Practical Post-Quantum Signatures for Privacy

The transition to post-quantum cryptography has been an enormous challenge and effort for cryptographers over the last decade, with impressive results such as the future NIST standards. However, the latter has so far only considered central cryptographic mechanisms (signatures or KEM) and not more advanced ones, e.g., targeting privacy-preserving applications. Of particular interest is the family of solutions called blind signatures, group signatures and anonymous credentials, for which standards already exist, and which are deployed in billions of devices. Such a family does not have, at this stage, an efficient post-quantum counterpart although very recent works improved this state of affairs by offering two different alternatives: either one gets a system with rather large elements but a security proved under standard assumptions or one gets a more efficient system at the cost of ad-hoc interactive assumptions or weaker security models. Moreover, all these works have only considered size complexity without implementing the quite complex building blocks their systems are composed of. In other words, the practicality of such systems is still very hard to assess, which is a problem if one envisions a post-quantum transition for the corresponding systems/standards.