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Cosa (chi) è residue cryptosystem - definizione

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

Residue (complex analysis)

COEFFICIENT OF THE TERM OF ORDER −1 IN THE LAURENT EXPANSION OF A FUNCTION HOLOMORPHIC OUTSIDE A POINT, WHOSE VALUE CAN BE EXTRACTED BY A CONTOUR INTEGRAL

Residue of an analytic function; Residue at a pole; Complex residue; Residue (mathematics)

In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities. (More generally, residues can be calculated for any function f\colon \mathbb{C} \setminus \{a_k\}_k \rightarrow \mathbb{C} that is holomorphic except at the discrete points {ak}k, even if some of them are essential singularities.

https://en.wikipedia.org/wiki/Residue_(complex_analysis)

Residue theorem

THE THEOREM THAT COMPLEX CONTOUR INTEGRALS ARE SIMPLY THE SUMS OF RESIDUES OF SINGULARITIES CONTAINED WITHIN THE CONTOUR

Cauchy residue theorem; Cauchy residue formula; Residue theory; Residue Theorem; Cauchy's Residue Theorem; Cauchys Residue Theorem; Cauchy Residue Theorem; Residue formula; Residue theorem of Cauchy; Cauchy's residue theorem

In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals and infinite series as well. It generalizes the Cauchy integral theorem and Cauchy's integral formula.

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

Poincaré residue

GENERALIZATION OF THE CONCEPT OF RESIDUE OF A HOLOMORPHIC FUNCTION TO HIGHER DIMENSIONS

Poincare residue; Draft:Residue in several complex variables; Residue (complex geometry); Draft:Residue (Complex Geometry); Draft:Residue (complex geometry)

In mathematics, the Poincaré residue is a generalization, to several complex variables and complex manifold theory, of the residue at a pole of complex function theory. It is just one of a number of such possible extensions.

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

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