4 papers · 1 filter
Additive index and Carlitz rank
Pierre-Yves Bienvenu, Arne Winterhof
We compare several complexity measures for self-mappings of finite fields. In particular, we show that Carlitz rank and additive index cannot be small simultaneously up to trivial…
Symmetric measures of pseudorandomness for binary sequences
Yixin Ren, Arne Winterhof
We compare ordinary and symmetric variants of two classical measures of pseudorandomness for binary sequences, the -adic complexity and the linear complexity. In the periodic se…
On the additive index of the Diffie-Hellman mapping and the discrete logarithm
Pierre-Yves Bienvenu, Arne Winterhof
Several complexity measures such as degree, sparsity and multiplicative index for cryptographic functions including the Diffie-Hellman mapping and the discrete logarithm in a finit…
Some notes on the pseudorandomness of Legendre symbol and Liouville function
Johannes Grünberger, Arne Winterhof
We improve bounds on the degree and sparsity of Boolean functions representing the Legendre symbol as well as on the th linear complexity of the Legendre sequence. We also prove…