aiqbench analysis
This research advances reversible circuit designs for elliptic-curve point addition, specifically optimizing record-and-replay arithmetic to reduce qubit counts and Toffoli gate operations for Shor's algorithm. By employing techniques like base-5 encoding and fused replay, the study demonstrates resource efficiencies that fall below current low-gate estimates while addressing specific correctness constraints in quantum-addressed window selection. These findings represent a significant step toward practical fault-tolerant implementations of discrete-logarithm attacks on secp256k1 curves.
Efficient Record-and-Replay Arithmetic for Quantum Elliptic-Curve Point Addition
arXiv:2609.28882v1 Announce Type: new Abstract: We study reversible secp256k1 point-addition circuits developed through ECDSA.Fail for Shor's elliptic-curve discrete-logarithm algorithm. Two complementary constructions improve record-and-replay GCD arithmetic: Jump-2 groups binary-GCD steps and compresses their decisions using base-5 encoding, while ping-pong uses fixed register alternation and one-bit decisions to avoid full-width comparisons and data-dependent swaps. Fused replay combines doubling and signed addition into one modular correction. Both constructions support quantum-addressed window selection with measurement-based lookup cleanup. We compare three circuits on 100,000 fresh inputs across nine lookup-table configurations. A separately tested repair uses 1,419 qubits and 1.356 million mean executed Toffolis, with no detected failures on another 100,000 inputs. Structured supported-input counterexamples remain, so these tests do not establish all-input correctness. We also provide conditional coherent-error analysis and reversible safegcd comparisons. Under the stated window allowance, repaired-circuit resources lie below Google's low-gate caps and Schrottenloher's low-gate estimates, but differing accounting and correctness evidence preclude formal dominance. The results concern individual window-selected additions, not complete Shor computations.
Authors:Jieyi Long, Theodore Pender, Zhao Huang, Manuel B. Santos, Samrendra Kumar Singh, Bartosz Naskręcki, BitWonka, Pierre-Luc Dallaire-Demers, Francesco Giannicola, Ruben M. L. Paschoarelli, Oli Freuler, Jackie Chia-Hsun Lee, Vasily Gnuchev, Gopi Kannappan, John Boyer, Xavier Butler, Akash Balasubramani, Jordan Newman, Bereket Dereje, Alexander Hertlein, Robert Kodra, Lucas Levy, Shaan Patel, JT Rose, Matt Zweil, Okechukwu Wisdom, Tarek El-Eter, Edison Lee, Michael Dong, Alan Li, Anto Joseph, Duy Nguyen, Gajesh Naik, Gautham Anant, Soubhik Deb, Justin Drake
Abstract:We study reversible secp256k1 point-addition circuits developed through this http URL for Shor's elliptic-curve discrete-logarithm algorithm. Two complementary constructions improve record-and-replay GCD arithmetic: Jump-2 groups binary-GCD steps and compresses their decisions using base-5 encoding, while ping-pong uses fixed register alternation and one-bit decisions to avoid full-width comparisons and data-dependent swaps. Fused replay combines doubling and signed addition into one modular correction. Both constructions support quantum-addressed window selection with measurement-based lookup cleanup. We compare three circuits on 100,000 fresh inputs across nine lookup-table configurations. A separately tested repair uses 1,419 qubits and 1.356 million mean executed Toffolis, with no detected failures on another 100,000 inputs. Structured supported-input counterexamples remain, so these tests do not establish all-input correctness. We also provide conditional coherent-error analysis and reversible safegcd comparisons. Under the stated window allowance, repaired-circuit resources lie below Google's low-gate caps and Schrottenloher's low-gate estimates, but differing accounting and correctness evidence preclude formal dominance. The results concern individual window-selected additions, not complete Shor computations.
35 pages, 2 figures. Technical companion to arXiv:2609.09582. Reproducibility artifacts: this https URL
arXiv:2609.28882 [quant-ph]
(or arXiv:2609.28882v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.28882 arXiv-issued DOI via DataCite (pending registration)
Full text under the publisher's open licence · 265 words
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