Related papers: On oriented supersingular elliptic curves
A fundamental theorem of Whitney from 1933 asserts that 2-connected graphs G and H are 2-isomorphic, or equivalently, their cycle matroids are isomorphic, if and only if G can be transformed into H by a series of operations called Whitney…
Twin-Field (TF) quantum key distribution (QKD) is a major candidate to be the new benchmark for far-distance QKD implementations, since its secret key rate can overcome the repeaterless bound by means of a simple interferometric…
Elliptic $K$-curves are elliptic curves defined over some field extension $L/K$ that are isogenous to all of their Galois conjugates. We present a new result on $K$-curves $E$ that are given by a $K$-rational orbit $\{\tau, -1/N\tau\}$ of…
The Diffie-Hellman key exchange plays a crucial role in conventional cryptography, as it allows two legitimate users to establish a common, usually ephemeral, secret key. Its security relies on the discrete-logarithm problem, which is…
An elliptic curve $E$ defined over a $p$-adic field $K$ with a $p$-isogeny $\phi:E\rightarrow E^\prime$ comes equipped with an invariant $\alpha_{\phi/K}$ that measures the valuation of the leading term of the formal group homomorphism…
We study the quantum spectral curve of the Argyres-Douglas theories in the Nekrasov-Sahashvili limit of the Omega-background. Using the ODE/IM correspondence we investigate the quantum integrable model corresponding to the quantum spectral…
Cryptographic protocols are the backbone of our information society. This includes two-party protocols which offer protection against distrustful players. Such protocols can be built from a basic primitive called oblivious transfer. We…
This paper presents protocols for Kak's cubic transformation and proposes a modification to Diffie-Hellman key exchange protocol in order to achieve asymmetric oblivious exchange of keys.
In this document, a privacy-preserving distributed profile matching protocol is proposed in a particular network context called \emph{mobile social network}. Such networks are often deployed in more or less hostile environments, requiring…
We develop a method for solving elliptic partial differential equations on surfaces described by CAD patches that may have gaps/overlaps. The method is based on hybridization using a three-dimensional mesh that covers the gap/overlap…
Device-independent quantum key distribution (DI-QKD) enables information-theoretically secure key exchange between remote parties without any assumptions on the internal workings of the devices used for its implementation. However, its…
The osmotic coefficient of solutions of rod-like polyelectrolytes is considered by comparing current theoretical treatments and simulations to recent experimental data. The discussion is restricted to the case of monovalent counterions and…
Post-quantum cryptography is inevitable. National Institute of Standards and Technology (NIST) starts standardizing quantum-resistant public-key cryptography (aka post-quantum cryptography). The reason is that investment in quantum…
In this paper we introduce and analyze the learning scenario of \emph{coupled nonlinear dimensionality reduction}, which combines two major steps of machine learning pipeline: projection onto a manifold and subsequent supervised learning.…
We generalize our earlier results concerning meshfree collocation methods for semilinear elliptic second order problems to the quasilinear case. The stability question, however, is treated differently, namely by extending a paper on…
Quantum key distribution (QKD) provides secure keys resistant to code-breaking quantum computers. As headed towards commercial application, it is crucial to guarantee the practical security of QKD systems. However, the difficulty of…
In this survey, we describe a general key exchange protocol based on semidirect product of (semi)groups (more specifically, on extensions of (semi)groups by automorphisms), and then focus on practical instances of this general idea. This…
To prove the security of quantum key distribution (QKD) protocols, several assumptions have to be imposed on users' devices. From an experimental point of view, it is preferable that such theoretical requirements are feasible and the number…
Out-of-distribution (OOD) detection is important for deploying machine learning models in the real world, where test data from shifted distributions can naturally arise. While a plethora of algorithmic approaches have recently emerged for…
We provide new distributed interactive proofs (DIP) for planarity and related graph families. The notion of a \emph{distributed interactive proof} (DIP) was introduced by Kol, Oshman, and Saxena (PODC 2018). In this setting, the verifier…