I'm a mathematician with an interest in quantum computing and cryptography. Currently I work as a principal research engineer at Cloudflare, to make the Internet post-quantum secure. Previously I worked at PQShield, UCL and the digital security group of the RU.
Publications and notes
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State of the post-quantum Internet in 2025
published [blog]
PQC is a fast moving field. A lot has happened in the last 20 months. High time for an update to the 2024 overview, to take another look where we are with the migration and what to expect for the coming years.
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Keeping the Internet fast and secure: introducing Merkle Tree Certificates
published [blog]
Cloudflare is launching an experiment with Chrome to evaluate fast, scalable, and quantum-ready Merkle Tree Certificates, all without degrading performance or changing WebPKI trust relationships.
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Private SCT Auditing, Revisited
We revisit the problem of private SCT auditing given the recent advances in PIR and changes to the certificate transparency ecosystem.
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A look at the latest post-quantum signature standardization candidates
published [blog]
We take another look at the current landscape of post-quantum signature schemes, and share some relevant surprising statistics on the median number of bytes transferred over a connection on the web.
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The state of the post-quantum Internet
published [blog]
We take measure of where we are in the migration, and what to expect for the coming years.
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X-Wing: The Hybrid KEM You've been Looking For
We propose X-Wing, a concrete, simple and IND-CCA secure PQ/T hybrid KEM based on X25519 and ML-KEM.
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Post-Quantum Privacy Pass via Post-Quantum Anonymous Credentials
submitted [eprint · code · demo · slides (rwc2023)]
We show how to construct a practical post-quantum anonymous credential scheme.
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Merkle Tree Certificates
adopted [I-D]
Large post-quantum signatures force us to rethink the WebPKI. While we’re at it, we simplify transparency.
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NIST's Pleasant Post-Quantum Surprise
published [blog]
I discuss the impact on the Web of NIST’s choices for post-quantum algorithms.
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Sizing Up Post Quantum Signatures
How much room does TLS have for the big post-quantum signatures? We had a look at Cloudflare: it’s tight.
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A Concrete Treatment of Efficient Continuous Group Key Agreement via Multi-Recipient PKEs
accepted (CCS) [eprint · code]
We proposed chained CmPKE, a Continuous Group Key Agreement and their underlying efficient Post-Quantum Multi-Recipient KEMs based on Kyber, NTRU LPRime, Frodo and SIKE.
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A computer scientist's reconstruction of quantum theory
invited [eprint]
Are there nice assumptions on a category such that any such category must be a category of quantum types with quantum programs between them?
(more) -
Implementing and measuring KEMTLS
We compare performance of PQ KEMTLS against other TLS variants on the drand system.
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Don't throw your nonces out with the bathwater
short note [eprint]
We suggest a small change to the Dilithium signature scheme that allows reusing computation between aborted attempts for a speed-up in signing time.
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The three types of normal sequential effect algebras
We show that any normal SEA splits as the direct sum of a complete Boolean algebra, a convex normal SEA and a so-called almost-convex normal SEA.
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Sign in finite fields
short note [eprint]
We show that there is a consistent choice of square root in a finite field \(\mathbb{F}_{p^k}\) for odd prime \(p \neq 1\) and \(k\neq 0\) if and only if \(k\) is odd.
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Dichotomy between deterministic and probabilistic models in countably additive effectus theory
A non-trivial σ-effectus with normalization has as scalars either {0,1} or [0,1]. When states and predicates are separating, then it must embed into the category Boolean algebras (in the first case) and into the category of Banach order-unit spaces in the second case.
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Preservation of Equations by Monoidal Monads
It’s known that affine and relevant monads preserve respectively drop and dup equations. We prove a converse.
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A characterization of ordered abstract probabilities
We prove a Representation Theorem for \(\omega\)-complete effect monoids.
(more) -
The universal property of infinite direct sums in C*- and W*-categories
The title says it all.
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Pure maps between Euclidean Jordan Algebras
We propose a definition of purity for positive linear maps between Euclidean Jordan Algebras.
(more) -
Doctoral thesis: Dagger and Dilation in the Category of Von Neumann Algebras
awarded [arXiv]
A mathematical study of quantum computing, concentrating on two related, but independent topics.
(more)
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Picture-perfect Quantum Key Distribution
submitted [arXiv]
We give a new way to bound the security of QKD using only the diagrammatic behavior of complementary observables and essential uniqueness of purification for quantum channels.
(more)
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Solving Binary MQ with Grover's algorithm
We explicitly construct oracles to solve binary MQ, which is the underlying hard problem of many proposed post-quantum cryptographic schemes.
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Paschke Dilations
published [arXiv · EPTCS · video · slides]
We generalize Stinespring’s Dilation Theorem to arbitrary completely positive normal maps between von Neumann algebra’s.
(more) -
A universal property for sequential measurement
published [journal (JMP)]
We study the sequential product, the operation \(p * q = \sqrt{p} q \sqrt{p}\) on the set of effects of a von Neumann algebra that represents sequential measurement of first \(p\) and then \(q\). We give four axioms which completely determine the sequential product.
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An Introduction to Effectus Theory
done [arXiv]
Effectus theory is a new branch of categorical logic that aims to capture the essentials of quantum logic, with probabilistic and Boolean logic as special cases.
(more) -
Quotient–Comprehension Chains
A universal property for \( A \mapsto \sqrt{B} A \sqrt{B} \) appears in a chain of adjunctions.
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States of Convex Sets
published [preprint · LNCS · slides]
State spaces in probabilistic and quantum computation are convex sets, that is, Eilenberg–Moore algebras of the distribution monad. This article studies some computationally relevant properties of convex sets.
(more) -
Unordered tuples in Quantum Computation
published [preprint · EPTCS · video · slides]
The star-algebra \( M_2 \otimes M_2 \) models a pair of qubits. We show in detail that \( M_3 \oplus \mathbb{C} \) models an unordered pair of qubits. Then we use the late 19th century Schur-Weyl duality, to characterize the star-algebra that models an unordered n-tuple of d-level quantum systems.
(more) -
A Kochen-Specker system has at least 22 vertices
published [preprint · EPTCS · journal · data · sourcecode · video · slides]
A Kochen-Specker system has at least 22 vertices.
(more) -
Statman's Hierarchy Theorem
A simplification and slight extension of Statman’s Hierarchy Theorem.
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Sequential product on effect logics
done supervised by prof. Bart Jacobs [pdf]
An investigation of the sequential product on predicates in the framework of Jacobs.
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On effective undecidability and Post's problem
done supervised by dr. Wim Veldman [pdf · arXiv]
We introduce several notions of effective undecidability and show they are equivalent to previously investigated notions of completeness and creativity.