Giacomo Borin

Giacomo Borin

PhD student ad UZH & IBM Zurich in the Foundations of Cryptography group. I like trains and mountains 🚞

Posts by Collection

portfolio

BeUnitn

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A custom beamer theme for the Math Department in Università di Trento (unofficial).

BSC Thesis

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Cryptographic Group Actions and Digital Signatures,
with a focus on Code Equivalence Problems

MSC Thesis

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Cryptographic Group Actions and Digital Signatures,
with a focus on Code Equivalence Problems

publications

On the Semidirect Discrete Logarithm Problem in Finite Groups

Published in ASIACRYPT 2024, 2024

This paper is about quantumly breaking the Semidirect Discrete Logarithm Problem on finite groups

Recommended citation: Christopher Battarbee, Giacomo Borin, Ryann Cartor, Nadia Heninger, David Jao, Delaram Kahrobaei, Laura Maddison, Edoardo Persichetti, Angela Robinson, Daniel Smith-Tone and Rainer Steinwandt. "On the Semidirect Discrete Logarithm Problem in Finite Groups". ASIACRYPT 2024.
Download Paper

talks

Coding Theory Cryptography and LEDAcrypt implementation

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For the course Applied Crptography I gave a short Presentation (🇬🇧) to an audience of engineers and mathematicians about the basics of linear coding theory and its application for post-quantum cryptography. In particular I’ve explained the key ideas behind McEliece Cryptosystem and one of its implementation: LEDAcrypt . This suite were designed by a group of italian researchers (Marco Baldi, Alessandro Barenghi, Franco Chiaraluce, Gerardo Pelosi, Paolo Santini) and reached the second round of the NIST Post-Quantum Cryptography Standardization process .

Commutative Algebra and Coding Theory

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A presentation (🇬🇧) for the final exam of the course Advanced Commutative Algebra . These slides where inspired by the wonderful book Codes, Cryptology and Curves with Computer Algebra containing two interesting intersections between coding theory and commutative algebra, that I have expanded and inserted in the slides (it is possible to have also the annotated version). The two main arguments are:

  • A general method for decoding Cyclic codes using Groebner basis, called Cooper’s Philosophy. I have also proposed a working example of the decoding in MAGMA (here the code), where is possible also to change the parameters to obtain different examples.
  • A link between Matroid and Coding theory, with some easy results.

Additional Functionalities for Code-Based Group Actions

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Group actions are fundamental mathematical tools, both for classical cryptography with discrete logarithm and for post-quantum cryptography, such as isogeny-based and code-based ones. They have received a lot of interest from the cryptographic community, who are also attracted by the possibility of defining additional functionalities over standard primitives. However, different families of group actions may differ significantly in their core characteristics, so some works usually focus on specific schemes, usually with abelian acting groups like CSI-FiSh. In this talk, we have seen some additional functionalities for general cryptographic group actions, particularly the one arising from isomorphism problems in coding theory used in LESS and MEDS signature schemes, such as a threshold implementation and different commitment design strategies.

Cryptographic Corollaries of the Classification of Finite Simple Groups

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The Semidirect Discrete Logarithm Problem (SDLP) is a potentially appealing generalisation of the standard Discrete Logarithm Problem (DLP) arising from a more involved algebraic structure. It was hoped that there would be a gap between the quantum complexity of SDLP and that of DLP, allowing for development of post-quantum schemes based on SDLP.Unfortunately, in the case of SDLP with respect to finite groups, this turns out not to be the case. In this talk we present two powerful tools allowing us to reach this conclusion: the first is a method of decomposition of a generic instance of SDLP into several instances of SDLP in a finite simple group; the second is a survey of SDLP in each finite simple group, aided by the celebrated classification theorem.

teaching

GTA for Linear Algebra & Calculus

Undergraduate course, University of Trento, Departments of Math & Physics, 2021

For two years I tutored first years undergraduated students attending Linear Algebra and Calculus courses.

TA for Codierungstheorie

Undergraduate and Graduate course, University of Zurich, Institute of Mathematics, 2024

I tutored the students providing exercises in Coding Theory and solving them in exercise sections.