic group action, we show that the Group Action Inverse Problem (GAIP) and other related problems cannot be NP-hard unless the Polynomial Hierarchy collapses. We show this via random self-reductions and the design of interactive proofs. Since cryptographic group actions are the building block of many security protocols, this result serves both as an upper bound on the worst-case complexity of some cryptographic assumptions and as proof that the hardness in the worst and in the average case coincide. We also point out the link with Graph Isomorphism and other related NP intermediate problems.

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Section: Cryptographic Assumptionsmentioning

confidence: 99%

Section: Cryptographic Assumptionsmentioning

confidence: 99%

“…In many of these applications is required an abelian group, however in this work we consider the generic case. An overview is given in [3].…”

Section: Cryptographic Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Note on the Hardness of Problems from Cryptographic Group Actions

D'Alconzo¹

2022

Preprint

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Compact, Efficient and UC-Secure Isogeny-Based Oblivious Transfer

Lai

Galbraith

Guilhem

2021

Lecture Notes in Computer Science

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LESS-FM: Fine-Tuning Signatures from the Code Equivalence Problem

Barenghi

Biasse

Persichetti

et al. 2021

Lecture Notes in Computer Science

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Code-based cryptographic schemes are highly regarded among the quantum-safe alternatives to current standards. Yet, designing codebased signatures using traditional methods has always been a challenging task, and current proposals are still far from the target set by other postquantum primitives (e.g. lattice-based). In this paper, we revisit a recent work using an innovative approach for signing, based on the hardness of the code equivalence problem. We introduce some optimizations and provide a security analysis for all variants considered. We then show that the new parameters produce instances of practical interest.Recently, cryptographic group actions came into the spotlight again, with several improvements over the original work of Couveignes [10] and Stolbunov [20]. This enabled many improvements in the field of isogeny-based cryptography, including primitives that were previously missing in the post-quantum scenario such as static-static key exchange protocols.

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Cryptographic Group Actions and Applications

Cited by 75 publications

References 68 publications

A Note on the Hardness of Problems from Cryptographic Group Actions

A Note on the Hardness of Problems from Cryptographic Group Actions

Compact, Efficient and UC-Secure Isogeny-Based Oblivious Transfer

LESS-FM: Fine-Tuning Signatures from the Code Equivalence Problem

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