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We study the problem of determining the probability that m vectors selected uniformly at random from the intersection of the full-rank lattice L in R^n and the window [0,B)^n generate $\Lambda$ when B is chosen to be appropriately large.
Über die Abschätzung des absoluten Betrages des Regulators eines algebraischen Zahlkörpers nach unten
R. Remak · 1932
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J. A. Buchmann · 1991
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Generalization of a theorem of Siegel
J. W. Sands · 1991
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A key-exchange protocol using real quadratic fields
R. Scheidler, J. A. Buchmann, and H. C. Williams · 1994
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The probability of generating some common families of finite groups
V. Acciaro · 1996
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A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone · 1997
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Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
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Trapdoors for hard lattices and new cryptographic constructions [extended abstract]
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Handbook of elliptic and hyperelliptic curve cryptography
H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, and F. Vercauteren, editors · 2006
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Math669: Combinatorics, geometry and complexity of integer points
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Asymptotic Evaluation of Certain Totient Sums
D. N. Lehmer
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The on-line encyclopedia of integer sequence http://oeis.org/A021002
Integer sequence A021002
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Quantum algorithms for one-dimensional infrastructures
P. Sarvepalli and P. Wocjan · 2011
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