Abstract
We propose a design for a privacy-friendly method of age restriction in e-commerce that is aligned with the principle of subsidiarity. The design is presented as an extension of a privacy-friendly payment protocol with a zero-knowledge scheme that cryprographically augments coins for this purpose. Our scheme enables buyers to prove to be of sufficient age for a particular transaction without disclosing it. Our modification preserves the privacy and security properties of the payment system such as the anonymity of minors as buyers as well as unlinkability of transactions. We show how our scheme can be instantiated with ECDSA as well with a variant of EdDSA, respectively, and how it can be integrated with the GNU Taler payment system. We provide formal proofs and implementation of our proposal. Key performance measurements for various CPU architectures and implementations are presented.
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Notes
- 1.
Upper indices on variables are not exponents.
- 2.
Using ECDSA is also not required: we have created an instantiation based on Edx25519 (Appendix A); ECDSA is merely one that permits a concise description.
- 3.
- 4.
The private key of the master public key must simply be deleted after creation, as it would enable minors to defeat the cut-and-choose protocol. Deriving commitments from the master key implies that computing the private key corresponding to the commitment is equivalent of solving DLOG for the master public key.
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A A Edx25519
A A Edx25519
Edx25519 is a signature scheme based on Ed25519 [Ber+12], but allows for derivation of private and public keys, independently, from existing ones. Private keys in Edx25519 are pairs (a, b) of 32 byte each. Initially they correspond to the result of the expansion and clamping in EdDSA. The scheme is as follows, in pseudo-code:
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Kesim, Ö., Grothoff, C., Dold, F., Schanzenbach, M. (2022). Zero-Knowledge Age Restriction for GNU Taler. In: Atluri, V., Di Pietro, R., Jensen, C.D., Meng, W. (eds) Computer Security – ESORICS 2022. ESORICS 2022. Lecture Notes in Computer Science, vol 13554. Springer, Cham. https://doi.org/10.1007/978-3-031-17140-6_6
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