Higher residuosity problem

In cryptography, most public key cryptosystems are founded on problems that are believed to be intractable. The higher residuosity problem (also called the n th-residuosity problem) is one such problem. This problem is easier to solve than integer factorization, so the assumption that this problem is hard to solve is stronger than the assumption that integer factorization is hard.

If n is an integer, then the integers modulo n form a ring. If n=pq where p and q are primes, then the Chinese remainder theorem tells us that

The group of units of any ring form a group, and the group of units in ${\displaystyle \mathbb {Z} /n\mathbb {Z} }$ is traditionally denoted ${\displaystyle (\mathbb {Z} /n\mathbb {Z} )^{*}}$.

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