Secure floating point arithmetic and private satellite collision analysis

Relational Analysis of Floating-Point Arithmetic

A set of abstract operations is given that allows the uniform analysis of integer and floating point arithmetic in the abstract domain of convex polyhedra. We show how to implement rounding faithfully and show that the modelling of rounding is necessary even for the analysis of integer variables. Different rounding modes occurring in floating point implementations are discussed and their implem...

Floating-Point Arithmetic

Precision Arithmetic: A New Floating-Point Arithmetic

A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid the excessive rounding error propagation of conventional floating-point arithmetic. Unlike interval arithmetic, its uncertainty tracking is based on statistics and the central limit theorem, with a much tighter bounding r...

Elements of Floating-point Arithmetic

Floating-point Arithmetic and Message Authentication

There is a well-known class of message authentication systems guaranteeing that attackers will have a negligible chance of successfully forging a message. This paper shows how one of these systems can hash messages at extremely high speed—much more quickly than previous systems at the same security level—using IEEE floating-point arithmetic. This paper also presents a survey of the literature i...