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What (who) is classical cryptosystem - definition

Damgaard-Jurik cryptosystem; Damgaard–Jurik cryptosystem; Damgård-Jurik cryptosystem; Damgard–Jurik cryptosystem; Damgard-Jurik cryptosystem

Goldwasser–Micali cryptosystem

ASYMMETRIC KEY ENCRYPTION ALGORITHM

Goldwasser-Micali; Goldwasser-Micali encryption; Goldwasser-Micali cryptosystem; Goldwasser-Micali encryption scheme

The Goldwasser–Micali (GM) cryptosystem is an asymmetric key encryption algorithm developed by Shafi Goldwasser and Silvio Micali in 1982. GM has the distinction of being the first probabilistic public-key encryption scheme which is provably secure under standard cryptographic assumptions.

https://en.wikipedia.org/wiki/Goldwasser–Micali_cryptosystem

Classical period (music)

GENRE OF WESTERN MUSIC (C. 1730–1820)

Classical Music Era; Classical Era (Music); Vienese classic; Classical music era; Wiener Klassik; Viennese classical; Classical period of music; Classical Period (music); Classical period music; Classical-period music; Classical era music; Classical-era music; Classical period in music; Classical era of music; Classical era in music; Classical music period; Classical music (period); Pre-Classical music; Pre-Classical period (music)

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The Classical period was an era of classical music between roughly 1750 and 1820.

The Classical period falls between the Baroque and the Romantic periods. Classical music has a lighter, clearer texture than Baroque music, but a more sophisticated use of form. It is mainly homophonic, using a clear melody line over a subordinate chordal accompaniment, but counterpoint was by no means forgotten, especially in liturgical vocal music and, later in the period, secular instrumental music. It also makes use of style galant which emphasized light elegance in place of the Baroque's dignified seriousness and impressive grandeur. Variety and contrast within a piece became more pronounced than before and the orchestra increased in size, range, and power.

The harpsichord was replaced as the main keyboard instrument by the piano (or fortepiano). Unlike the harpsichord, which plucks strings with quills, pianos strike the strings with leather-covered hammers when the keys are pressed, which enables the performer to play louder or softer (hence the original name "fortepiano," literally "loud soft") and play with more expression; in contrast, the force with which a performer plays the harpsichord keys does not change the sound. Instrumental music was considered important by Classical period composers. The main kinds of instrumental music were the sonata, trio, string quartet, quintet, symphony (performed by an orchestra) and the solo concerto, which featured a virtuoso solo performer playing a solo work for violin, piano, flute, or another instrument, accompanied by an orchestra. Vocal music, such as songs for a singer and piano (notably the work of Schubert), choral works, and opera (a staged dramatic work for singers and orchestra) were also important during this period.

The best-known composers from this period are Joseph Haydn, Wolfgang Amadeus Mozart, Ludwig van Beethoven, and Franz Schubert; other names in this period include: Carl Philipp Emanuel Bach, Johann Christian Bach, Luigi Boccherini, Domenico Cimarosa, Joseph Martin Kraus, Muzio Clementi, Christoph Willibald Gluck, Carl Ditters von Dittersdorf, André Grétry, Pierre-Alexandre Monsigny, Leopold Mozart, Michael Haydn, Giovanni Paisiello, Johann Baptist Wanhal, François-André Danican Philidor, Niccolò Piccinni, Antonio Salieri, Georg Christoph Wagenseil, Georg Matthias Monn, Johann Gottlieb Graun, Carl Heinrich Graun, Franz Benda, Georg Anton Benda, Johann Georg Albrechtsberger, Mauro Giuliani, Christian Cannabich and the Chevalier de Saint-Georges. Beethoven is regarded either as a Romantic composer or a Classical period composer who was part of the transition to the Romantic era. Schubert is also a transitional figure, as were Johann Nepomuk Hummel, Luigi Cherubini, Gaspare Spontini, Gioachino Rossini, Carl Maria von Weber, Jan Ladislav Dussek and Niccolò Paganini. The period is sometimes referred to as the era of Viennese Classicism (German: Wiener Klassik), since Gluck, Haydn, Salieri, Mozart, Beethoven, and Schubert all worked in Vienna.

https://en.wikipedia.org/wiki/Classical_period_(music)

Classical group

GROUPS REPRESENTABLE AS MATRIX GROUPS OVER A REAL DIVISION ASSOCIATIVE ALGEBRA (REALS, COMPLEXES, OR QUATERNIONS) THAT PRESERVE A CERTAIN BILINEAR FORM (SYMMETRIC, SKEW-SYMMETRIC, HERMITIAN, SKEW-HERMITIAN, ETC.)

Classical groups; Classical Lie groups; Classical Lie group; Standard representation; Classical compact groups

In mathematics, the classical groups are defined as the special linear groups over the reals , the complex numbers and the quaternions together with specialHere, special means the subgroup of the full automorphism group whose elements have determinant 1. automorphism groups of symmetric or skew-symmetric bilinear forms and Hermitian or skew-Hermitian sesquilinear forms defined on real, complex and quaternionic finite-dimensional vector spaces.

https://en.wikipedia.org/wiki/Classical_group

Wikipedia

Damgård–Jurik cryptosystem

The Damgård–Jurik cryptosystem is a generalization of the Paillier cryptosystem. It uses computations modulo $n^{s+1}$ where $n$ is an RSA modulus and $s$ a (positive) natural number. Paillier's scheme is the special case with $s=1$ . The order $\varphi (n^{s+1})$ (Euler's totient function) of $Z_{n^{s+1}}^{*}$ can be divided by $n^{s}$ . Moreover, $Z_{n^{s+1}}^{*}$ can be written as the direct product of $G\times H$ . $G$ is cyclic and of order $n^{s}$ , while $H$ is isomorphic to $Z_{n}^{*}$ . For encryption, the message is transformed into the corresponding coset of the factor group $G\times H/H$ and the security of the scheme relies on the difficulty of distinguishing random elements in different cosets of $H$ . It is semantically secure if it is hard to decide if two given elements are in the same coset. Like Paillier, the security of Damgård–Jurik can be proven under the decisional composite residuosity assumption.

https://en.wikipedia.org/wiki/Damgård–Jurik cryptosystem