Simpler and faster BFV bootstrapping for arbitrary plaintext modulus from CKKS
Bootstrapping is currently the only known method for constructing fully homomorphic
encryptions. In the BFV scheme specifically, bootstrapping aims to reduce the error of a …
encryptions. In the BFV scheme specifically, bootstrapping aims to reduce the error of a …
Security guidelines for implementing homomorphic encryption
JP Bossuat, R Cammarota, I Chillotti… - Cryptology ePrint …, 2024 - eprint.iacr.org
Abstract Fully Homomorphic Encryption (FHE) is a cryptographic primitive that allows
performing arbitrary operations on encrypted data. Since the conception of the idea in …
performing arbitrary operations on encrypted data. Since the conception of the idea in …
Bootstrapping for BGV and BFV Revisited
R Geelen, F Vercauteren - Journal of Cryptology, 2023 - Springer
We unify the state-of-the-art bootstrapping algorithms for BGV and BFV in a single
framework and show that both schemes can be bootstrapped with identical complexity. This …
framework and show that both schemes can be bootstrapped with identical complexity. This …
Cryptanalysis of symmetric primitives over rings and a key recovery attack on Rubato
L Grassi, I Manterola Ayala, MN Hovd… - Annual International …, 2023 - Springer
Symmetric primitives are a cornerstone of cryptography, and have traditionally been defined
over fields, where cryptanalysis is now well understood. However, a few symmetric …
over fields, where cryptanalysis is now well understood. However, a few symmetric …
Homomorphic polynomial evaluation using galois structure and applications to BFV bootstrapping
BGV and BFV are among the most widely used fully homomorphic encryption (FHE)
schemes. Both schemes have a common plaintext space, with a rich algebraic structure. Our …
schemes. Both schemes have a common plaintext space, with a rich algebraic structure. Our …
Relaxed functional bootstrapping: A new perspective on BGV/BFV bootstrapping
BGV and BFV are among the most widely used fully homomorphic encryption (FHE)
schemes, supporting evaluations over a finite field. To evaluate a circuit with arbitrary depth …
schemes, supporting evaluations over a finite field. To evaluate a circuit with arbitrary depth …
The patching landscape of elisabeth-4 and the mixed filter permutator paradigm
Filter permutators are a family of stream cipher designs that are aimed for hybrid
homomorphic encryption. While originally operating on bits, they have been generalized to …
homomorphic encryption. While originally operating on bits, they have been generalized to …
Faster BGV Bootstrapping for Power-of-Two Cyclotomics Through Homomorphic NTT
S Ma, T Huang, A Wang, X Wang - … on the Theory and Application of …, 2025 - Springer
Power-of-two cyclotomics is a popular choice when instantiating the BGV scheme because
of its efficiency and compliance with the FHE standard. However, in power-of-two …
of its efficiency and compliance with the FHE standard. However, in power-of-two …
Accelerating BGV Bootstrapping for Large p Using Null Polynomials over
S Ma, T Huang, A Wang, X Wang - … on the Theory and Applications of …, 2024 - Springer
The BGV scheme is one of the most popular FHE schemes for computing homomorphic
integer arithmetic. The bootstrapping technique of BGV is necessary to evaluate arbitrarily …
integer arithmetic. The bootstrapping technique of BGV is necessary to evaluate arbitrarily …
Fully Homomorphic Encryption for Cyclotomic Prime Moduli
R Geelen, F Vercauteren - Cryptology ePrint Archive, 2024 - eprint.iacr.org
This paper presents a Generalized BFV (GBFV) fully homomorphic encryption scheme that
encrypts plaintext spaces of the form $\mathbb {Z}[x]/(\Phi_m (x), t (x)) $ with $\Phi_m (x) …
encrypts plaintext spaces of the form $\mathbb {Z}[x]/(\Phi_m (x), t (x)) $ with $\Phi_m (x) …