arXiv subjects

Francesco Sica

Publications and source records attributed to Francesco Sica.

3 recordsLinked to original sources

arXiv2024

TPU as Cryptographic Accelerator

Cryptographic schemes like Fully Homomorphic Encryption (FHE) and Zero-Knowledge Proofs (ZKPs), while offering powerful privacy-preserving capabilities, are often hindered by their computational complexity. Polynomial multiplication, a core operation in these schemes, is a major performance bottleneck. While algorithmic advancements and specialized hardware like GPUs and FPGAs have shown promise in accelerating these computations, the recent surge in AI accelerators (TPUs/NPUs) presents a new opportunity. This paper explores the potential of leveraging TPUs/NPUs to accelerate polynomial multiplication, thereby enhancing the performance of FHE and ZKP schemes. We present techniques to adapt polynomial multiplication to these AI-centric architectures and provide a preliminary evaluation of their effectiveness. We also discuss current limitations and outline future directions for further performance improvements, paving the way for wider adoption of advanced cryptographic tools.

cs.CR↗

arXiv2017

Factoring with Hints

We introduce a new deterministic factoring algorithm, which could be described in the cryptographically fashionable term of "factoring with hints": we show that, given the knowledge of the factorisations of $O(N^{1/3+ε})$ terms surrounding $N=pq$ product of two large primes, we can recover deterministically $p$ and $q$ in $O(N^{1/3+ε})$ bit operations. Although this is slower than the current best factoring algorithms, this method shows that the factorisations of close integers are related and that consequently one can expect more results along this line of thought.

math.NT↗

arXiv2011

Four-Dimensional Gallant-Lambert-Vanstone Scalar Multiplication

The GLV method of Gallant, Lambert and Vanstone (CRYPTO 2001) computes any multiple $kP$ of a point $P$ of prime order $n$ lying on an elliptic curve with a low-degree endomorphism $Φ$ (called GLV curve) over $\mathbb{F}_p$ as [kP = k_1P + k_2Φ(P), \quad\text{with} \max{|k_1|,|k_2|}\leq C_1\sqrt n] for some explicit constant $C_1>0$. Recently, Galbraith, Lin and Scott (EUROCRYPT 2009) extended this method to all curves over $\mathbb{F}_{p^2}$ which are twists of curves defined over $\mathbb{F}_p$. We show in this work how to merge the two approaches in order to get, for twists of any GLV curve over $\mathbb{F}_{p^2}$, a four-dimensional decomposition together with fast endomorphisms $Φ, Ψ$ over $\mathbb{F}_{p^2}$ acting on the group generated by a point $P$ of prime order $n$, resulting in a proved decomposition for any scalar $k\in[1,n]$ $$ kP=k_1P+ k_2Φ(P)+ k_3Ψ(P) + k_4ΨΦ(P)\quad \text{with} \max_i (|k_i|)< C_2\, n^{1/4} $$ for some explicit $C_2>0$. Furthermore, taking the best $C_1, C_2$, we get $C_2/C_1<408$, independently of the curve, ensuring a constant relative speedup. We also derive new families of GLV curves, corresponding to those curves with degree 3 endomorphisms.

cs.CR↗