EPSRC Centre for Doctoral Training in Cyber Security

Luciano Maino

luciano.maino@bristol.ac.uk

Year 4 Student – 2020 Intake – Cohort 2

I am a PhD student at the University of Bristol, Centre for Doctoral Training in Cyber Security. Previously, I obtained my bachelor and master degrees in Mathematics. I am interested in post-quantum cryptography. Currently, I am focussing on isogeny-based cryptography, in particular on employing higher-dimensional objects in existing cryptosystems. Other interests include formal verification methods, computer algebra, algebraic number theory, and algebraic geometry.

PhD Project

Factoring Isogenies in Higher Dimension and Applications

Recent advancements in quantum computing are undermining the security of the current public-key infrastructure. To counter this threat, a new branch of cryptography, called post-quantum cryptography, has emerged. The primary objective of post-quantum cryptography is to develop cryptosystems that can not only run on ordinary laptops but also remain resistant to quantum attacks. Some of the cryptosystems suggested so far rely on special maps, known as isogenies, between elliptic curves. Arguably, the most influential cryptosystem in this field is Supersingular Isogeny Diffie-Hellman (SIDH), which serves as the key exchange underlying the key encapsulation mechanism SIKE. SIKE was one of the most promising candidates in the NIST Post-Quantum standardisation process.

These special maps, isogenies, can be generalised to higher-dimensional mathematical objects, such as surfaces. It turns out that looking at surfaces provides a practical algorithm for factoring isogenies between elliptic curves. This is the main idea behind the attack on SIDH that I have coauthored. In the aftermath of this attack, the next step for isogeny-based cryptography is to utilise this insight to design and improve quantum-resistant cryptosystems. This constitutes my current research interest.

Supervisors: Dr Chloe Martindale  (Bristol), Dr Matthew Bisatt (Bristol), and Dr François Dupressoir (Bristol)

PhD Poster

View poster here

Events Attended

• M0lecon 2023, Turin, 2 December, 2023, Speaker (https://m0lecon.it/speakers.html)
• Isogeny Club, 14th November 2023, Online talk (https://isogeny.club/)
• Leuven Isogeny Days 4 – 11/12/13 October 2023 - An annual meeting for the isogeny community
• Latincrypt 2023, Quito, Ecuador, October 4-6, Paper Presentation (https://www.espe.edu.ec/latincrypt/)
•  BIRS Workshop, Isogeny Workshop, Bristol, 21-25th August 2023 - The aim of this workshop was to outline future directions for isogeny-based cryptography and stat new collaborations.
•  CFAIL 2023 (an affiliated event of Crypto 2023), August 19, 2023, Santa Barbara, USA, Speaker (https://www.cfail.org/cfail2023)
•  SIAM Conference on Applied Algebraic Geometry (AG23), July 10 - 14, 2023, Eindhoven, The Netherlands, Gave a Talk (https://www.siam.org/conferences/cm/program/program-and-abstracts/ag23-program-abstracts)
•  CYBER INNOVATION ROUNDTABLE, 24 May, 2023, Quantum Technology Innovation Centre, Bristol - I attended this event dedicated to exploring the opportunities at the intersection of quantum technology and cybersecurity (https://techspark.co/blog/2023/06/28/quantum-cybersecurity-innovation/)
•  Arithmetic, Geometry, Cryptography and Coding Theory, 5 – 9 June, 2023, Marseille, Gave a Talk (https://conferences.cirm-math.fr/2889.html)
•  Eurocrypt 2023, April 23-27, 2023 Lyon, France - I gave a pleanary presentation at this flagship conference. The paper I presented received an honorable mention and has been invited to the Journal of Cryptology (https://eurocrypt.iacr.org/2023/)
•  XMaths Workshop 2022, Bari, December 21-22, 2022, Gave a Talk (https://xmathsworkshop.weebly.com/history.html)
•  PQCifris 2022, School & Workshop on Post-Quantum Cryptography, Trento, 10-14 October 2022, Gave a Talk (https://sites.google.com/unitn.it/pqcifris2022)
•  Leuven Isogeny Days 3 – 21/22/23 September 2022 - An annual meeting for the isogeny community
•  Fifteenth Algorithmic Number Theory Symposium, ANTS-XV, University of Bristol, August 8 - 12, 2022, Gave a Talk (https://people.maths.bris.ac.uk/~jb12407/ANTS-XV/index.html)
•  SUMMER SCHOOL IN POST-QUANTUM CRYPTOGRAPHY 2022, Budapest, August 1–5, 2022 - I was a teaching assistant (https://pqcsummerschool2022.inf.elte.hu/)

Year 1 Academic and Industry Placements

Academic placement, Dr Chloe Martindale: Two-week placement to study isogenies between principally polarised abelian varieties.

Industry placement, ARQIT: Three-week internship under the supervision of Dr Daniel Shiu.

Internships

Publications / Presented Papers

"Towards a Quantum-Resistant Weak Verifiable Delay Function.", with Thomas Decru, and Antonio Sanso. Progress in Cryptology – LATINCRYPT 2023. Lecture Notes in Computer Science, vol 14168. Springer, Cham. https://doi.org/10.1007/978-3-031-44469-2_8

"A Direct Key Recovery Attack on SIDH.", with Chloe Martindale, Lorenz Panny, Giacomo Pope, and Benjamin Wesolowski. Advances in Cryptology - EUROCRYPT 2023 - 42nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Lyon, France, April 23-27, 2023, Proceedings, Part V. https://doi.org/10.1007/978-3-031-30589-4_16

"A Review of Mathematical and Computational Aspects of CSIDH Algorithms.", with Marzio Mula, and Federico Pintore. To appear in Journal of Algebra and Its Applications, Special Issue on Recent Advancements in Coding Theory & Cryptography. (2023) https://doi.org/10.1142/S0219498825300028

"Mathematical and Computational aspects of CSIDH-based Algorithms", with Federico Pintore. Algebra For Cryptography, Aracne Editrice, Collectio Ciphrarum 1. (2021)

PREPRINT:

"An Algorithmic Approach to (2,2)-isogenies in the Theta Model and Applications to Isogeny-based Cryptography.", with Pierrick Dartois, Giacomo Pope and Damien Robert. eprint version: https://eprint.iacr.org/2023/1747

Personal Research Website 

Social Media

https://www.linkedin.com/in/luciano-m-4b22261bb