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CORR
2010
Springer

Ideal forms of Coppersmith's theorem and Guruswami-Sudan list decoding

8 years 5 months ago
Ideal forms of Coppersmith's theorem and Guruswami-Sudan list decoding
: We develop a framework for solving polynomial equations with size constraints on solutions. We obtain our results by showing how to apply a technique of Coppersmith for finding small solutions of polynomial equations modulo integers to analogous problems over polynomial rings, number fields, and function fields. This gives us a unified view of several problems arising naturally in cryptography, coding theory, and the study of lattices. We give (1) a polynomial-time algorithm for finding small solutions of polynomial equations modulo ideals over algebraic number fields, (2) a faster variant of the Guruswami-Sudan algorithm for list decoding of Reed-Solomon codes, and (3) an algorithm for list decoding of algebraic-geometric codes that handles both single-point and multi-point codes. Coppersmith’s algorithm uses lattice basis reduction to find a short vector in a carefully constructed lattice; powerful analogies from algebraic number theory allow us to identify the appropriate...
Henry Cohn, Nadia Heninger
Added 24 Jan 2011
Updated 24 Jan 2011
Type Journal
Year 2010
Where CORR
Authors Henry Cohn, Nadia Heninger
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