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AbstractA tangential quadrilateral is a convex quadrilateral whose sides are simultaneously tangent to a single circle. In this paper, the primary objective is to construct rational tangential quadrilaterals characterized by having rational area, as well as rational side and diagonal lengths. We relate the existence of such tangential quadrilaterals to properties of a certain elliptic curve. Studying the curve, we are able to construct an infinite family of rational tangential quadrilaterals. [ABSTRACT FROM AUTHOR]

In our work we focus on the geometry of elliptic normal curves of degree 6 embedded in P 5 . We determine the space of quadric hypersurfaces through an elliptic normal curve of degree 6 and find the explicit equations of generators of I ( Sec (C 6)) . We study the images C p and C p q of a sextic C 6 under the projection from a general point P ∈ P 5 and a general line P Q ¯ ⊂ P 5 . In particular, we show that C p is k-normal for all k ≥ 2 and I (C p) is generated by three homogeneous polynomials of degree 2 and two homogeneous polynomials of degree 3. We then show that C p q is k-normal for all k ≥ 3 and I (C p q) is generated by two homogeneous polynomials of degree 3 and three homogeneous polynomials of degree 4. [ABSTRACT FROM AUTHOR]

The classical AGM produces wonderful infinite sequences of arithmetic and geometric means with common limit. For finite fields F q , with q ≡ 3 (mod 4) , we introduce a finite field analogue AGM F q that spawns directed finite graphs instead of infinite sequences. The compilation of these graphs reminds one of a jellyfish swarm, as the 3D renderings of the connected components resemble jellyfish (i.e., tentacles connected to a bell head). These swarms turn out to be more than the stuff of child's play; they are taxonomical devices in number theory. Each jellyfish is an isogeny graph of elliptic curves with isomorphic groups of F q -points, which can be used to prove that each swarm has at least (1 / 2 − ε) q jellyfish. This interpretation also gives a description of the class numbers of Gauss, Hurwitz, and Kronecker which is akin to counting types of spots on jellyfish. [ABSTRACT FROM AUTHOR]

The aim of the article is to initiate a new study in the framework of algebraic hyperfields, with an applicative impact in cryptography. First we define the notions of generalized Weierstrass equation and elliptic hypercurve on Krasner hyperfields, as a generalization of the notion of elliptic curve on fields. Then we investigate properties of the hypergroups derived from elliptic hypercurves and of the associated Hv-groups. Finally, we present a class of canonical hypergroups, which can be used as an alphabet in a special cryptographic system. [ABSTRACT FROM AUTHOR]

In a digital multisignature scheme, two or more signers are allowed to produce a single signature on a common message, which can be verified by anyone. In the literature, many schemes are available based on the public key infrastructure or identity-based cryptosystem with bilinear pairing and map-to-point (MTP) hash function. The bilinear pairing and the MTP function are time-consuming operations and they need a large super-singular elliptic curve group. Moreover, the cryptosystems based on them are difficult to implement and less efficient for practical use. To the best of our knowledge, certificateless digital multisignature scheme without pairing and MTP hash function has not yet been devised and the same objective has been fulfilled in this paper. Furthermore, we formally prove the security of our scheme in the random oracle model under the assumption that ECDLP is hard. [ABSTRACT FROM PUBLISHER]

Elliptic curves over a finite fieldwithj-invariant 0 or 1728, both supersingular and ordinary, whose embedding degreekis low are studied. In the ordinary case we give conditions characterizing such elliptic curves with fixed embedding degree with respect to a subgroup of prime order ℓ. For, these conditions give parameterizations ofqin terms of ℓ and two integersm,n. We show several examples of families with infinitely many curves. Similar parameterizations forneed a fixedkth root of the unity in the underlying field. Moreover, when the elliptic curve admits distortion maps, an example is provided. [ABSTRACT FROM AUTHOR]

In this paper, we propose a secure electronic medical record (EMR) service system, named the ECC-based Secure EMR Transmission System (ESEMRT for short) which employs a cloud database, an elliptic curve cryptography (ECC) integration unit, a smart card, and portable devices to provide users with a secure environment for EMR transmission. The ECC integration unit, which integrates a 256-bit ECC chip, wireless transceiver, smart card reader, and USB interface for fast computing and reducing the communication load of a portable device, can securely protect the EMRs when these EMRs are delivered between the cloud database and the portable device so as to enhance their transmission security and the patient care quality. Besides, the data leakage prevention scheme is also implemented in the ESEMRT to avoid illegal duplication. Our simulation shows that the proposed system can provide a higher security level and reduce portable devices’ hardware resource requirements. [ABSTRACT FROM AUTHOR]

In recent years, the increasing development of wireless communication technologies and IPv6 is enabling a seamless integration of smart objects into the Internet infrastructure. This extension of technology to common environments demands greater security restrictions, since any unexpected information leakage or illegitimate access to data could present a high impact in our lives. Additionally, the application of standard security and access control mechanisms to these emerging ecosystems has to face new challenges due to the inherent nature and constraints of devices and networks which make up this novel landscape. While these challenges have been usually addressed by centralized approaches, in this work we present a set of Elliptic Curve Cryptography optimizations for point and field arithmetic which are used in the design and implementation of a security and capability-based access control mechanism (DCapBAC) on smart objects. Our integral solution is based on a lightweight and flexible design that allows this functionality is embedded on resource-constrained devices, providing the advantages of a distributed security approach for Internet of Things (IoT) in terms of scalability, interoperability and end-to-end security. Additionally, our scheme has been successfully validated by using AVISPA tool and implemented on a real scenario over the Jennic/NXP JN5148 chipset based on a 32-bit RISC CPU. The results demonstrate the feasibility of our work and show DCapBAC as a promising approach to be considered as security solution for IoT scenarios. [ABSTRACT FROM AUTHOR]

We introduce a protocol based on blind signatures using elliptic curves that allows to trace those users of any service,traitors, that share their legitimate license with other people, avoiding the abuse or the unauthorized use of legal licenses. We show that our protocol is incapable of implicating innocent users in the illegal distribution of licenses and that tracing produces indisputable proof for the implication of the traitors. We also show that our protocol provides anonymity to users unless they share their private information and compare it to other existing schemes. We also provide an implementation showing its practical application. [ABSTRACT FROM PUBLISHER]

We prove the-invariant of an irreducible elliptic curve associated with a 3-by-3 or 4-by-4 matrix is real and greater than or equal to 1. Additionally, we correct an erroneous statement appearing in Kippenhahn’s argument about the boundary generating curves of the numerical ranges ofmatrices. [ABSTRACT FROM AUTHOR]

This paper proposes the generalization of our previous work to the ring A n = F 3 d [ X ] / ( X n ) . All results found before in A 2 , A 3 and A 4 [1–3] hold in A n ; but the approach here is clearly different, and has given more interesting results, specially when 3 does not divide # E a 0 , b 0 1 ; the elliptic curve over the ring A n is a direct sum of the elliptic curve over the field F 3 d and, unexpectedly its own subgroup of elements with the third projective coordinate not invertible, instead of F 3 d n as it was thought in the earlier works. Other results are deduced from, we cite the equivalence of the Discrete Logarithm Problem (DLP) on the elliptic curve over the ring A n and the field F 3 d , which is beneficial for cryptanalysts and cryptographers as well, and we will set the theoretic foundations to build a cryptosystem similar to the one in [4] with more benefits, which will be specified later. [ABSTRACT FROM AUTHOR]

In this work, we are going to study the elliptic curves over the ring A 3 = ( F 2 d [ X ] ) / ( X 3 ) , precisely we will establish the short exact sequence which is split, and we will define the group extension E a , b ( A 3 ) of E a 0 , b 0 ( F 2 d ) by Ker ( π 3 ) which seems to be beneficial and interesting in ECC. [ABSTRACT FROM AUTHOR]

In this article, we study some cohomology groups and quadratic twists of elliptic curves, and apply Tate local duality and the results of Kramer–Tunnell on local norm cokernel to give a refined version of Yu's formula in the case of elliptic curves. Then, by using this refinement formula, we obtain explicit orders of Shafarevich–Tate groups of some elliptic curves in quadratic number fields, including a few unconditional cases. [ABSTRACT FROM AUTHOR]

A provably secure certificateless digital signature scheme using elliptic curve cryptography is presented in this paper. Since the certificateless public key cryptosystem removes the complex certificate management procedure and the private key escrow problem of traditional public key cryptography (PKC) and identity-based cryptosystem (IBC), respectively, and as a result, the proposed scheme is more efficient than IBC- and PKC-based signatures. Besides, the bilinear pairing and map-to-point hash function are time-consuming operations, and thus the signatures without these two operations are more attractive in real applications and the present work has been carried out in this direction. Based on the elliptic curve discrete logarithm assumption, it is shown that the proposed scheme is unforgeable under the adaptive chosen message and identity attacks in the random oracle model against variety of adversaries. Finally, our signature scheme is compared with a number of competitive schemes and the satisfactory performance has been achieved. [ABSTRACT FROM AUTHOR]