Exact-Answer Benchmarks for Quantum Cryptanalysis Resource Estimation: Known-Key Instances, Published-Estimate Regression Targets, and Closed-Form Reference Values

Published estimates of the quantum resources needed to break RSA and elliptic-curve cryptography differ by orders of magnitude, and the software that reproduces or extends them is rarely tested against anything with a known answer. Borrowing the practice of verifying three-dimensional plasma-equilibrium codes against closed-form exact solutions, we propose an open suite of exact-answer benchmarks for quantum cryptanalysis tooling. It has four parts: (i) known-answer order-finding (Shor factoring) instances whose full measurement distribution has a closed form, checked against statevector simulation in Qiskit and against an OpenQASM 3 export and re-import; (ii) known-key elliptic-curve discrete-logarithm instances on toy prime-order curves, with an exact closed-form law for the ideal Z_q variant and cross-checked independent implementations for the qubit variant; (iii) regression targets transcribed from published resource estimates, together with arithmetic-consistency checks that recompute each paper's headline numbers from its own stated inputs; and (iv) 50-digit reference values for Weibull and lognormal arrival-time models. All 24 factoring instances (up to 24 qubits) agree with the closed form to a total-variation distance of at most 7.5e-12, and all ECDLP instances agree to machine precision. The regression checks reproduce the published physical-qubit total of 897,864 for RSA-2048 exactly, show that several commonly quoted closed-form expressions deviate from their own papers' tables by up to 22%, and flag one typographical slip. Running a closed-source estimator against the suite as a black box shows that a model calibrated at one key size can differ from the published per-run runtime by a factor of 2.3 at another. We document all AI assistance and release the suite for versioned reuse.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-11
DOI
https://doi.org/10.5281/zenodo.24136744
Primary Topic
Quantum Computing Algorithms and Architecture
Type
preprint
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preprint

Exact-Answer Benchmarks for Quantum Cryptanalysis Resource Estimation: Known-Key Instances, Published-Estimate Regression Targets, and Closed-Form Reference Values

Leandro França de Mello
Zenodo (CERN European Organization for Nuclear Research)
Quantum Computing Algorithms and Architecture
preprint

Exact-Answer Benchmarks for Quantum Cryptanalysis Resource Estimation: Known-Key Instances, Published-Estimate Regression Targets, and Closed-Form Reference Values

Leandro França de Mello
preprint en

Abstract

Published estimates of the quantum resources needed to break RSA and elliptic-curve cryptography differ by orders of magnitude, and the software that reproduces or extends them is rarely tested against anything with a known answer. Borrowing the practice of verifying three-dimensional plasma-equilibrium codes against closed-form exact solutions, we propose an open suite of exact-answer benchmarks for quantum cryptanalysis tooling. It has four parts: (i) known-answer order-finding (Shor factoring) instances whose full measurement distribution has a closed form, checked against statevector simulation in Qiskit and against an OpenQASM 3 export and re-import; (ii) known-key elliptic-curve discrete-logarithm instances on toy prime-order curves, with an exact closed-form law for the ideal Z_q variant and cross-checked independent implementations for the qubit variant; (iii) regression targets transcribed from published resource estimates, together with arithmetic-consistency checks that recompute each paper's headline numbers from its own stated inputs; and (iv) 50-digit reference values for Weibull and lognormal arrival-time models. All 24 factoring instances (up to 24 qubits) agree with the closed form to a total-variation distance of at most 7.5e-12, and all ECDLP instances agree to machine precision. The regression checks reproduce the published physical-qubit total of 897,864 for RSA-2048 exactly, show that several commonly quoted closed-form expressions deviate from their own papers' tables by up to 22%, and flag one typographical slip. Running a closed-source estimator against the suite as a black box shows that a model calibrated at one key size can differ from the published per-run runtime by a factor of 2.3 at another. We document all AI assistance and release the suite for versioned reuse.

Zenodo (CERN European Organization for Nuclear Research)
Quantum Computing Algorithms and Architecture
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