Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userImproved torsion point attacks on SIDH variants
55
0
0.0
(
0
)
Added by
Katherine E. Stange
Publication date
2020
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
SIDH is a post-quantum key exchange algorithm based on the presumed difficulty of finding isogenies between supersingular elliptic curves. However, SIDH and related cryptosystems also reveal additional information: the restriction of a secret isogeny to a subgroup of the curve (torsion point information). Petit (2017) was the first to demonstrate that torsion point information could noticeably lower the difficulty of finding secret isogenies. In particular, Petit showed that overstretched parameterizations of SIDH could be broken in polynomial time. However, this did not impact the security of any cryptosystems proposed in the literature. The contribution of this paper is twofold: First, we strengthen the techniques of Petit by exploiting additional information coming from a dual and a Frobenius isogeny. This extends the impact of torsion point attacks considerably. In particular, our techniques yield a classical attack that completely breaks the n-party group key exchange of Azarderakhsh et al. for 6 parties or more, and a quantum attack for 3 parties or more that improves on the best known asymptotic complexity. We also provide a Magma implementation of our attack for 6 parties. We give the full range of parameters for which our attacks apply. Second, we construct SIDH variants designed to be weak against our attacks; this includes backdoor choices of starting curve, as well as backdoor choices of base field prime. We stress that our results do not degrade the security of, or reveal any weakness in the NIST submission SIKE.
rate research
Read More
Robustness against image perturbations bounded by a $ell_p$ ball have been well-studied in recent literature. Perturbations in the real-world, however, rarely exhibit the pixel independence that $ell_p$ threat models assume. A recently proposed Wasserstein distance-bounded threat model is a promising alternative that limits the perturbation to pixel mass movements. We point out and rectify flaws in previous definition of the Wasserstein threat model and explore stronger attacks and defenses under our better-defined framework. Lastly, we discuss the inability of current Wasserstein-robust models in defending against perturbations seen in the real world. Our code and trained models are available at https://github.com/edwardjhu/improved_wasserstein .
3D deep learning has been increasingly more popular for a variety of tasks including many safety-critical applications. However, recently several works raise the security issues of 3D deep models. Although most of them consider adversarial attacks, we identify that backdoor attack is indeed a more serious threat to 3D deep learning systems but remains unexplored. We present the backdoor attacks in 3D point cloud with a unified framework that exploits the unique properties of 3D data and networks. In particular, we design two attack approaches on point cloud: the poison-label backdoor attack (PointPBA) and the clean-label backdoor attack (PointCBA). The first one is straightforward and effective in practice, while the latter is more sophisticated assuming there are certain data inspections. The attack algorithms are mainly motivated and developed by 1) the recent discovery of 3D adversarial samples suggesting the vulnerability of deep models under spatial transformation; 2) the proposed feature disentanglement technique that manipulates the feature of the data through optimization methods and its potential to embed a new task. Extensive experiments show the efficacy of the PointPBA with over 95% success rate across various 3D datasets and models, and the more stealthy PointCBA with around 50% success rate. Our proposed backdoor attack in 3D point cloud is expected to perform as a baseline for improving the robustness of 3D deep models.
We give a classification of the cuspidal automorphic representations attached to rational elliptic curves with a non-trivial torsion point of odd order. Such elliptic curves are parameterizable, and in this paper, we find the necessary and sufficient conditions on the parameters to determine when split or non-split multiplicative reduction occurs. Using this and the known results on when additive reduction occurs for these parametrized curves, we classify the automorphic representations in terms of the parameters.
Transferability of adversarial examples is a key issue to study the security of multimedia forensics (MMF) techniques relying on Deep Learning (DL). The transferability of the attacks, in fact, would open the way to the deployment of successful counter forensics attacks also in cases where the attacker does not have a full knowledge of the to-be-attacked system. Some preliminary works have shown that adversarial examples against CNN-based image forensics detectors are in general non-transferrable, at least when the bas
Let $K$ be a number field, and let $E/K$ be an elliptic curve over $K$. The Mordell--Weil theorem asserts that the $K$-rational points $E(K)$ of $E$ form a finitely generated abelian group. In this work, we complete the classification of the finite groups which appear as the torsion subgroup of $E(K)$ for $K$ a cubic number field. To do so, we determine the cubic points on the modular curves $X_1(N)$ for [N = 21, 22, 24, 25, 26, 28, 30, 32, 33, 35, 36, 39, 45, 65, 121.] As part of our analysis, we determine the complete list of $N$ for which $J_0(N)$ (resp., $J_1(N)$, resp., $J_1(2,2N)$) has rank 0. We also provide evidence to a generalized version of a conjecture of Conrad, Edixhoven, and Stein by proving that the torsion on $J_1(N)(mathbb{Q})$ is generated by $text{Gal}(bar{mathbb{Q}}/mathbb{Q})$-orbits of cusps of $X_1(N)_{bar{mathbb{Q}}}$ for $Nleq 55$, $N eq 54$.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
