Petr Lisoněk

On steganographic embedding efficiency

In this paper, we study embedding efficiency, which is an important attribute of steganographic schemes directly influencing their security. It is defined as the expected number of embedded random message bits per one embedding change. Constraining ourselves to embedding realized using linear covering codes (so called matrix embedding), we show that the quantity that determines embedding efficiency is not the covering radius but the average distance to code. We demonstrate that for linear codes of fixed block length and dimension, the highest embedding efficiency (the smallest average distance to code) is not necessarily achieved using codes with the smallest covering radius. Nevertheless, we prove that with increasing code length and fixed rate (i.e., fixed relative message length), the relative average distance to code and the relative covering radius coincide. Finally, we describe several specific examples of q-ary linear codes with q matched to the embedding operation and experimentally demonstrate the improvement in steganographic security when incorporating the coding methods to digital image steganography.

On the Connection between Kloosterman Sums and Elliptic Curves

We explore the known connection of Kloosterman sums on fields of characteristic 2 and 3 with the number of points on certain elliptic curves over these fields. We use this connection to prove results on the divisibility of Kloosterman sums, and to compute numerical examples of zeros of Kloosterman sums on binary and ternary fields of large orders. We also show that this connection easily yields some formulas due to Carlitz that were recently used to prove certain non-existence results on Kloosterman zeros in subfields.

Applications of integer relation algorithms

Let

Selected Areas in Cryptography -- SAC 2013

a

Kochen-Specker set with seven contexts

be a~vector of real numbers. By an integer relation for

Computational investigations of the Prouhet-Tarry-Escott problem

a

Improvement of the Degree Setting in Gosper's Algorithm

we mean a~non-zero integer vector

Symbolic Computation Approach to Nonlinear Dynamics

c

A family of complete caps in PG( n , 2)

such that

Closed forms for the number of polygon dissections

ca^T=0