On Multiple Symmetric Fixed Points in GOST

On Multiple Symmetric Fixed Points in GOST

In this article the author revisits the oldest attack on GOST known, the Kara Reflection attack, and another totally unrelated truncated differential attack by Courtois and Misztal. It is hard to imagine that there could be any relationship between two so remote attacks which have nothing in common. However, there is one: Very surprisingly, both properties can be combined and lead the fastest a...

Fixed Points of Symmetric Product Mappings

On fixed points of fundamentally nonexpansive mappings in Banach spaces

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

Fixed Points of Multiple-valued Transformations

A multiple-valued transformation T from a space X to a space Y is a function assigning to each point x o f X a nonempty closed subset T(x) of F. The graph of T comprises those points (x, y) in the topological product X Y for which y belongs to T(x). All spaces to be considered shall be compact metric and all transformations T shall be upper semi-continuous, meaning that their graphs are closed,...

On Common Fixed Points

Some fixed point theorems based on an asymptotic regularity condition have been obtained, which generalize the previously well-known results. 2000 Mathematics Subject Classification: 47H10, 54H25.