Optimized Point Addition Circuits for Elliptic Curve Discrete Logarithms [pdf]
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The paper discusses optimized point addition circuits for elliptic curve discrete logarithms, addressing the challenges posed by quantum computing to cryptography. It builds on recent advancements in reducing the costs associated with Shor's algorithm. The proposed quantum logical circuit architecture achieves comparable results to previous works while slightly increasing qubit usage.
- ▪Shor's algorithm poses a significant threat to cryptography due to the capabilities of quantum computers.
- ▪Recent research has focused on reducing the costs of quantum algorithms for factoring RSA and computing elliptic curve discrete logarithms.
- ▪The new circuit architecture presented in this paper offers a slight increase in qubit count but a reduction in Toffoli gate count.
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Quantum Physics arXiv:2606.02235 (quant-ph) [Submitted on 1 Jun 2026] Title:Optimized Point Addition Circuits for Elliptic Curve Discrete Logarithms Authors:André Schrottenloher View a PDF of the paper titled Optimized Point Addition Circuits for Elliptic Curve Discrete Logarithms, by Andr\'e Schrottenloher View PDF HTML (experimental) Abstract:Shor's algorithm represents the main threat of quantum computers to cryptography. In order to precisely understand its feasibility, many authors have worked towards reducing its costs, either at the logical level (assuming a fault-tolerant architecture), or at the physical level (taking into account the constraints of envisioned hardware). In particular, recent works by Chevignard et al.
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