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» Widening Integer Arithmetic
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ARITH
2005
IEEE
14 years 1 months ago
Arithmetic Operations in the Polynomial Modular Number System
We propose a new number representation and arithmetic for the elements of the ring of integers modulo p. The socalled Polynomial Modular Number System (PMNS) allows for fast polyn...
Jean-Claude Bajard, Laurent Imbert, Thomas Plantar...
EUROCRYPT
2010
Springer
14 years 6 days ago
Fully Homomorphic Encryption over the Integers
We describe a very simple “somewhat homomorphic” encryption scheme using only elementary modular arithmetic, and use Gentry’s techniques to convert it into a fully homomorph...
Marten van Dijk, Craig Gentry, Shai Halevi, Vinod ...
CONCUR
2005
Springer
14 years 28 days ago
Termination Analysis of Integer Linear Loops
Usually, ranking function synthesis and invariant generation oop with integer variables involves abstracting the loop to have real variables. Integer division and modulo arithmetic...
Aaron R. Bradley, Zohar Manna, Henny B. Sipma
SAS
2007
Springer
124views Formal Methods» more  SAS 2007»
14 years 1 months ago
Arithmetic Strengthening for Shape Analysis
Abstract. Shape analyses are often imprecise in their numerical reasoning, whereas numerical static analyses are often largely unaware of the shape of a program’s heap. In this p...
Stephen Magill, Josh Berdine, Edmund M. Clarke, By...
JAR
2006
236views more  JAR 2006»
13 years 7 months ago
Deciding Boolean Algebra with Presburger Arithmetic
We describe an algorithm for deciding the first-order multisorted theory BAPA, which combines 1) Boolean algebras of sets of uninterpreted elements (BA) and 2) Presburger arithmeti...
Viktor Kuncak, Huu Hai Nguyen, Martin C. Rinard