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Elliptic-curve cryptography

Elliptic-curve cryptography is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC requires smaller keys compared to non-EC cryptography to provide equivalent security. Elliptic curves are applicable for key agreement, digital signatures, pseudo-random generators and other tasks. Indirectly, they can be used for encryption by combining the key agreement with a symmetric encryption scheme, they are used in several integer factorization algorithms based on elliptic curves that have applications in cryptography, such as Lenstra elliptic-curve factorization. Public-key cryptography is based on the intractability of certain mathematical problems. Early public-key systems are secure assuming that it is difficult to factor a large integer composed of two or more large prime factors. For elliptic-curve-based protocols, it is assumed that finding the discrete logarithm of a random elliptic curve element with respect to a publicly known base point is infeasible: this is the "elliptic curve discrete logarithm problem".

The security of elliptic curve cryptography depends on the ability to compute a point multiplication and the inability to compute the multiplicand given the original and product points. The size of the elliptic curve determines the difficulty of the problem; the U. S. National Institute of Standards and Technology has endorsed elliptic curve cryptography in its Suite B set of recommended algorithms elliptic-curve Diffie–Hellman for key exchange and Elliptic Curve Digital Signature Algorithm for digital signature; the U. S. National Security Agency allows their use for protecting information classified up to top secret with 384-bit keys. However, in August 2015, the NSA announced that it plans to replace Suite B with a new cipher suite due to concerns about quantum computing attacks on ECC. While the RSA patent expired in 2000, there may be patents in force covering certain aspects of ECC technology; however some argue that the US government elliptic curve digital signature standard and certain practical ECC-based key exchange schemes can be implemented without infringing them, including RSA Laboratories and Daniel J. Bernstein.

The primary benefit promised by elliptic curve cryptography is a smaller key size, reducing storage and transmission requirements, i.e. that an elliptic curve group could provide the same level of security afforded by an RSA-based system with a large modulus and correspondingly larger key: for example, a 256-bit elliptic curve public key should provide comparable security to a 3072-bit RSA public key. The use of elliptic curves in cryptography was suggested independently by Neal Koblitz and Victor S. Miller in 1985. Elliptic curve cryptography algorithms entered wide use in 2004 to 2005. For current cryptographic purposes, an elliptic curve is a plane curve over a finite field which consists of the points satisfying the equation y 2 = x 3 + a x + b, along with a distinguished point at infinity, denoted ∞; this set together with the group operation of elliptic curves is an abelian group, with the point at infinity as an identity element. The structure of the group is inherited from the divisor group of the underlying algebraic variety.

D i v 0 → P i c 0 ≃ E, Several discrete logarithm-based protocols have been adapted to elliptic curves, replacing the group × with an elliptic curve: The Elliptic Curve Diffie–Hellman key agreement scheme is based on the Diffie–Hellman scheme, The Elliptic Curve Integrated Encryption Scheme known as Elliptic Curve Augmented Encryption Scheme or the Elliptic Curve Encryption Scheme, The Elliptic Curve Digital Signature Algorithm is based on the Digital Signature Algorithm, The deformation scheme using Harrison's p-adic Manhattan metric, The Edwards-curve Digital Signature Algorithm is based on Schnorr signature and uses twisted Edwards curves, The ECMQV key agreement scheme is based on the MQV key agreement scheme, The ECQV implicit certificate scheme. At the RSA Conference 2005, the National Security Agency announced Suite B which uses ECC for digital signature generation and key exchange; the suite is intended to protect both classified and unclassified national security systems and information.

A large number of cryptographic primitives based on bilinear mappings on various elliptic curve groups, such as the Weil and Tate pairings, have been introduced. Schemes based on these primitives provide efficient identity-based encryption as well as pairing-based signatures, key agreement, proxy re-encryption; some common implementation considerations include: To use ECC, all parties must agree on all the elements defining the elliptic curve, that is, the domain parameters of the scheme. The field is defined by the pair of m and f in the binary case; the elliptic curve is defined by b used in its defining equation. The cyclic subgroup is defined by its generator G. For cryptographic a

Las leyendas: el origen

Legend Quest: The Origin is an upcoming Mexican animated horror-comedy film as part of the Leyendas animated franchise. Produced by Ánima Estudios, it will be an origin story focused on the little Calavera duo and Moribunda who must leave their home in Pueblo Calaca looking out for a human baby, it is planned for release on April 2020 in Mexico. Two Calavera children must look after a human infant after crossing through an eternal mirror, absorbing energy of a portal that separates the worlds between life and death. Mayte Cordeiro Annie Rojas Eduardo España Paola Ramones Bruno Bichir Ricardo Arnaiz, the creator of the Leyendas characters, serves as the director of the film, marking his return to the franchise since The Legend of La Nahuala and his first collaboration outside of Animex Producciones; the film was titled tentatively as The Legend of... and The Legend of Finado and Moribunda. The film was first teased on social media; the film will utilize 2D traditional animation over the tween-style animation.

The film's teaser trailer was released on 1 November 2019. Las leyendas: el origen on IMDb

Seven Sacraments (Poussin)

The Seven Sacraments refers to two series of paintings of the seven sacraments by the French painter Nicholas Poussin. Painted between 1637 and 1640, the first series was commissioned by Cassiano del Pozzo in the second half of the 1630s and was sold to the Dukes of Rutland in 1784. One of the seven, was destroyed in a fire at the Rutlands' Belvoir Castle in 1816, Baptism was acquired by the National Gallery of Art in Washington DC in 1939, where it still resides; the remaining five were still at Belvoir Castle at the time when Anthony Blunt wrote his catalogue in 1966 and were on show at the National Gallery in London until recently. All five of these paintings in the National Gallery were taken off show in November 2010 prior to the attempted sale of Ordination on 8 December that year. Ordination was purchased by the Kimbell Art Museum for US$24.3 million and was displayed for the first time there on September 14, 2011. The Fitzwilliam Museum in Cambridge in 2013 bought Extreme Unction from the Duke of Rutland, who retains ownership of the remaining three works in the series.

The images listed below are the remaining six paintings of the first series: Baptism Ordination Confirmation Penance Eucharist Marriage Extreme Unction The second series was painted for Paul Fréart de Chantelou from 1644 to 1648 and was acquired by Francis Egerton, 3rd Duke of Bridgewater in 1798. The paintings passed by descent to the Earls of Ellesmere, the last of whom became the Duke of Sutherland in 1964. All of the second series, commissioned by Chantelou, is on loan at the Scottish National Gallery, Edinburgh as part of the Bridgewater Loan

Orbital Railway Line

The Barcelona orbital line is a railway project forming part of both the Pla d'infraestructures de Catalunya, a long-term development plan due for completion in 2026, the Pla de transport de viatgers de Catalunya, a short-term plan due for completion in 2012. In following perimeter routes the orbital line and another railway project, the Eix Transversal Ferroviari de Catalunya, are the first railway schemes to depart from the radial system developed so far in the Barcelona area. Known as the Quart cinturó ferroviari, the orbital line will connect Rodalies Barcelona services between Vilanova i la Geltrú and Mataró via a 119 kilometres line passing through Granollers, Terrassa and Vilafranca del Penedès, but avoiding the actual city of Barcelona; some sections will make use of existing track belonging to Administrador de Infraestructuras Ferroviarias and operated by Renfe Operadora, whilst 68 km of track - of which 46 kilometres in tunnels - and 23 new stations will be constructed

List of colleges and universities in Delaware

There are eight colleges and universities in Delaware. These institutions include two research universities, one master's university, one baccalaureate college, two associate's colleges, two special-focus institutions. Five of Delaware's post-secondary institutions are private and three are public. Delaware's oldest post-secondary institution is the University of Delaware, chartered by the Delaware General Assembly as a degree-granting college in 1833; the University of Delaware is the state's largest institution of higher learning in terms of enrollment, as it had 23,009 students as of late 2014. According to the United States Department of Education Institute of Education Sciences, the Delaware College of Art and Design is the state's smallest institution of higher learning with an enrollment of 170. Wilmington University is Delaware's largest private post-secondary institution, with an enrollment of 15,316. Delaware has the University of Delaware; the University of Delaware is the state's sole participant in the National Sea Grant College Program and the National Space Grant College and Fellowship Program.

In addition, Delaware State University is the one black college and university in the state, is a member of the Thurgood Marshall College Fund. Delaware had two private post-secondary institutions for men and women respectively: St. Mary's College and Wesleyan Female College respectively; the state does not have a medical school, but the Delaware Institute of Medical Education and Research reserves spaces for Delaware students at two medical schools in Philadelphia. Delaware has Widener University Delaware Law School. All eight of Delaware's post-secondary institutions are regionally accredited by the Middle States Commission on Higher Education. Higher education in the United States List of recognized higher education accreditation organizations Lists of American institutions of higher education Explanatory notes Citations Media related to Universities and colleges in Delaware at Wikimedia Commons United States Department of Education listing of accredited institutions in Delaware

Sophia Historic District

Sophia Historic District is a national historic district located at Sophia, Raleigh County, West Virginia. It encompasses 22 contributing buildings located in the central business district of Sophia; the consist of one and two story masonry buildings with storefronts on the first floor and housing in the upper stories. Notable buildings include the Filling Station, Reck's Place/The Chestnut Tree Café and Art Gallery, Attili Building, Visionz Lounge, LB & J Antiques, Ben Franklin / Federated Department Store, Sophia Theater, it was listed on the National Register of Historic Places in 2006