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Proving primality in essentially quartic random time
 Math. Comp
, 2003
"... Abstract. This paper presents an algorithm that, given a prime n, finds and verifies a proof of the primality of n in random time (lg n) 4+o(1). Several practical speedups are incorporated into the algorithm and discussed in detail. 1. ..."
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Cited by 18 (0 self)
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Abstract. This paper presents an algorithm that, given a prime n, finds and verifies a proof of the primality of n in random time (lg n) 4+o(1). Several practical speedups are incorporated into the algorithm and discussed in detail. 1.
List decoding for binary Goppa codes
, 2008
"... This paper presents a listdecoding algorithm for classical irreducible binary Goppa codes. The algorithm corrects, in polynomial time, approximately n − p n(n − 2t − 2) errors in a lengthn classical irreducible degreet binary Goppa code. Compared to the best previous polynomialtime listdecoding ..."
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Cited by 10 (4 self)
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This paper presents a listdecoding algorithm for classical irreducible binary Goppa codes. The algorithm corrects, in polynomial time, approximately n − p n(n − 2t − 2) errors in a lengthn classical irreducible degreet binary Goppa code. Compared to the best previous polynomialtime listdecoding algorithms for the same codes, the new algorithm corrects approximately t 2 /2n extra errors. 1.
Reducing lattice bases to find smallheight values of univariate polynomials
 in [13] (2007). URL: http://cr.yp.to/papers.html#smallheight. Citations in this document: §A
, 2004
"... Abstract. This paper generalizes several previous results on finding divisors in residue classes (Lenstra, Konyagin, Pomerance, Coppersmith, HowgraveGraham, Nagaraj), finding divisors in intervals (Rivest, Shamir, Coppersmith, HowgraveGraham), finding modular roots (Hastad, Vallée, Girault, Toffin ..."
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Cited by 8 (4 self)
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Abstract. This paper generalizes several previous results on finding divisors in residue classes (Lenstra, Konyagin, Pomerance, Coppersmith, HowgraveGraham, Nagaraj), finding divisors in intervals (Rivest, Shamir, Coppersmith, HowgraveGraham), finding modular roots (Hastad, Vallée, Girault, Toffin, Coppersmith, HowgraveGraham), finding highpower divisors (Boneh, Durfee, HowgraveGraham), and finding codeword errors beyond half distance (Sudan, Guruswami, Goldreich, Ron, Boneh) into a unified algorithm that, given f and g, finds all rational numbers r such that f(r) and g(r) both have small height. 1.