### Project 05: "Digital expansions with applications in cryptography"

*This project was running from 2010 until 2014.*

Principal investigator: Clemens Heuberger

Graz University of Technology, Austria.

*Mentor for*: Barroero, Frei, Greinecker.

### DK Student

**First phase of the doctoral program:**-
**Daniel Krenn**(Austria; November 2010–January 2013)

Personal homepage;*Email*: daniel.krenn@tugraz.at

*Mentors*: Peter Grabner, Jörg Thuswaldner.

*PhD Defense*: January 25, 2013.

*Referees*: C. Heuberger, T. Lange (Eindhoven), J. Thuswaldner (Leoben).

*Examiners*: C. Heuberger, J. Thuswaldner (Leoben).

### Associated Students

**First phase of the doctoral program:**-
**Nina Schmuck**(Austria; since October 2010)

(on maternity since January 2013)

*Email*: nina.schmuck@tugraz.at

*Mentors:*Peter Kirschenhofer, Bettina Klinz.

### Project description

C. Heuberger's research interests include the asymptotic and probabilistic analysis of algorithms in the sense of D. Knuth (e.g., the expected occurrences of sub-blocks in certain digital expansions), cryptography (e.g., the design of sub-linear scalar multiplication algorithms on Koblitz curves), graph theory (e.g. optimising some graph theoretical indices), number theory (e.g., algorithmic solution of Diophantine equations) and combinatorial optimisation (in particular, inverse optimisation).