4,349 research outputs found
Group law computations on Jacobians of hyperelliptic curves
We derive an explicit method of computing the composition step in Cantor’s algorithm for group operations on Jacobians of hyperelliptic curves. Our technique is inspired by the geometric description of the group law and applies to hyperelliptic curves of arbitrary genus. While Cantor’s general composition involves arithmetic in the polynomial ring F_q[x], the algorithm we propose solves a linear system over the base field which can be written down directly from the Mumford coordinates of the group elements. We apply this method to give more efficient formulas for group operations in both affine and projective coordinates for cryptographic systems based on Jacobians of genus 2 hyperelliptic curves in general form
Computing Heavy Elements
Reliable calculations of the structure of heavy elements are crucial to
address fundamental science questions such as the origin of the elements in the
universe. Applications relevant for energy production, medicine, or national
security also rely on theoretical predictions of basic properties of atomic
nuclei. Heavy elements are best described within the nuclear density functional
theory (DFT) and its various extensions. While relatively mature, DFT has never
been implemented in its full power, as it relies on a very large number (~
10^9-10^12) of expensive calculations (~ day). The advent of leadership-class
computers, as well as dedicated large-scale collaborative efforts such as the
SciDAC 2 UNEDF project, have dramatically changed the field. This article gives
an overview of the various computational challenges related to the nuclear DFT,
as well as some of the recent achievements.Comment: Proceeding of the Invited Talk given at the SciDAC 2011 conference,
Jul. 10-15, 2011, Denver, C
Semantic Modeling of Analytic-based Relationships with Direct Qualification
Successfully modeling state and analytics-based semantic relationships of
documents enhances representation, importance, relevancy, provenience, and
priority of the document. These attributes are the core elements that form the
machine-based knowledge representation for documents. However, modeling
document relationships that can change over time can be inelegant, limited,
complex or overly burdensome for semantic technologies. In this paper, we
present Direct Qualification (DQ), an approach for modeling any semantically
referenced document, concept, or named graph with results from associated
applied analytics. The proposed approach supplements the traditional
subject-object relationships by providing a third leg to the relationship; the
qualification of how and why the relationship exists. To illustrate, we show a
prototype of an event-based system with a realistic use case for applying DQ to
relevancy analytics of PageRank and Hyperlink-Induced Topic Search (HITS).Comment: Proceedings of the 2015 IEEE 9th International Conference on Semantic
Computing (IEEE ICSC 2015
Hard isogeny problems over RSA moduli and groups with infeasible inversion
We initiate the study of computational problems on elliptic curve isogeny
graphs defined over RSA moduli. We conjecture that several variants of the
neighbor-search problem over these graphs are hard, and provide a comprehensive
list of cryptanalytic attempts on these problems. Moreover, based on the
hardness of these problems, we provide a construction of groups with infeasible
inversion, where the underlying groups are the ideal class groups of imaginary
quadratic orders.
Recall that in a group with infeasible inversion, computing the inverse of a
group element is required to be hard, while performing the group operation is
easy. Motivated by the potential cryptographic application of building a
directed transitive signature scheme, the search for a group with infeasible
inversion was initiated in the theses of Hohenberger and Molnar (2003). Later
it was also shown to provide a broadcast encryption scheme by Irrer et al.
(2004). However, to date the only case of a group with infeasible inversion is
implied by the much stronger primitive of self-bilinear map constructed by
Yamakawa et al. (2014) based on the hardness of factoring and
indistinguishability obfuscation (iO). Our construction gives a candidate
without using iO.Comment: Significant revision of the article previously titled "A Candidate
Group with Infeasible Inversion" (arXiv:1810.00022v1). Cleared up the
constructions by giving toy examples, added "The Parallelogram Attack" (Sec
5.3.2). 54 pages, 8 figure
Pairing computation on hyperelliptic curves of genus 2
Bilinear pairings have been recently used to construct cryptographic schemes with new and novel properties, the most celebrated example being the Identity Based Encryption scheme of Boneh and Franklin. As pairing computation is generally the most computationally intensive part of any painng-based cryptosystem, it is essential to investigate new ways in which to compute pairings efficiently.
The vast majority of the literature on pairing computation focuscs solely on using elliptic curves. In this thesis we investigate pairing computation on supersingular hyperelliptic curves of genus 2 Our aim is to provide a practical alternative to using elliptic curves for pairing based cryptography. Specifically, we illustrate how to implement pairings efficiently using genus 2 curves, and how to attain performance comparable to using elliptic curves.
We show that pairing computation on genus 2 curves over F2m can outperform elliptic curves by using a new variant of the Tate pairing, called the r¡j pairing, to compute the fastest pairing implementation in the literature to date We also show for the first time how the final exponentiation required to compute the Tate pairing can be avoided for certain hyperelliptic curves.
We investigate pairing computation using genus 2 curves over large prime fields, and detail various techniques that lead to an efficient implementation, thus showing that these curves are a viable candidate for practical use
KALwEN: a new practical and interoperable key management scheme for body sensor networks
Key management is the pillar of a security architecture. Body sensor networks (BSNs) pose several challenges–some inherited from wireless sensor networks (WSNs), some unique to themselves–that require a new key management scheme to be tailor-made. The challenge is taken on, and the result is KALwEN, a new parameterized key management scheme that combines the best-suited cryptographic techniques in a seamless framework. KALwEN is user-friendly in the sense that it requires no expert knowledge of a user, and instead only requires a user to follow a simple set of instructions when bootstrapping or extending a network. One of KALwEN's key features is that it allows sensor devices from different manufacturers, which expectedly do not have any pre-shared secret, to establish secure communications with each other. KALwEN is decentralized, such that it does not rely on the availability of a local processing unit (LPU). KALwEN supports secure global broadcast, local broadcast, and local (neighbor-to-neighbor) unicast, while preserving past key secrecy and future key secrecy (FKS). The fact that the cryptographic protocols of KALwEN have been formally verified also makes a convincing case. With both formal verification and experimental evaluation, our results should appeal to theorists and practitioners alike
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