## 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.