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Planning the transition to quantum-safe cryptosystems requires understanding the cost of quantum attacks on vulnerable cryptosystems.
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Vlad Gheorghiu and Michele Mosca · 1902
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“Revisiting Shor’s quantum algorithm for computing general discrete logarithms”
Martin Ekerå · 1905
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“Flexible layout of surface code computations using AutoCCZ states”
Craig Gidney and Austin. Fowler · 1905
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“Approximate encoded permutations and piecewise quantum adders”
Craig Gidney · 1905
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“Windowed quantum arithmetic”
Craig Gidney · 1905
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“A method for obtaining digital signatures and public-key cryptosystems”
R.. Rivest, A. Shamir and L. Adleman · 1978
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“Algorithms for quantum computation: Discrete logarithms and factoring”
Peter Shor · 1994
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“On Shor’s quantum factor finding algorithm: Increasing the probability of success and tradeoffs involving the Fourier Transform modulus”, 1995
E Knill · 1995
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“Efficient networks for quantum factoring”
David Beckman, Amalavoyal. Chari, Srikrishna Devabhaktuni and John Preskill · 1996
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“Quantum networks for elementary arithmetic operations”
Vlatko Vedral, Adriano Barenco and Artur Ekert · 1996
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“Fast versions of Shor’s quantum factoring algorithm”
Christof Zalka · 1998
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“The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer”
Michele Mosca and Artur Ekert · 1999
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“Fast parallel circuits for the quantum Fourier transform”
R. Cleve and J. Watrous · 2000
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“Efficient Factorization with a Single Pure Qubit and N Mixed Qubits”
S. Parker and M.. Plenio · 2000
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“Fast heuristic minimization of exclusive-sums-of-products”, 2001
Alan Mishchenko and Marek Perkowski · 2001
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“An approximate Fourier transform useful in quantum factoring”
D. Coppersmith · 2002
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“Classical and Quantum Computation”
A. Kitaev, A. Shen and M. Vyalyi · 2002
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“Circuit for Shor’s algorithm using 2n+3 qubits”
S. Beauregard · 2003
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“Fast quantum modular exponentiation”
Rodney Van and Kohei. Itoh · 2005
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“Shor’s algorithm on a nearest-neighbor machine”
Samuel. Kutin · 2006
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“Shor’s algorithm with fewer (pure) qubits”
Christof Zalka · 2006
Cited alongside, same era.
“Offloading Quantum Computation by Superposition Masking”
Samuel Jaques and Craig Gidney · 2008
Cited alongside, same era.
“New Attack on AES” Accessed: 2025-02-14, https://www.schneier.com/blog/archives/2009/07/new_attack_on_a.html , 2009
Bruce Schneier · 2009
Cited alongside, same era.
“A fault tolerant, area efficient architecture for Shor’s factoring algorithm”
Mark. Whitney, Nemanja Isailovic, Yatish Patel and John Kubiatowicz · 2009
Cited alongside, same era.
“Distributed quantum computation architecture using semiconductor nanophotonics”
Rodney Van, Thaddeus Ladd, Austin Fowler and Yoshihisa Yamamoto · 2010
Cited alongside, same era.
“Surface codes: Towards practical large-scale quantum computation” arXiv:1208.0928
“Halving the cost of quantum addition”
Craig Gidney · 2018
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“A game of surface codes: Large-scale quantum computing with lattice surgery”
Daniel Litinski · 2018
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“Qubitization of Arbitrary Basis Quantum Chemistry by Low Rank Factorization”
Dominic Berry, Craig Gidney, Mario Motta, Jarrod McClean and Ryan Babbush · 2019
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“On post-processing in the quantum algorithm for computing short discrete logarithms”
Martin Ekerå · 2020
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“Quantum algorithms for computing general discrete logarithms and orders with tradeoffs”
Martin Ekerå · 2020
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A.. Fowler, M. Mariantoni, J.. Martinis and A.. Cleland · 2012
Cited alongside, same era.
“Surface code quantum computing by lattice surgery”
Dominic Horsman, Austin Fowler, Simon Devitt and Rodney Van · 2012
Cited alongside, same era.
“Layered Architecture for Quantum Computing”
N. Jones, Rodney Van, Austin. Fowler, Peter. McMahon, Jungsang Kim, Thaddeus. Ladd and Yoshihisa Yamamoto · 2012
Cited alongside, same era.
“Low-overhead constructions for the fault-tolerant Toffoli gate”
Cody Jones · 2013
Cited alongside, same era.
“Fast quantum modular exponentiation architecture for Shor’s factoring alogrithm”
Archimedes Pavlidis and Dimitris Gizopoulos · 2014
Cited alongside, same era.
“Optimal ancilla-free Clifford+T approximation of z-rotations”
Neil. Ross and Peter Selinger · 2014
Cited alongside, same era.
“Modifying Shor’s algorithm to compute short discrete logarithms” https://eprint.iacr.org/2016/1128 , Cryptology ePrint Archive, Report 2016/1128, 2016
Martin Ekerå · 2016
Cited alongside, same era.
“Approximate quantum Fourier transform with O(n log(n)) T gates”
Yunseong Nam, Yuan Su and Dmitri Maslov · 2020
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“How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits”
Craig Gidney and Martin Ekerå · 2021
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“Universal Quantum Computing with Twist-Free and Temporally Encoded Lattice Surgery”
Christopher Chamberland and Earl. Campbell · 2022
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“Active volume: An architecture for efficient fault-tolerant quantum computers with limited non-local connections”
Daniel Litinski and Naomi Nickerson · 2022
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“Quantum Period Finding is Compression Robust”
Alexander May and Lars Schlieper · 2022
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“Rapid initial state preparation for the quantum simulation of strongly correlated molecules”
Dominic. Berry, Yu Tong, Tanuj Khattar, Alec White, Tae Kim, Sergio Boixo, Lin Lin, Seunghoon Lee, Garnet-Lic Chan, Ryan Babbush and Nicholas. Rubin · 2024
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“Reducing the Number of Qubits in Quantum Factoring”, Cryptology ePrint Archive, Paper 2024/222, 2024
Clémence Chevignard, Pierre-Alain Fouque and André Schrottenloher · 2024
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“Magic state cultivation: growing T states as cheap as CNOT gates”
Craig Gidney, Noah Shutty and Cody Jones · 2024
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“Trading T gates for dirty qubits in state preparation and unitary synthesis”
Guang Low, Vadym Kliuchnikov and Luke Schaeffer · 2024
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“NIST IR 8547 ipd: Transition to Post-Quantum Cryptography Standards”
Dustin Moody, Ray Perlner, Andrew Regenscheid, Angela Robinson and David Cooper · 2024
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“An Efficient Quantum Factoring Algorithm”
Oded Regev · 2024
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“Yoked surface codes”
Craig Gidney, Michael Newman, Peter Brooks and Cody Jones · 2025
Closest in time.
“Data for "How to factor 2048 bit RSA integers with a million noisy qubits"”
Craig Gidney · 2025
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“Optimized circuits for windowed modular arithmetic with applications to quantum attacks against RSA”
Alessandro Luongo, Varun Narasimhachar and Adithya Sireesh · 2025
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“RSA numbers - RSA-2048” Accessed: 2024-12-19, 2024
Wikipedia · 2048
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