T-functions revisited: New criteria for bijectivity/transitivity

The paper presents new criteria for bijectivity/transitivity of T-functions and fast knapsack-like algorithm of evaluation of a T-function. Our approach is based on non-Archimedean ergodic theory: Both the criteria and algorithm use van der Put series to represent 1-Lipschitz $p$-adic functions and to study measure-preservation/ergodicity of these

linear weaknesses in t-functions

We find linear (as well as quadratic) relations in a very large class of T-functions. The relations may be used in analysis of T-function-based stream ciphers. © 2012 Springer-Verlag.Univ. Waterloo, Dep. Electr. Comput. Eng.; The Fields Institute for Research in Mathematical Sciences; The Mprime Network Inc.; The Ontario Research Fund Research ExcellenceWe find linear (as well as quadratic) relations in a very large class of T-functions. The relations may be used in analysis of T-function-based stream ciphers. © 2012 Springer-Verlag