Optimized quantum implementation of elliptic curve arithmetic over binary fields

Quantum Information and Computation

Volumn 5, Issue 6, 2005, Pages 474-491

  Kaye, Phillip R ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Algorithm; Circuit; Cryptography; Cryptosystem; Elliptic; Euclidean; Quantum; Shor

Indexed keywords

ALGORITHMS; CRYPTOGRAPHY; ECONOMIC AND SOCIAL EFFECTS; GEOMETRY; NETWORKS (CIRCUITS); QUANTUM THEORY; QUBITS;

ELLIPTIC; ELLIPTIC CURVE ARITHMETIC; ELLIPTIC CURVE CRYPTOSYSTEMS; EUCLIDEAN; EXTENDED EUCLIDEAN ALGORITHM; QUANTUM; SHOR; SHOR'S QUANTUM ALGORITHMS;

CURVE FITTING;

EID: 23744513194     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (7)

1. Christof Zalka, John Proos. "Shor's discrete logarithm quantum algorithm for elliptic curves", QIC Vol. 3 No. 4, pp 317-344 (2003), also quant-ph/0301141.
2. Peter Shor, "Algorithms for Quantum Computation: Discrete Logarithms and Factoring", Proceedings of the 35th Annual Symposium on Foundations of Computer Science (1994), 124-134.
3. D. Hankerson, A. Menezes and S. Vanstone, "Guide to Elliptic Curve Cryptography", Springer-Verlag, 2003.
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5. Stephane Beauregard, Gilles Brassard, Jose Manuel Fernandez, "Quantum Arithmetic on Galois Fields", Quant-ph/0301163.
6. V. Vedral, A. Barenco, A. Ekert, "Quantum networks for elementary arithmetic operations", Phys. Rev. A, 54, 147.
7. A. Barenco, C.H. Bennett, R. Cleve, D.P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin, H. Weinfurter, "Elementary gates for quantum computation", Phys. Rev. A, 52:3457-3476, 1995.