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Questions tagged [quadratic-residuosity]

A residue of order 2. A number $a$ for which the congruence $x^2 ≡ a \pmod m$ has a solution is called a quadratic residue modulo $m$.

A residue of order 2. A number $a$ for which the congruence $x^2 ≡ a \pmod m$ has a solution is called a quadratic residue modulo $m$; in other words, $a$ is a quadratic residue modulo $m$ if for a certain integer $x$ the number $x^2 − a$ is divisible by $m$; if this congruence has no solution, then $a$ is called a quadratic nonresidue.

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How the coin flipping protocol prevent Alice from generating $ n $ from many primes?

This is a question from reading the paper 'Coin Flipping by Telephone - a protocol for solving impossible problems'. The fact that the coin is unbiased is based on the fact that if n is a product of two primes, then there should be exactly four…
Andrew Au
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Checking both Quadratic residuosity and Jacobi symbol simultaneously and efficiently

I have to randomly generate a number $u$ such that $u \in J(N)-Q(N)$ where $J(N)$ denotes the set of elements less than $N$, whose Jacobi symbol value is equal to 1; and $Q(N)$ denotes the set of quadratic residues in $J(N)$ . What is the best…
hanugm
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Goldwasser-Micali variation

I try to create a valid decryption function for a modified the Goldwasser-Micali scheme $pk = (N,p,q)$ where N is a Blum-Number $(p = q = 3 \bmod 4)$ $Enc_{pk}(m) = (-1)^{m} \cdot r^{2} \bmod N \text{ where } r \in_{R} \mathbb{Z}^{*}_{N}$ Now…
atcheckmate
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