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No, exactly equal length of primes $p$ and $q$ is not mandatory for security (or proper functioning) in the Pailler cryptosystem. Sufficient requirements are that $p$ and $q$ are prime, $N=p q$ is hard to factor, and $\gcd(p q,(p-1)(q-1))=1$. The requirement that $p$ and $q$ are of exactly equal size is usually made in the Pailler cryptosystem because this ...



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