Minimum Sparsity of S-Decoding Polynomials
Prior state unknown→proved
conditional on a plausible number-theoretic conjecture; unconditional through s = 15
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theoretical-computer-science / Private information retrieval
Minimum Sparsity of S-Decoding Polynomials
Can an $S$-decoding polynomial modulo a suitable product of $k$ primes attain the lower-bound minimum of $k + 1$ nonzero coefficients? A construction matches the bound for special products of $k$ primes, yielding exponentially fewer-server PIR.
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Can an $S$-decoding polynomial modulo a suitable product of $k$ primes attain the lower-bound minimum of $k + 1$ nonzero coefficients? A construction matches the bound for special products of $k$ primes, yielding exponentially fewer-server PIR.
conditional on a plausible number-theoretic conjecture; unconditional through s = 15
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