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- W2799900113 abstract "An indexing of a finite set $S$ is a bijection $D : {1,...,|S|} rightarrow S$. We present an indexing for the set of quadratic residues modulo $N$ that is decodable in polynomial time on the size of $N$, given the factorization of $N$. We derive two information theoretical consequences from this indexing. The first consequence is a procedure for sampling quadratic residues modulo $N$, when the factorization of $N$ is known, that runs in strict polynomial time and requires the theoretical minimum amount of random bits (i.e., $log{(phi(N)/2^r)}$ bits, where $phi(N)$ is Euler's totient function and $r$ is the number of distinct prime factors of $N$). A previously known procedure for this same problem runs in expected (not strict) polynomial time and requires more random bits. The second consequence is a tighter upper bound for the time-bounded Kolmogorov Complexity of strings consisting of multiple quadratic residues modulo $N$." @default.
- W2799900113 created "2018-05-17" @default.
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- W2799900113 date "2018-05-12" @default.
- W2799900113 modified "2023-09-27" @default.
- W2799900113 title "An Indexing for Quadratic Residues Modulo $N$ and a Non-uniform Efficient Decoding Algorithm" @default.
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