Linear Recurrences with Polynomial Coefficients and Application to Integer Factorization and Cartier–Manin Operator

Abstract

We study the complexity of computing one or several terms (not necessarily consecutive) in a recurrence with polynomial coefficients. As applications, we improve the best currently known upper bounds for factoring integers deterministically and for computing the Cartier–Manin operator of hyperelliptic curves.

MSC codes

  1. 11Y16
  2. 68Q25
  3. 11Y05

Keywords

  1. linear recurrences
  2. factorization
  3. Cartier–Manin operator

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Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 1777 - 1806
ISSN (online): 1095-7111

History

Submitted: 17 May 2004
Accepted: 14 September 2006
Published online: 22 March 2007

MSC codes

  1. 11Y16
  2. 68Q25
  3. 11Y05

Keywords

  1. linear recurrences
  2. factorization
  3. Cartier–Manin operator

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