A lower bound on the release of differentially private integer partitions

Francesco Aldà, Hans Ulrich Simon

Abstract: Highlights•Lower bound on minimax risk for releasing integer partitions under differential privacy.•For large non-negative integers N, a lower bound of order Ω(N/ε)<math><mi mathvariant="normal" is="true">Ω</mi><mo stretchy="false" is="true">(</mo><msqrt is="true"><mrow is="true"><mi is="true">N</mi><mo stretchy="false" is="true">/</mo><mi is="true">ε</mi></mrow></msqrt><mo stretchy="false" is="true">)</mo></math> is provided.•For small values of N, an optimal lower bound of order Ω(N)<math><mi mathvariant="normal" is="true">Ω</mi><mo stretchy="false" is="true">(</mo><mi is="true">N</mi><mo stretchy="false" is="true">)</mo></math> is provided.