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// Cryptography and Mathematics Researcher (Ph.D. in Mathematics)

Luca Dall'Ava

I am a researcher in Mathematics and Cryptography working as a Cryptography Researcher at ICME Labs focusing on post-quantum cryptography (at the interesection of cryptography and AI security) working on lattice- and isogeny-based approaches to folding schemes and zero-knowledge.

Luca Dall'Ava

Somewhere in Italy, 2025
May 2026

I'll be attending zkSummit14 in Rome, Italy (May 7th 2026).

May 2026

I'll be attending ZKProof 8 in Rome, Italy (May 9th-10th 2026).

01 — About

I am a researcher in Mathematics and Cryptography working as a Cryptography Researcher at ICME Labs focusing on post-quantum cryptography (at the interesection of cryptography and AI security) working on lattice- and isogeny-based approaches to folding schemes and zero-knowledge.

Before that, I worked as a Cryptography Researcher (ZKP) at Tokamak Network (batch verification and sybil-resistant algorithms), as a Cryptographic Engineer at zkFold (zkRollups for the Cardano blockchain), and as a Cryptographic Researcher at Nethermind (temporary position, working on Zinc).

I spent a few years in academia, working as a postdoctoral researcher in Mathematics (Number Theory and Algebraic Geometry) at Università degli Studi di Milano and Università degli Studi di Padova. You can have a look at my old Google website for some more details.

I obtained my Ph.D. degree in mathematics at Universität Duisburg-Essen (ESAGA) in September 2021.

02 — Research

Research Interests

Cryptography: I am interested in the application of (algebraic and analytic) number theory and algebraic geometry to cryptography. Lately, I have been working on folding schemes (mainly Lattice-based) and zero-knowledge protocols (EC-, Isogeny-, and Lattice-based). I'm also interested in lookup arguments, IVCs, and sybil-resistant algorithms.

Mathematics: My research interests lie in the broad area of elliptic curves, special values of p-adic and complex L-functions (mainly triple product L-functions), and automorphic representations. I am particularly interested in the arithmetic aspect of modular forms and automorphic forms on quaternion algebras, both from a theoretical and a computational point of view. I am also keen on the geometry of eigenvarieties and their relation with quaternion algebras.



Peer-Reviewed Publications

2025

Succinct Arguments with Small Arithmetization Overheads from IOPs of Proximity to the Integers

Annual International Cryptology Conference (CRYPTO 2025)

A. Albert Garreta, H. Waldner, K. Hristova, L. Dall'Ava (& M. Cupic, M. Klein, I. Vlasov)

2023

Approximations of the balanced triple product p-adic L-function

Journal of Number Theory, Vol. 250, pp. 106–167

L. Dall'Ava

2023

Hida theory for special orders

International Journal of Number Theory, Vol. 19, No. 04, pp. 883–916

L. Dall'Ava



Preprints & Technical Notes

2026

Batched verification of the Tokamak zkSNARK

Technical Note (Tokamak Network)

L. Dall'Ava

2024

Balanced triple product p-adic L-functions and Stark points

ArXiv preprint 2403.05183

L. Dall'Ava, A. Horawa



Research and Study Notes

2025

MSM delegation by Benny Pinkas

Tokamak Network ZKP Seminar

L. Dall'Ava

2025

The Forking Lemma a brief introduction

Tokamak Network ZKP Seminar

L. Dall'Ava

2025

Circle STARKs

Tokamak Network ZKP Seminar

L. Dall'Ava



Dissertations/Theses

2021

Quaternionic Hida families and the triple product p-adic L-function

PhD Thesis, Universität Duisburg-Essen

L. Dall'Ava

2017

Arithmetic of special values of triple product L-functions

ALGANT Master Thesis, Universität Duisburg-Essen & Università degli Studi di Milano

L. Dall'Ava


Be aware of mistakes, typos, and grammatical errors.

GitHub Projects

Cryptography
2026

Quaternionic LWE

This is a toy project for expanding my understanding of PQ-safe cryptography, signature schemes, and Rust programming language. The project implements an experimental Learning With Errors (LWE) scheme based on Quaternion Algebras over finite fields; quaternion algebras are an example of non-commutative division algebras.

Cryptography
2024

GGH

A toy implementation of the Goldreich-Goldwasser-Halevi (GGH) cryptosystem in Rust. Based on the description in §7.8 “An Introduction to Mathematical Cryptography” by Hoffstein, Pipher, and Silverman.

Number Theory
2024

Computing-Gross-Pizer-Prasad-Eigenspaces

This repository provides algorithms in Magma designed to compute eigenspaces of quaternionic modular forms with level structure given by Special (Bass) order. The focus is on definite quaternion algebras. The repository includes examples and supports the theoretical results in Balanced triple product p-adic L-functions and Stark points and Approximations of the balanced triple product p-adic L-function.

Number Theory
2024

Characters-of-Dihedral-representations

Given a dihedral weight 1 modular form g and a quadratic (CM) field K, this repository provides tools to output pairs of Hecke characters over K. It demonstrates that the Galois representation of g is isomorphic to the induction of any of these characters. The repository includes code and examples to illustrate the computations, and supports the theoretical results in Balanced triple product p-adic L-functions and Stark points.

Number Theory
2023 (on hold)

Level_Raising_Modular_forms

This project implements a SageMath function to determine if two modular forms are related through level raising. Currently, the initial form must have rational coefficients. The repository includes examples and documentation.

04 — Get in touch

Let's talk research.

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