Post-quantum Blockchains using hash functions using higher dimensional special linear groups over finite fields as platforms

Delaram Kahrobaei (CUNY, New York)

Jul 17. 2023, 11:00 — 11:45

It is projected that by 2025, approximately 10% of the worldwide gross domestic product (GDP) will be stored using blockchain technology. Blockchains are digital tools that employ cryptography techniques to safeguard information against unauthorized alterations. The foundation of the Bitcoin cryptocurrency relies on this technology. Blockchain-based products find applications across various sectors such as finance, manufacturing, and healthcare, contributing to a market valued at over US$150 billion. Functioning as a secure digital record or ledger, a blockchain is collectively maintained by users worldwide, eliminating the need for a central administration. 

To design such a Blockchain network, we need to construct the "blocks" which contain the information about the transaction and unique value to identify this block; known as a “Hash”.

We define new families of Tillich-Zémor hash functions, using higher dimensional special linear groups over finite fields as platforms. The Cayley graphs of these groups combine fast mixing properties and high girth, which together give rise to good preimage and collision resistance of the corresponding hash functions. We use a theorem by Arzhantseva and Biswas  (2018) concerning the expanding properties of the Cayley graphs of these groups. We justify the claim that the resulting hash functions are post-quantum secure.

This is a joint work with C. Le Coz, C. Battarbee, R. Flores, T. Koberda.

Further Information
ESI Schrödinger and Boltzmann Lecture Hall
Associated Event:
Geometric and Asymptotic Group Theory with Applications 2023 - Groups and Dynamics (Workshop)
Christopher Cashen (U of Vienna)
Javier de la Nuez González (KIAS, Seoul)
Alexandra Edletzberger (U of Vienna)
Yash Lodha (U of Hawaii, Honolulu)