LEONARDO COLÒ

NUMBER THEORY & CRYPTOGRAPHY

Leonardo Colo

In my research I investigate questions related to supersingular elliptic curves, their endomorphism ring and associated isogeny graphs. I am particularly interested in: cryptography, elliptic curves, abelian varieties, algorithms for number theory, class field theory and modular curves.

Below you can find a list of ongoing projects I am involved in:

  1. Zero-Knowledge Proofs of Isogeny Diamonds

    With Maher Mamah, Youcef Mokrani, Bruno Sterner, Nic Swanson

  2. Supersingular isogeny graphs and Hecke modules with level structure

    With David Kohel

  3. CSI-Dragon

    With Andrea Basso, Jolijn Cottaar, Yi-Fu Lai, Jeanne Laflamme, Tanja Lange, Jason T.~LeGrow, Ha Tran

  4. Formal group orientations

In my research I investigate questions related to supersingular elliptic curves, their endomorphism ring and associated isogeny graphs. I am particularly interested in: cryptography, elliptic curves, abelian varieties, algorithms for number theory, class field theory and modular curves.

Below you can find a list of ongoing projects I am involved in:

Zero-Knowledge Proofs of Isogeny Diamonds

With Maher Mamah, Youcef Mokrani, Bruno Sterner and Nic Swanson.

Supersingular isogeny graphs and Hecke modules with level structure

With David Kohel.

CSI-Dragon

With Andrea Basso, Jolijn Cottaar, Yi-Fu Lai, Jeanne Laflamme, Tanja Lange, Jason T.~LeGrow and Ha Tran.

Formal group orientations

PREPRINTS

  1. From orientations to ℓ-adic period vectors

    > preprint

  2. Weber modular curves and modular isogenies

    With David Kohel
    > preprint

  3. On a modular approach to the OSIDH protocol

    With David Kohel
    > preprint

PREPRINTS

From orientations to ℓ-adic period vectors

> preprint

Weber modular curves and modular isogenies

With David Kohel.

> preprint

On a modular approach to the OSIDH protocol

With David Kohel.

> preprint

ARTICLES

  1. Orienting supersingular isogeny graphs

    With David Kohel
    Journal of Mathematical Cryptology, vol. 14.1, pp. 414 - 437
    > ePrint arXiv HAL

ARTICLES

Orienting supersingular isogeny graphs

With David Kohel.

Journal of Mathematical Cryptology, vol. 14.1, pp. 414 - 437 (2020).

> ePrint arXiv HAL

THESIS

  1. Oriented supersingular elliptic curves and class group actions

    Supervisor: Prof. David Kohel.
    Defense: November 18, 2022. Aix-Marseille Université, Marseille (FR).
    > manuscript

  2. p-adic abelian integrals: from theory to practice

    Supervisor: Prof. Fabrizio Andreatta.
    Defense: July 16, 2018. Universität Regensburg, Regensburg (DE).
    > manuscript

THESIS

Oriented supersingular elliptic curves and class group actions

PhD thesis.

Supervisor: Prof. David Kohel.

Defense: November 18, 2022. Aix-Marseille Université, Marseille (FR).

> manuscript

p-adic abelian integrals: from theory to practice

MSc thesis.

Supervisor: Prof. Fabrizio Andreatta.

Defense: July 16, 2018. Universität Regensburg, Regensburg (DE).

> manuscript

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