Abstract
Lattices are discrete sets of points in the n-dimensional Euclidean space \(\mathbb {R}^n\), which are described as all integer linear combinations of independent vectors.
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References
M. Bhargava, J. Hanke, Universal quadratic forms and the 290 theorem. Invent. Math. (to appear)
J.H. Conway, N.J.A. Sloane, Sphere-Packings, Lattices, and Groups (Springer, New York, 1998)
W. Ebeling, Lattices and Codes (Springer, Berlin, 2013)
J. Martinet, Perfect Lattices in Euclidean Spaces (Springer, Berlin, 2013)
D. Micciancio, O. Regev, Lattice-Based Cryptography. Post-Quantum Cryptography (Springer, Berlin, 2009)
C. Peikert, A decade of lattice cryptography. Found. Trends®; Theor. Comput. Sci. 10(4), 283–424 (2016)
P.W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)
R. Zamir, Lattice Coding for Signals and Networks: A Structured Coding Approach to Quantization, Modulation, and Multiuser Information Theory (Cambridge University Press, Cambridge, 2014)
Acknowledgment
The authors wish to thank the reviewer for the interesting and pertinent suggestions presented and the important support provided by SBMAC (Brazilian Society of Computational and Applied Mathematics) and FAPESP foundation during the elaboration of this Springer Briefs book.
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Costa, S.I.R., Oggier, F., Campello, A., Belfiore, JC., Viterbo, E. (2017). Introduction. In: Lattices Applied to Coding for Reliable and Secure Communications. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-67882-5_1
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DOI: https://doi.org/10.1007/978-3-319-67882-5_1
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