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Paper 1

A Note on Output Length of One-Way State Generators and EFIs

Minki Hhan, Tomoyuki Morimae, Takashi Yamakawa

Year

2023

Journal

arXiv preprint

DOI

arXiv:2312.16025

arXiv

2312.16025

We study the output length of one-way state generators (OWSGs), their weaker variants, and EFIs. - Standard OWSGs. Recently, Cavalar et al. (arXiv:2312.08363) give OWSGs with $m$-qubit outputs for any $m=ω(\log λ)$, where $λ$ is the security parameter, and conjecture that there do not exist OWSGs with $O(\log \log λ)$-qubit outputs. We prove their conjecture in a stronger manner by showing that there do not exist OWSGs with $O(\log λ)$-qubit outputs. This means that their construction is optimal in terms of output length. - Inverse-polynomial-advantage OWSGs. Let $ε$-OWSGs be a parameterized variant of OWSGs where a quantum polynomial-time adversary's advantage is at most $ε$. For any constant $c\in \mathbb{N}$, we construct $λ^{-c}$-OWSGs with $((c+1)\log λ+O(1))$-qubit outputs assuming the existence of OWFs. We show that this is almost tight by proving that there do not exist $λ^{-c}$-OWSGs with at most $(c\log λ-2)$-qubit outputs. - Constant-advantage OWSGs. For any constant $ε>0$, we construct $ε$-OWSGs with $O(\log \log λ)$-qubit outputs assuming the existence of subexponentially secure OWFs. We show that this is almost tight by proving that there do not exist $O(1)$-OWSGs with $((\log \log λ)/2+O(1))$-qubit outputs. - Weak OWSGs. We refer to $(1-1/\mathsf{poly}(λ))$-OWSGs as weak OWSGs. We construct weak OWSGs with $m$-qubit outputs for any $m=ω(1)$ assuming the existence of exponentially secure OWFs with linear expansion. We show that this is tight by proving that there do not exist weak OWSGs with $O(1)$-qubit outputs. - EFIs. We show that there do not exist $O(\log λ)$-qubit EFIs. We show that this is tight by proving that there exist $ω(\log λ)$-qubit EFIs assuming the existence of exponentially secure PRGs.

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Paper 2

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

Lei Zhang, Zhiyuan Chen

Year

2026

Journal

arXiv preprint

DOI

arXiv:2605.01008

arXiv

2605.01008

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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