I'm Thomas Espitau - エスピト トマ- and I am a senior researcher at PQShield.

I pursued my Ph.D. in algorithmic number theory at Sorbonne University in Paris, advised by prof. Antoine Joux and prof. Pierre-Alain Fouque. I then joined the research labs of NTT in Tokyo, Japan.

I am an avid freeride skier and surfer. You can probably find me around 東浪 and 一宮's breaks during typhoons or in Hakuba valley or Hokkaido in winter.

PQShield is hiring !

Have a look at the careers webpage on PQShield's website. We are also looking for excellent permanent as well as PhD/post-doctoral researchers to work within our research team. Contact me directly if you are interested, fundings are available. I am also looking for very talented interns (M2 or PhD students). Drop me a line with your CV and background if you are interested.

Research Interests

Geometry of numbers and lattices
  • Theta function of lattices
  • Discrete geometry
  • Arakelov theory on F1
(Algorithmic) Number theory
  • Reduction of vector bundles over arithmetic curves curves
  • Class group computation
  • Effective Arakelov theory
  • Lattice-based cryptography
  • Statistical learning and cryptanalysis
  • Secure and efficient implementation
Program verification
  • Verification of probabilistic programs
  • Coupling-based techniques
  • Relational methods

Selected works           All Publications (via Scholar)

Mitaka (三鷹): A Simpler, Parallelizable, Maskable Variant of Falcon

We describe the 三鷹 signature scheme: a new hash-and-sign scheme over NTRU lattices which can be seen as a variant of NIST finalist FALCON. It achieves comparable efficiency but is considerably simpler, online/offline, and easier to parallelize and protect against side- channels, thus offering significant advantages from an implementation standpoint. It is also much more versatile in terms of parameter selection..

On Gaussian sampling, smoothing parameter and application to signatures

We present a general framework for polynomial-time lattice Gaussian sampling. It revolves around a systematic study of the discrete Gaussian measure and its samplers under extensions of lattices; we first show that given lattices Λ′ ⊂ Λ we can sample efficiently in Λ if we know how to do so in Λ′ and the quotient Λ/Λ′, regardless of the primitivity of Λ′. As a direct applications, we tackle the problem of domain extension and restriction for sampling and propose a sampler tailored for lattice filtrations, which can be seen as a broad generalization of the celebrated Klein’s sampler.

The nearest-colattice algorithm: time-approximation tradeoff for approx-CVP

We exhibit a hierarchy of polynomial time algorithms solving approximate variants of the Closest Vector Problem. Our contributions is on the one hand a heuristic algorithm achieving the same distance as HSVP algorithms, and on the other hand a proven reduction from approximating the closest vector with a factor \(\approx n^{\frac32}\beta^{\frac{3n}{2\beta}}\) to the Shortest Vector Problem in dimension \(\beta\).

Algebraic and euclidean lattices: optimal lattice reduction and beyond

We introduce a framework for polynomial time reduction of lattices over number fields, leveraging their recursive and symplectic structures.
Implementation page Talk at Simons Institute

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