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2020 | OriginalPaper | Buchkapitel

Calamari and Falafl: Logarithmic (Linkable) Ring Signatures from Isogenies and Lattices

verfasst von : Ward Beullens, Shuichi Katsumata, Federico Pintore

Erschienen in: Advances in Cryptology – ASIACRYPT 2020

Verlag: Springer International Publishing

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Abstract

We construct efficient ring signatures (RS) from isogeny and lattice assumptions. Our ring signatures are based on a logarithmic OR proof for group actions. We instantiate this group action by either the CSIDH group action or an MLWE-based group action to obtain our isogeny-based or lattice-based RS scheme, respectively. Even though the OR proof has a binary challenge space and therefore requires a number of repetitions which is linear in the security parameter, the sizes of our ring signatures are small and scale better with the ring size N than previously known post-quantum ring signatures. We also construct linkable ring signatures (LRS) that are almost as efficient as the non-linkable variants. The isogeny-based scheme produces signatures whose size is an order of magnitude smaller than all previously known logarithmic post-quantum ring signatures, but it is relatively slow (e.g. 5.5 KB signatures and 79 s signing time for rings with 8 members). In comparison, the lattice-based construction is much faster, but has larger signatures (e.g. 30 KB signatures and 90 ms signing time for the same ring size). For small ring sizes our lattice-based ring signatures are slightly larger than state-of-the-art schemes, but they are smaller for ring sizes larger than \(N \approx 1024\).

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Vorheriges Kapitel B-SIDH: Supersingular Isogeny Diffie-Hellman Using Twisted Torsion

Nächstes Kapitel Radical Isogenies

We compare only signature sizes since, to the best of our knowledge, ours is the only post-quantum logarithmic (linkable) ring signature with an implementation.

We used the Dilithium III parameters, 168-bit seeds and commitment randomness, and a challenge space of size \(2^{168}\), which suffices to achieve NIST level II for low MAXDEPTH.

A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible.

To be accurate, we prove knowledge of \(s_I \in S_2 + S_3\), as we consider “relaxed” special soundness.

For simplicity, we will assume that N is a power of 2. If this is not the case we add additional dummy commitments to make the number of leaves a power of 2.

We note that the notion of collision in \(\mathcal {O}\) may seem non-standard at this point since the truth table of \(\mathcal {O}\) is typically filled in one at a time when queried so it is not clear who is querying the \(\mathcal {O}\) right now. However, we observe that this non-standard notion suffices for our (linkable) ring signature application w.l.o.g.

To be accurate, we prove knowledge of \(s_I \in S_2 + S_3\), as we consider “relaxed” special soundness.

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Titel: Calamari and Falafl: Logarithmic (Linkable) Ring Signatures from Isogenies and Lattices
verfasst von: Ward Beullens
Shuichi Katsumata
Federico Pintore
Verlag: Springer International Publishing
Buch: Advances in Cryptology – ASIACRYPT 2020
Print ISBN: 978-3-030-64833-6

Electronic ISBN: 978-3-030-64834-3

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-64834-3_16

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