arXiv subjects

Bo-Yin Yang

Publications and source records attributed to Bo-Yin Yang.

5 recordsLinked to original sources

arXiv2024

Isogeny-based Group Signatures and Accountable Ring Signatures in QROM

We present the first provably secure isogeny-based group signature (GS) and accountable ring signature (ARS) in the quantum random oracle model (QROM). We do so via introducing and constructing an intermediate primitive called the openable sigma protocol and demonstrating that any such protocol gives rise to a secure GS and ARS. Furthermore, QROM security is guaranteed if an additional perfect unique-response property (which is achieved via our tailored construction) is satisfied. Previous works by Beullens et al. (Eurocrypt 2022, Asiacrypt 2020) proposed isogeny-based GS and ARS with better efficiency but were only analyzed in the classical random oracle model (CROM). It is well-known that CROM security does not generally translate to QROM security; with the growing relevance of isogeny-based constructions in post-quantum cryptography, the current state of the art is unsatisfactory. Moreover, the aforementioned existing isogeny-based signatures were recently affected by the Fiat-Shamir with aborts (FSwA) flaw discovered by Barbosa et al. and Devevey et al. (CRYPTO 2023), leaving the provable security of isogeny-based signatures open to question once again. Our constructions are not only immune to the FSwA flaw but also provide stronger QROM security. As current QROM-secure ARS and GS schemes are mostly lattice-based, we offer a robust post-quantum alternative should lattice assumptions weaken.

cs.CR↗

arXiv2022

A physical study of the LLL algorithm

This paper presents a study of the LLL algorithm from the perspective of statistical physics. Based on our experimental and theoretical results, we suggest that interpreting LLL as a sandpile model may help understand much of its mysterious behavior. In the language of physics, our work presents evidence that LLL and certain 1-d sandpile models with simpler toppling rules belong to the same universality class. This paper consists of three parts. First, we introduce sandpile models whose statistics imitate those of LLL with compelling accuracy, which leads to the idea that there must exist a meaningful connection between the two. Indeed, on those sandpile models, we are able to prove the analogues of some of the most desired statements for LLL, such as the existence of the gap between the theoretical and the experimental RHF bounds. Furthermore, we test the formulas from the finite-size scaling theory (FSS) against the LLL algorithm itself, and find that they are in excellent agreement. This in particular explains and refines the geometric series assumption (GSA), and allows one to extrapolate various quantities of interest to the dimension limit. In particular, we predict the empirical average RHF converges to $\approx 1.02265$ as dimension goes to infinity.

cond-mat.stat-mech↗

arXiv2018

Multiplying boolean Polynomials with Frobenius Partitions in Additive Fast Fourier Transform

We show a new algorithm and its implementation for multiplying bit-polynomials of large degrees. The algorithm is based on evaluating polynomials at a specific set comprising a natural set for evaluation with additive FFT and a high order element under Frobenius map of $\mathbb{F}_{2}$. With the high order element, we can derive more values of the polynomials under Frobenius map. Besides, we also adapt the additive FFT to efficiently evaluate polynomials at the set with an encoding process. For the implementation, we reorder the computations in the additive FFT for reducing the number of memory writes and hiding the latency for reads. The algebraic operations, including field multiplication, bit-matrix transpose, and bit-matrix multiplication, are implemented with efficient SIMD instructions. As a result, we effect a software of best known efficiency, shown in our experiments.

cs.SC↗

arXiv2018

Frobenius Additive Fast Fourier Transform

In ISSAC 2017, van der Hoeven and Larrieu showed that evaluating a polynomial P in GF(q)[x] of degree <n at all n-th roots of unity in GF($q^d$) can essentially be computed d-time faster than evaluating Q in GF($q^d$)[x] at all these roots, assuming GF($q^d$) contains a primitive n-th root of unity. Termed the Frobenius FFT, this discovery has a profound impact on polynomial multiplication, especially for multiplying binary polynomials, which finds ample application in coding theory and cryptography. In this paper, we show that the theory of Frobenius FFT beautifully generalizes to a class of additive FFT developed by Cantor and Gao-Mateer. Furthermore, we demonstrate the power of Frobenius additive FFT for q=2: to multiply two binary polynomials whose product is of degree <256, the new technique requires only 29,005 bit operations, while the best result previously reported was 33,397. To the best of our knowledge, this is the first time that FFT-based multiplication outperforms Karatsuba and the like at such a low degree in terms of bit-operation count.

cs.SC↗

arXiv2018

Faster Multiplication for Long Binary Polynomials

We set new speed records for multiplying long polynomials over finite fields of characteristic two. Our multiplication algorithm is based on an additive FFT (Fast Fourier Transform) by Lin, Chung, and Huang in 2014 comparing to previously best results based on multiplicative FFTs. Both methods have similar complexity for arithmetic operations on underlying finite field; however, our implementation shows that the additive FFT has less overhead. For further optimization, we employ a tower field construction because the multipliers in the additive FFT naturally fall into small subfields, which leads to speed-ups using table-lookup instructions in modern CPUs. Benchmarks show that our method saves about $40 \%$ computing time when multiplying polynomials of $2^{28}$ and $2^{29}$ bits comparing to previous multiplicative FFT implementations.

cs.SC↗