Results 1 
2 of
2
The Bit Extraction Problem or tResilient Functions
, 1985
"... \Gamma We consider the following adversarial situation. Let n, m and t be arbitrary integers, and let f : f0; 1g n 7! f0; 1g m be a function. An adversary, knowing the function f , sets t of the n input bits, while the rest (n \Gamma t input bits) are chosen at random (independently and with un ..."
Abstract

Cited by 171 (11 self)
 Add to MetaCart
\Gamma We consider the following adversarial situation. Let n, m and t be arbitrary integers, and let f : f0; 1g n 7! f0; 1g m be a function. An adversary, knowing the function f , sets t of the n input bits, while the rest (n \Gamma t input bits) are chosen at random (independently and with uniform probability distribution). The adversary tries to prevent the outcome of f from being uniformly distributed in f0; 1g m . The question addressed is for what values of n, m and t does the adversary necessarily fail in biasing the outcome of f : f0; 1g n 7! f0; 1g m , when being restricted to set t of the input bits of f . We present various lower and upper bounds on m's allowing an affirmative answer. These bounds are relatively close for t n=3 and for t 2n=3. Our results have applications in the fields of faulttolerance and cryptography. 1. INTRODUCTION The bit extraction problem formulated above The bit extraction problem was suggested by Brassard and Robert [BRref] and by V...
Randomness, Pseudorandomness, and its Applications to Cryptography
, 1998
"... Introduction What does it mean for something to be random? What is a random number? Is 2 a random number? If one has a truly random number, and then proceeds to show it to everyone in the world and use it in every application, does it remain a random number? Intuitively, we all have a feel for perf ..."
Abstract
 Add to MetaCart
(Show Context)
Introduction What does it mean for something to be random? What is a random number? Is 2 a random number? If one has a truly random number, and then proceeds to show it to everyone in the world and use it in every application, does it remain a random number? Intuitively, we all have a feel for performing some sort of action "at random". It is natural to think of choosing something "randomly " by selecting it out of a set of objects without any indication as to which object is chosen. As a result, the notions of probability and uniformness are often mentioned. But what does this phrase really mean? Can it be defined quantitatively? In particular, can this be done in a mathematical sense? In the field of computer science, there is an overwhelming tendency to avoid answering these questions. A formal definition of randomness is often seen as unnecessary and tedious. In addition, the generation of random numbers is often seen as a "Black Box", i.e. one does not know how it is don