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2020 | OriginalPaper | Buchkapitel

Bringing Order to Chaos: The Case of Collision-Resistant Chameleon-Hashes

verfasst von : David Derler, Kai Samelin, Daniel Slamanig

Erschienen in: Public-Key Cryptography – PKC 2020

Verlag: Springer International Publishing

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Abstract

Chameleon-hash functions, introduced by Krawczyk and Rabin at NDSS 2000, are trapdoor collision-resistant hash-functions parametrized by a public key. If the corresponding secret key is known, arbitrary collisions for the hash function can be efficiently found. Chameleon-hash functions have prominent applications in the design of cryptographic primitives, such as lifting non-adaptively secure signatures to adaptively secure ones. Recently, this primitive also received a lot of attention as a building block in more complex cryptographic applications ranging from editable blockchains to advanced signature and encryption schemes.

We observe that in latter applications various different notions of collision-resistance are used, and it is not always clear if the respective notion does really cover what seems intuitively required by the application. Therefore, we revisit existing collision-resistance notions in the literature, study their relations, and—using the example of the recent redactable blockchain proposals—discuss which practical impact different notions of collision-resistance might have. Moreover, we provide a stronger, and arguably more desirable, notion of collision-resistance than what is known from the literature. Finally, we present a surprisingly simple and efficient black-box construction of chameleon-hash functions achieving this strong notion.

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Vorheriges Kapitel Constraining and Watermarking PRFs from Milder Assumptions

Nächstes Kapitel Concretely-Efficient Zero-Knowledge Arguments for Arithmetic Circuits and Their Application to Lattice-Based Cryptography

The requirement for an invertible encoding into the group introduces an enormous efficiency penalty, and thus their instantiation is incomplete. Moreover, it is possible that their schemes do meet our stronger definition of full collision-resistance, but we neither prove nor disprove this statement here.

We note that the randomness r is also sometimes called “check value” [4].

In the case \((h'^*, m'^*)\) is the new hash/message pair, simply switch names.

A slightly stronger notion has been proposed by Zhang in [46] where the adversary sees a hash on a random message and is then given a single collision on a message of its choice. We do not cover this notion here as it seems to be tailored to the specific applications in [46] and all notions stronger than \(\mathsf {W\text {-}CollRes}\) considered here cover more general cases.

Lifting this definition to also cover those parameters is straightforward.

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Titel: Bringing Order to Chaos: The Case of Collision-Resistant Chameleon-Hashes
verfasst von: David Derler
Kai Samelin
Daniel Slamanig
Verlag: Springer International Publishing
Buch: Public-Key Cryptography – PKC 2020
Print ISBN: 978-3-030-45373-2

Electronic ISBN: 978-3-030-45374-9

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-45374-9_16

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