Abstract
On the one hand, the web needs to be secured from malicious activities such as bots or DoS attacks; on the other hand, such needs ideally should not justify services tracking people’s activities on the web. Anonymous tokens provide a nice tradeoff between allowing an issuer to ensure that a user has been vetted and protecting the users’ privacy. However, in some cases, whether or not a token is issued reveals a lot of information to an adversary about the strategies used to distinguish honest users from bots or attackers.
In this work, we focus on designing an anonymous token protocol between a client and an issuer (also a verifier) that enables the issuer to support its fraud detection mechanisms while preserving users’ privacy. This is done by allowing the issuer to embed a hidden (from the client) metadata bit into the tokens. We first study an existing protocol from CRYPTO 2020 which is an extension of Privacy Pass from PoPETs 2018; that protocol aimed to provide support for a hidden metadata bit, but provided a somewhat restricted security notion. We demonstrate a new attack, showing that this is a weakness of the protocol, not just the definition. In particular, the metadata bit hiding is weak in the setting where the attacker can redeem some tokens and get feedback on whether the bit extraction succeeded.
We then revisit the formalism of anonymous tokens with private metadata bit, consider the more natural notion, and design a scheme which achieves it. In order to design this new secure protocol, we base our construction on algebraic MACs instead of PRFs. Our security definitions capture a realistic threat model where adversaries could, through direct feedback or side channels, learn the embedded bit when the token is redeemed. Finally, we compare our protocol with one of the CRYPTO 2020 protocols. We obtain 20% more efficient performance.
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Notes
- 1.
We provide a more precise analysis in the full version of this paper [12].
- 2.
[5] addresses this by making non-standard assumptions about the extraction properties of Fiat-Shamir.
- 3.
A protocol with this m option is available in the full version of this paper [12].
- 4.
In the common reference string model, the CRS \(\textsf{cpp}\) comes with a trapdoor \(\textsf{td}\).
- 5.
In their \(\textsf{OMUF}\) security definition, the first condition says that both \(q_0 \le \ell \) AND \(q_1 \le \ell \) where \(q_b\) is the number of oracle queries with bit b. Suppose, the adversary made 10 queries with \(b=0\) (\(q_0 = 10\)) and 1000 queries with \(b=1\) (\(q_1 = 1000\)). If the adversary forges 11 tokens with \(b = 0\), for this to succeed as a forgery, \(\ell \) must be at least 1000. If it is not, this does not succeed.
- 6.
For protocols with no public metadata m, the variables \(n_{b,m}\) in the game shall be changed to \(n_b\) and input m shall be removed from \(\textsf{AT}\) algorithms.
- 7.
\(\textsf{PMBT}\) code is available at https://github.com/mmaker/anonymous-tokens.
- 8.
In this count, we took the computation of \((1-b)C_y\) as free. Furthermore, the computation of \(r_dV\) and \(a_dV\) are done twice but count for a single operation.
- 9.
By setting \(t_S=\textsf{Hash}(U)\), the issuer would not have to send \(t_S\) any longer and save the transmission of one \(\mathbb {Z}_p\) element.
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Acknowledgements
We heartily thank Greg Zaverucha, Michele Orrù, and Nirvan Tyagi for the insightful discussions and fruitful comments on the early version of the paper. We are also very thankful to Kim Laine, Radames Cruz Moreno, and Wei Dai for their valuable time and help with the implementation of the protocols and benchmarks in Rust.
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Chase, M., Durak, F.B., Vaudenay, S. (2023). Anonymous Tokens with Stronger Metadata Bit Hiding from Algebraic MACs. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14082. Springer, Cham. https://doi.org/10.1007/978-3-031-38545-2_14
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