Recent publications & preprints

Diophantine equations

  • On the Nagell-Ljunggren equation (joint with Y. Bugeaud)
  • On solutions of the equation $x^n + y^n = b z^n$ with prime $n|z$.
  • On the equation $x^n - 1 = b z^n$.
  • Reflection, Bernoulli numbers and the proof of Catalan's conjecture.
  • Cyclotomic investigation of the Fermat - Catalan equation.
  • On the class groups of cyclotomic extensions in presence of a solution to Catalan's equation.
  • Class number conditions for the diagonal case of the equation of Nagell -- Ljunggren.
  • New bounds and conditions for the equation of Nagell -- Ljunggren.
  • Algorithmic number theory

  • Fast convolutions meet Montgomery.
  • Cyclotomy primality proofs and their certificates.
  • Dual elliptic primes and applications to cyclotomic primality proving.
  • Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using abelian lifts (joint with F. Morain and E. Schost).
  • Elliptic gauss sums and applications to point counting (joint with V. Vuletescu).
  • Efficient "quasi"-deterministic primality test in proving AKS (joint with R. Avanzi).
  • Biometry and security

  • Entropy sensitive minutiae extraction (joint with A. Munk and K. Mieloch)
  • Dynamic threshold using polynomial surface regression with application to the binarisation of fingerprints (joint with A. Munk and K. Mieloch).
  • The fuzzy vault for fingerprints is vulnerable to attacks.