Giacomo Borin

Giacomo Borin

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

Talks and presentations

Cryptographic Corollaries of the Classification of Finite Simple Groups

July 10, 2024

Talk, NIST Crypto Reading Club, NIST Campus, USA

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.

Additional Functionalities for Code-Based Group Actions

November 08, 2023

Seminar, University of St. Gallen, St. Gallen, Switzerland

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.

Commutative Algebra and Coding Theory

May 11, 2022

Exam, University of Trento, Trento, Italy

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.

Coding Theory Cryptography and LEDAcrypt implementation

December 16, 2021

Talk, University of Trento, Applied Crptography lectures 2021, Trento, Italy

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 .