FDFB^2 Functional Bootstrapping via Sparse Polynomial Multiplication

Kamil Kluczniak

secunet Security Networks AG

 

Abstract:

Fully homomorphic encryption schemes are methods to perform computations over encrypted data. Since its introduction by Gentry, significant research efforts have been devoted to optimizing these initially inefficient cryptosystems. Over time, different families have emerged. On the one hand, schemes such as BGV, BFV, or CKKS excel at performing coefficient-wise addition or multiplication over vectors of encrypted data. In contrast, accumulator-based schemes like FHEW and TFHE are well-suited for evaluating Boolean circuits and efficiently computing functions over small plaintext spaces, typically up to 4-5 bits. In this talk, I will introduce the concept of Full Domain Functional Bootstrapping and show a new algorithm that achieves significant speedup compared to previous work in certain applications. Finally, I will demonstrate a FHE library implementing full domain functional bootstrapping and discuss further directions and open problems.

Biography:

Kamil Kluczniak is currently a senior cryptography consultant at secunet Security Networks AG, where he supports standardization efforts conducted by the European Commission and the German Federal Office for Information Security (BSI), and also advises the CTO-Office on matters related to advanced cryptography and AI. Before that, he joined the CISPA-Stanford Center in 2018 and subsequently held a visiting assistant professorship at Stanford University from 2019 to 2021. From 2017 to 2018, he was a postdoctoral researcher at the Hong Kong Polytechnic University. He obtained his Ph.D. (summa cum laude) in cryptography from the Polish Academy of Sciences in 2016 for his work on Privacy-Preserving Signatures for Electronic Identity Documents. His current research focuses on high-performance secure computing and fully homomorphic encryption schemes. But during his academic career, he worked on privacy-preserving authentication schemes, zero-knowledge proofs, cryptographic obfuscation, key establishment protocols, and post-quantum cryptography. He has published his work at top conferences (Eurocrypt, CCS, Asiacrypt) and has presented numerous papers at topical conferences like CHES, Financial Cryptography, AsiaCCS, and the Public Key Cryptography Conference. He has successfully secured research funding through public competitions, managed research grants, and consulted for the Polish Ministry of Digital Affairs and industry partners such as GlobalLogic.