84 research outputs found
Novel Polynomial Basis and Its Application to Reed-Solomon Erasure Codes
In this paper, we present a new basis of polynomial over finite fields of
characteristic two and then apply it to the encoding/decoding of Reed-Solomon
erasure codes. The proposed polynomial basis allows that -point polynomial
evaluation can be computed in finite field operations with
small leading constant. As compared with the canonical polynomial basis, the
proposed basis improves the arithmetic complexity of addition, multiplication,
and the determination of polynomial degree from
to . Based on this basis, we then develop the encoding and
erasure decoding algorithms for the Reed-Solomon codes. Thanks to
the efficiency of transform based on the polynomial basis, the encoding can be
completed in finite field operations, and the erasure decoding
in finite field operations. To the best of our knowledge, this
is the first approach supporting Reed-Solomon erasure codes over
characteristic-2 finite fields while achieving a complexity of ,
in both additive and multiplicative complexities. As the complexity leading
factor is small, the algorithms are advantageous in practical applications
Magnetism, FeS colloids, and Origins of Life
A number of features of living systems: reversible interactions and weak
bonds underlying motor-dynamics; gel-sol transitions; cellular connected
fractal organization; asymmetry in interactions and organization; quantum
coherent phenomena; to name some, can have a natural accounting via
interactions, which we therefore seek to incorporate by expanding the horizons
of `chemistry-only' approaches to the origins of life. It is suggested that the
magnetic 'face' of the minerals from the inorganic world, recognized to have
played a pivotal role in initiating Life, may throw light on some of these
issues. A magnetic environment in the form of rocks in the Hadean Ocean could
have enabled the accretion and therefore an ordered confinement of
super-paramagnetic colloids within a structured phase. A moderate H-field can
help magnetic nano-particles to not only overcome thermal fluctuations but also
harness them. Such controlled dynamics brings in the possibility of accessing
quantum effects, which together with frustrations in magnetic ordering and
hysteresis (a natural mechanism for a primitive memory) could throw light on
the birth of biological information which, as Abel argues, requires a
combination of order and complexity. This scenario gains strength from
observations of scale-free framboidal forms of the greigite mineral, with a
magnetic basis of assembly. And greigite's metabolic potential plays a key role
in the mound scenario of Russell and coworkers-an expansion of which is
suggested for including magnetism.Comment: 42 pages, 5 figures, to be published in A.R. Memorial volume, Ed
Krishnaswami Alladi, Springer 201
RESCUE: Evaluation of a Fragmented Secret Share System in Distributed-Cloud Architecture
Scaling big data infrastructure using multi-cloud environment has led to the demand for highly secure, resilient and reliable data sharing method. Several variants of secret sharing scheme have been proposed but there remains a gap in knowledge on the evaluation of these methods in relation to scalability, resilience and key management as volume of files generated increase and cloud outages persist. In line with these, this thesis presents an evaluation of a method that combines data fragmentation with Shamir’s secret sharing scheme known as Fragmented Secret Share System (FSSS). It applies data fragmentation using a calculated optimum fragment size and encrypts each fragment using a 256-bit AES key length before dispersal to cloudlets, the encryption key is managed using secret sharing methods as used in cryptography.Four experiments were performed to measure the scalability, resilience and reliability in key management. The first and second experiments evaluated scalability using defined fragment blocks and an optimum fragment size. These fragment types were used to break file of varied sizes into fragments, and then encrypted and dispersed to the cloud, and recovered when required. Both were used in combination of different secret sharing policies for key management. The third experiment tested file recovery during cloud failures, while the fourth experiment focused on efficient key management.The contributions of this thesis are of two ways: development of evaluation frameworks to measure scalability and resilience of data sharing methods; and the provision of information on relationships between file sizes and share policies combinations. While the first aimed at providing platform to measure scalability from the point of continuous production as file size and volume increase, and resilience as the potential to continue operation despite cloud outages; the second provides experimental frameworks on the effects of file sizes and share policies on overall system performance.The results of evaluation of FSSS with similar methods showed that the fragmentation method has less overhead costs irrespective of file sizes and the share policy combination. That the inherent challenges in secret sharing scheme can only be solved through alternative means such as combining secret sharing with other data fragmentation method. In all, the system is less of any erasure coding technique, making it difficult to detect corrupt or lost fragment during file recovery
Existence and Uniqueness of Minimizers for A Nonlocal Variational Problem
Nonlocal modeling is a rapidly growing field, with a vast array of applications and connections to questions in pure math. One goal of this work is to present an approachable introduction to the field and an invitation to the reader to explore it more deeply. In particular, we explore connections between nonlocal operators and classical problems in the calculus of variations. Using a well-known approach, known simply as The Direct Method, we establish well-posedness for a class of variational problems involving a nonlocal first-order differential operator. Some simple numerical experiments demonstrate the behavior of these problems for specific choices of kernel and boundary conditions
2019 GREAT Day Program
SUNY Geneseo’s Thirteenth Annual GREAT Day.https://knightscholar.geneseo.edu/program-2007/1013/thumbnail.jp
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