The highest priorities for the transition to post-quantum cryptography are the basic building blocks of authenticated key-agreement protocols such as TLS. Without these building blocks in place, secure communication on the Internet will not be possible once cryptographically relevant quantum computers come online. However, today we rely on quantum-vulnerable cryptography for much more than TLS. Privacy Pass is a protocol used by site operators like Cloudflare to help protect applications from abuse. One way we do this is by rate limiting individual clients so that no one client consumes too many of the site’s resources. Normally this involves some combination of friction or loss of privacy for users: CAPTCHAs or other challenges to moderate traffic, along with accounts and fingerprinting to identify traffic. Privacy Pass was designed to avoid this tradeoff between friction and privacy. The basic idea is that a client gets issued a number of tokens , which they can redeem in exchange for access to the site. Crucially, each token is unlinkable to the client it was issued to, ensuring the client can use the site as they always had without sacrificing privacy. With 10 years of deployment experience under our belts — using Privacy Pass for applications such as privacy proxies (like iCloud Private Relay) and relays (like Privacy Gateway) — we, along with others , are collaborating to bring the next generation of this technology to the web. One of our goals is to develop more sophisticated tools for managing agentic traffic that would otherwise consume too many resources and degrade performance for human visitors. Another goal is to foster a more open ecosystem by making it easier for more types of clients to participate. Achieving these goals requires developing new capabilities beyond what Privacy Pass offers today. Given the trajectory, in this post we look at the prospects for post-quantum. In fact, we’re in better shape than one might think. Privacy Pass still relies on classical cryptography, like RSA and elliptic curves. This means that a quantum attacker will be able to forge tokens at will and use them to bypass whatever security mechanism the site operator wants to implement (such as rate limiting). On the other hand, Privacy Pass is unconditionally private, meaning no attacker, quantum or not, can link the redemption of a token to its issuance. What’s more, the new capabilities we’re developing for this new generation of private authentication technology can and will be instantiated in a way that upholds the same guarantee: your interaction remains private even after Q-day. This gives us a little breathing room, but we will need an alternative soon. This is an active area of research that has made significant strides in recent years. Still, just as is the case with other aspects of the transition, the primary challenge is the sheer size of post-quantum alternatives: ML-DSA-44 signatures are a whopping 2,420 bytes, while ECDSA-P256 signatures are just 64 bytes. And there’s not much hope for drop-in replacements any time soon. Just as for TLS, we’ll have to settle for primitives with higher cost and re-engineer our systems to bear this cost . But what will those primitives be? In this post, we’ll explore one potential future for post-quantum privacy on the web, made possible by a recent breakthrough in the design of blind signatures. What we need to build: a brief look at MOLE
Let’s start with an overview of this new technology, which is presently called MOLE ("Moderation Of unLinkable Endorsements"). We’ll have much more to say about MOLE later on, but for now we’ll highlight the details that are most relevant to cryptography. One of the core components of Privacy Pass is a blind signature scheme, which allows a client to obtain a signature under an issuer’s secret key without revealing to the issuer the message that it signed. The client can then reveal the message and blind signature later on without linking the signature to its issuance. One type of Privacy Pass token consists of the message and blindly issued signature. To verify the token, the verifier needs the issuer’s public key, and so necessarily learns the identity of the issuer. Thus while these tokens protect the identity of the client, they don’t protect the identity of the issuer. Of course, this is exactly what we want for some use cases. The identity of the issuer tells us something about what type of client is connecting to our edge, a signal we use to make decisions in some of our products and for some of our customers. For instance, a client might use a token issued by one of our customers to prove it is authorized to use the customer’s VPN product. However, for many use cases, this is more information than we actually need to make a decision to grant a client access to a resource. Normally we only care that the token was issued by some entity we trust. In fact, MOLE takes this a step further: the token should hide the identity of the issuer altogether so that we can’t treat tokens differently based on who issued them. This guarantees equal treatment regardless of the type of client, making it easier for more clients to participate. This issuer-hiding property is achieved through a new object called an endorsement . An endorsement is issued by an anchor and redeemed by a moderator . Before redemption, the client and moderator agree on an anchor set , the public keys of the anchors trusted by the moderator. During redemption, the client proves it was issued an endorsement by one of the anchors in the anchor set without revealing which one. Upon acceptance, the moderator issues the client the MOLE credential it will use to moderate the client’s interaction with the site. An endorsement can take many forms, but its key property is that it can be redeemed while hiding the identity of the anchor that issued it. There will also be many types of credentials, but because they’re intended to be used by a particular moderator, they needn’t be anchor-hiding or even publicly verifiable. This means that everything from blind signatures to anonymous credit tokens or anonymous rate-limited credentials can be used to instantiate MOLE credentials. Now that we have a sense of what we’re building, let’s look at our options for post quantum. A feast of cryptography
When designing cryptographic protocols, adaptability and efficiency are often in tension. Sometimes we know exactly what we want to build and can tailor a construction for that purpose; but the more we tailor the protocol for that use case, the harder it becomes to adapt that construction to a different use case. Adaptability is essential for a system like MOLE. We’re not just building one kind of credential system, but many. And the types of credentials we need are likely to change over time, especially on the web where we must constantly adapt to new traffic patterns and attacker behavior. To keep up, we need a set of building blocks that can be composed together into different protocols to meet different requirements. Most of the post-quantum cryptographic schemes in wide use today come from larger families of constructions, but have been tuned for their particular application. ML-DSA is a good example here: the cryptographic framework from which this scheme was derived can be used to build a variety of things, but to make ML-DSA as compact as possible, its parameters have been carefully tailored to build an efficient and secure digital signature scheme. However, the same parameters would not necessarily be secure for other use cases. We have come to view this as the central challenge for post-quantum anonymous credentials: to decouple parameter selection from protocol design . Classical credential systems take this for granted: for the most part, protocol designers don’t need to think about the parameters of the elliptic curve they’re using, allowing even non-experts in the design of elliptic curve cryptography to build useful things with it. Unfortunately, designing efficient post-quantum credentials still requires an enormous amount of expertise . This situation seems to have changed, however. Earlier this year, we saw a breakthrough that represents a potential sea change for anonymous credentials. VOLE-in-the-Head
The roots of this breakthrough go back several years. We’ll pick up the story three years ago, with the VOLE-in-the-Head (VOLEitH) zero-knowledge proof system ( Baum et al. , Crypto 2023 ). A zero-knowledge proof system allows one to prove knowledge of a hidden witness, satisfying some public statement while keeping the witness private. For example, a zero-knowledge proof can be used to prove knowledge of an AES key K for which Y=AES(K,X) , where X,Y are public. This proof can be transformed into a digital signature whose security reduces to the security of AES, with X,Y as the public key and K as the secret key. This is exactly the FAEST digital signature, a candidate in NIST’s ongoing signature competition . Compared to many contemporary proof systems, VOLEitH is relatively simple to understand and implement securely. VOLE stands for "Vector Oblivious Linear Evaluation" and is an interactive technique that gives two parties correlated random values. These correlations act like authentication tags, allowing the verifier to check that a computation on the hidden witness was performed correctly. In VOLEitH, the prover prepares locally what the two parties would normally generate together — hence “in the head” — then commits to those values and uses the Fiat-Shamir transformation (a widely used tool in cryptography) to select the parts the verifier checks. This step turns the interactive VOLE process into a non-interactive zero-knowledge proof. Apart from its simplicity, VOLEitH is a fairly unremarkable proof system. It’s not succinct in the way many other proof systems are: its proofs are asymptotically linear in the size of the witness and the arithmetic complexity of the statement being proved. However, VOLEitH is concretely very efficient for a particular type of statement, namely one that can be expressed as a set of equations over small binary fields. One example is the relation Y=AES(K,X) we just discussed. We don’t normally think of AES as a set of equations, but many of its computations are designed around arithmetic in GF(2 8 ), a field whose elements are single bytes. FAEST proofs for this statement are only about 4KB (NIST Round 3, 128s). Another example is the KuMQuat signature scheme, in which the signer proves an instance of the Multivariate Quadratic (MQ) problem. Here we’re given a system of random, quadratic equations of multiple variables over a small field, like GF(2 8 ). Mathematically, this MQ map P looks something like P(s) = (s T A 1 s + b 1 s,…,s T A m s + b m s) where s and each b i are length n vectors and each A i is an n-by-n matrix. Given P,P(s) for random s, the MQ problem is to find s. We call it quadratic because we multiply the elements of s by itself. The MQ problem is believed to be hard to solve even for a quantum computer. But because P is made up of quadratic equations, proving knowledge of a solution with VOLEitH is fairly cheap, yielding KuMQuat signatures as small as 2. 6KB. When compared to other post-quantum signatures like ML-DSA or FN-DSA, these numbers don’t look especially impressive. But how VOLEitH compares to other schemes in a particular category of constructions is beside the point. For MOLE, we’ll need to strike a balance between performance and the ability to build many types of credential systems. To that end, we need one more ingredient. Multivariate signatures
Another way to build signatures from MQ maps involves embedding some additional mathematical structure into the map. In the Unbalanced Oil and Vinegar (UOV) signature scheme, the public key is an MQ map P , and a signature is a vector s satisfying P(s) = t , where t is obtained by hashing and salting the message to be signed. The secret key for this signature scheme is a trapdoor for P with which the signer can derive solutions to the MQ equations. The trapdoor reveals to the signer a hidden partitioning of the variables of each quadratic equation into “oil” and “vinegar” variables. Oil variables are never multiplied by one another, so fixing the vinegar values turns the equations into a linear system that the signer can solve for the oil values. In the public key, oil and vinegar variables are mixed together in a way that hides this structure in the map. UOV is also a candidate in NIST’s ongoing signature standardization effort. It has one of the smallest signatures among the candidates, at just 135 bytes. The trade-off is that it has the largest public keys, at 46. 6KB. MAYO is another multivariate candidate with much smaller public keys, at the cost of slightly larger signatures. The key thing to take away here is that the arithmetic complexity of evaluating a UOV (or MAYO) signature is comparable to evaluating an MQ instance. Both are public quadratic maps over small binary fields, making them a good fit for VOLEitH. This brings us to the breakthrough. Blind signatures from VOLE-in-the-Head and UOV
Earlier this year, a blind signature called PoMFRIT was published ( Baum et al. , USENIX Security 2026 ) that achieved what at the time was a record for candidate post-quantum constructions: 6…