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We consider a quantum polynomial-time algorithm which solves the discrete logarithm problem for points on elliptic curves over $GF(2^m)$.
A theory of Galois switching functions
D. K. Pradhan · 1978
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Reversible computing
T. Toffoli · 1980
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VLSI designs for multiplication over finite fields G F ( 2 m ) GF(2^{m})
E. D. Mastrovito · 1988
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VLSI Architectures for Computation in Galois Fields
E. D. Mastrovito · 1991
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An implementation of elliptic curve cryptosystems over G F ( 2 155 ) GF(2^{155})
G. B. Agnew, R. C. Mullin, and S. A. Vanstone · 1993
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Reducing elliptic curve logarithms to logarithms in a finite field
A. J. Menezes, T. Okamoto, and S. A. Vanstone · 1993
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Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
P. W. Shor · 1997
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R. Cleve and J. Watrous · 2000
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Software implementation of elliptic curve cryptography over binary fields
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M. Nielsen and I. Chuang · 2000
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S. Beauregard, G. Brassard, and J. M. Fernandez · 2003
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Shor’s discrete logarithm quantum algorithm for elliptic curves
Certicom announces elliptic curve cryptography challenge winner
Certicom · 2004
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Low complexity bit parallel architectures for polynomial basis multiplication over G F ( 2 m ) GF(2^{m})
A. Reyhani-Masoleh and M. A. Hasan · 2004
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Elliptic Curve Cryptography: The next generation of wireless security
S. A. Vanstone · 2004
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Optimized quantum implementation of elliptic curve arithmetic over binary fields
P. Kaye · 2005
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Fast quantum modular exponentiation
R. Van Meter and K. M. Itoh · 2005
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Shor’s algorithm on a nearest-neighbor machine
S. A. Kutin · 2007
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J. Proos and C. Zalka · 2003
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http://www.nsa.gov/ia/industry/crypto_suite_b.cfm
NSA Suite B Factsheet
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Computation at a distance, January 2007, arXiv:quant-ph/0701194
S. A. Kutin, D. P. Moulton, and L. M. Smithline · 2007
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