Fetching the paper…
Reading the bibliography…
We use Shor's algorithm for the computation of elliptic curve private keys as a case study for resource estimates in the silicon-photonics-inspired active-volume architecture.
C. Gidney, Windowed quantum arithmetic, arXiv:1905.07682 (2019a)
1905
Earlier work this paper cites.
C. Gidney, Approximate encoded permutations and piecewise quantum adders, arXiv:1905.08488 (2019b)
1905
Earlier work this paper cites.
P. L. Montgomery, Modular multiplication without trial division, Mathematics of computation 44
1985
Earlier work this paper cites.
P. Shor, Algorithms for quantum computation: discrete logarithms and factoring, Proceedings 35th Annual Symposium on Foundations of Computer Science , 124 (1994)
1994
Earlier work this paper cites.
B. S. Kaliski, The montgomery inverse and its applications, IEEE transactions on computers 44
1995
Earlier work this paper cites.
P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Journal on Computing 26
1997
Earlier work this paper cites.
S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary, arXiv:quant-ph/9811052 (1998)
1998
Earlier work this paper cites.
J. Proos and C. Zalka, Shor’s discrete logarithm quantum algorithm for elliptic curves, arXiv:quant-ph/0301141 (2003)
2003
Earlier work this paper cites.
A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. 303
2003
Earlier work this paper cites.
R. P. Brent and P. Zimmermann, Modern computer arithmetic , Vol. 18 (Cambridge University Press, 2010) pp. 67–68
2010
Earlier work this paper cites.
A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86
2012
Earlier work this paper cites.
A. G. Fowler, Time-optimal quantum computation, arXiv:1210.4626 (2012)
2012
Earlier work this paper cites.
E. Barker, W. Burr, A. Jones, T. Polk, S. Rose, M. Smid, Q. Dang, et al. , Recommendation for key management part 3: Application-specific key management guidance, NIST special publication 800
2015
Cited alongside, same era.
B. M. Terhal, Quantum error correction for quantum memories, Rev. Mod. Phys. 87
2015
Cited alongside, same era.
N. Courtois, G. Song, and R. Castellucci, Speed optimizations in bitcoin key recovery attacks, Tatra Mountains Mathematical Publications-The Journal of Slovak Academy of Sciences 67
2016
Cited alongside, same era.
2017
Cited alongside, same era.
E. T. Campbell, B. M. Terhal, and C. Vuillot, Roads towards fault-tolerant universal quantum computation, Nature 549
C. Gidney, Quantum block lookahead adders and the wait for magic states, arXiv:2012.01624 (2020)
2020
Later among the works it cites.
I. D. Kivlichan, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, W. Sun, Z. Jiang, N. Rubin, A. Fowler, A. Aspuru-Guzik, H. Neven, and R. Babbush, Improved fault-tolerant quantum simulation of condensed-phase correlated electrons via trotterization, Quantum 4
2020
Later among the works it cites.
2021
Later among the works it cites.
C. Gidney and M. Ekerå, How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits, Quantum 5
2021
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2017
Cited alongside, same era.
2018
Cited alongside, same era.
C. Gidney, Halving the cost of quantum addition, Quantum 2
2018
Cited alongside, same era.
R. Rines and I. Chuang, High performance quantum modular multipliers, arXiv:1801.01081 (2018)
2018
Cited alongside, same era.
2018
Cited alongside, same era.
D. Litinski, A game of surface codes: Large-scale quantum computing with lattice surgery, Quantum 3
2019
Cited alongside, same era.
T. Häner, S. Jaques, M. Naehrig, M. Roetteler, and M. Soeken, Improved quantum circuits for elliptic curve discrete logarithms, Post-Quantum Cryptography , 425 (2020)
2020
Cited alongside, same era.
C. Chamberland and E. T. Campbell, Universal quantum computing with twist-free and temporally encoded lattice surgery, PRX Quantum 3
2022
Later among the works it cites.
C. Chamberland, K. Noh, P. Arrangoiz-Arriola, E. T. Campbell, C. T. Hann, J. Iverson, H. Putterman, T. C. Bohdanowicz, S. T. Flammia, A. Keller, G. Refael, J. Preskill, L. Jiang, A. H. Safavi-Naeini, O. Painter, and F. G. Brandão, Building a fault-tolerant quantum computer using concatenated cat codes, PRX Quantum 3
2022
Later among the works it cites.
2022
Later among the works it cites.
L. Chen, D. Moody, K. Randall, A. Regenscheid, and A. Robinson, Recommendations for discrete logarithm-based cryptography: Elliptic curve domain parameters, (2023), 10.6028/NIST.SP.800-186
2023
Closest in time.
2023
Closest in time.
S. Bartolucci, P. Birchall, H. Bombin, H. Cable, C. Dawson, M. Gimeno-Segovia, E. Johnston, K. Kieling, N. Nickerson, M. Pant, F. Pastawski, T. Rudolph, and C. Sparrow, Fusion-based quantum computation, Nature Communications 14
2023
Closest in time.
H. Bombín, C. Dawson, R. V. Mishmash, N. Nickerson, F. Pastawski, and S. Roberts, Logical blocks for fault-tolerant topological quantum computation, PRX Quantum 4
2023
Closest in time.