Linear recurrences with polynomial coefficients and application to integer factorization and Cartier-Manin operator

Alin Bostan (1) , Pierrick Gaudry (2, 3) , Eric Schost (4)

1 ALGO - Algorithms
2 SPACES - Solving problems through algebraic computation and efficient software
3 TANC - Algorithmic number theory for cryptology
4 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

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.

Domaines: Cryptographie et sécurité [cs.CR]

Alin Bostan, Pierrick Gaudry, Eric Schost. Linear recurrences with polynomial coefficients and application to integer factorization and Cartier-Manin operator. SIAM Journal on Computing, 2007, 36 (6), pp.1777-1806. ⟨10.1137/S0097539704443793⟩. ⟨inria-00103401v1⟩