Pinpointing Super-Quadratic Quantum Enumeration Speedups: Exact and Certified Evaluation of the Guessing-Moment Exponent under Product-Distribution Advice
Researchers give an exact method to measure super-quadratic quantum speedups from product side-channel advice.
The paper provides a finite-size method for measuring the quantum-versus-classical guessing-moment gap when cryptanalytic search has product-form probabilistic advice, such as side-channel leakage on independent key coordinates. Classical and quantum moments reduce to functionals of a one-dimensional surprisal distribution; commensurate surprisals give exact finite sums, and general cases receive a certified binning-error bound. Applied to cold-boot leakage, template-attack posteriors, and synthetic Bernoulli posteriors calibrated to Keccak side-channel residual ranks for ML-KEM and ML-DSA, exponents reached up to 3.97, above Grover's quadratic factor.
- Gives a finite-size method for quantum-classical guessing-moment separation.
- Commensurate surprisals yield exact finite sums without discretization error.
- General product advice receives a certified binning-error bound.
- Synthetic models reach a speedup exponent of up to 3.97.
- Cases include cold-boot leakage and ML-KEM and ML-DSA side channels.
From the original article
1 min read at arxiv.orgGrover's algorithm gives an optimal quadratic query advantage for black-box search. In cryptanalysis, however, the search often comes with additional probabilistic advice over the candidates, frequently of product form, e. g.
By Carsten Schubert · arxiv.org
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