### Reminder

In all DK related publications, it is required to acknowledge support of the FWF. The following naming convention must be used in all cases:

**Austrian Science Fund (FWF): W1230 **

For example, you may include a sentence such as "The author acknowledges the support of the Austrian Science Fund (FWF): W1230." Please do not forget!

### Project 5:

Digital expansions with applications in cryptography

#### Publications 2016

[17] | Compositions into Powers of $b$: Asymptotic Enumeration and Parameters, Algorithmica, 75(4), 606—631, (2016).
[bib] [arXiv] [MR] [doi/article] | ,

#### Publications 2015

[16] | Multi-Base Representations of Integers: Asymptotic Enumeration and Central Limit Theorems, Appl. Anal. Discrete Math., 9(2), 285—312, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

[15] | Canonical Trees, Compact Prefix-free Codes and Sums of Unit Fractions: A Probabilistic Analysis, SIAM J. Discrete Math., 29(3), 1600—1653, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

#### Publications 2014

[14] | The Number of Compositions into Powers of $b$, Chapter in 25th Int. Conf. Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'14), BA, 241-252, (2014).
[bib] [doi/article] | ,

[13] | On the Number of Multi-Base Representations of an Integer, Chapter in 25th Int. Conf. Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'14), BA, 229-240, (2014).
[bib] [doi/article] | ,

#### Publications 2013

[12] | Analysis of the Width-$w$ Non-Adjacent Form in Conjunction with Hyperelliptic Curve Cryptography and with Lattices, Theoretical Computer Science, 491, 47-70, (2013).
[bib] [arXiv] [MR] [doi/article] | ,

[11] | Digit Expansions with Applications in Cryptography, PhD thesis, Graz, University of Technology, (2013).
[bib] [doi/article] | ,

[10] | On linear combinations of units with bounded coefficients and double-base digit expansions, Monatshefte für Mathematik, 171(3-4), 377-394, (2013).
[bib] [arXiv] [MR] [doi/article] | ,

[9] | Optimality of the Width-$w$ Non-adjacent Form: General Characterisation and the Case of Imaginary Quadratic Bases, Journal of Théorie des Nombres de Bordeaux, 25(2), 353-386, (2013).
[bib] [arXiv] [MR] [doi/article] | ,

[8] | Analysis of Width-$w$ Non-Adjacent Forms to Imaginary Quadratic Bases, Journal of Number Theory, 133(5), 1752-1808, (2013).
[bib] [arXiv] [MR] [doi/article] | ,

[7] | Existence and Optimality of $w$-non-adjacent Forms with an Algebraic Integer Base, Acta Mathematica Hungarica, 140(1-2), 90-104, (2013).
[bib] [arXiv] [MR] [doi/article] | ,

[6] | Analysis of Parameters of Trees Corresponding to Huffman Codes and Sums of Unit Fractions, Chapter in Proc.\ ANALCO 2013 (Mcw.\arkus Nebel, W.\ Szpankowski, eds.), SIAM, 33-42, (2013).
[bib] [MR] [doi/article] | ,

[5] | Sylow $p$-groups of polynomial permutations on the integers mod $p^n$, Journal of Number Theory, 133(12), 4188-4199, (2013).
[bib] [arXiv] [MR] [doi/article] | ,

[4] | The number of Huffman codes, compact trees, and sums of unit fractions, IEEE Transactions on Information Theory, 59, 1065-1075, (2013).
[bib] [arXiv] [MR] [doi/article] | ,

#### Publications 2012

[3] | Greedy trees, caterpillars, and Wiener-type graph invariants, Chapter in Distance in Molecular Graphs --- Theory (Ivan Gutman, Boris Furtula, eds.), University of Kragujevac and Faculty of Science Kragujevac, 12, 195-214, (2012).
[bib] | ,

[2] | Greedy trees, caterpillars, and Wiener-type graph invariants, MATCH. Communications in Mathematical and in Computer Chemistry, 68(1), 273-292, (2012).
[bib] [MR] [doi/article] | ,

#### Publications 2011

[1] | The Wiener maximum quadratic assignment problem, Discrete Optimization, 8, 411-416, (2011).
[bib] [arXiv] [MR] [doi/article] | ,