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arXiv · 2605.01008

Semantics-Based Verification of an Implemented Shor Oracle for ECDLP in Qrisp

Lei Zhang·Zhiyuan Chen
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Abstract

Shor-style quantum algorithms for the elliptic-curve discrete logarithm problem (ECDLP) are highly sensitive to the exact semantics of their group-operation oracles. Consequently, minor implementation choices can invalidate the intended mathematical model and lead to misleading conclusions. This paper introduces a semantics-first verification perspective for an end-to-end, compilable ECDLP implementation built on Qrisp. We specify the implemented oracle at the level of program semantics, derive refinement-style verification obligations for its key components, and provide a high-level complexity argument for the resulting oracle family. A small case study highlights that (i) the core point-update primitive agrees with a classical reference on well-formed inputs, yet (ii) controlled execution may violate the expected control law under the evaluated toolchain, despite a passing trivial control sanity check. These results position semantic auditing as a practical prerequisite for trustworthy ECDLP-oriented quantum software.

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Lei Zhang, Zhiyuan Chen. 2026-05-01. Semantics-Based Verification of an Implemented Shor Oracle for ECDLP in Qrisp. https://arxiv.org/abs/2605.01008

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