Deterministic extractors for small-space sources
نویسندگان
چکیده
منابع مشابه
Deterministic Extractors for Algebraic Sources
An algebraic source is a random variable distributed uniformly over the set of common zeros of one or more multivariate polynomials defined over a finite field F. Our main result is the construction of an explicit deterministic extractor for algebraic sources over exponentially large prime fields. More precisely, we give an explicit (and arguably simple) function E : Fn 7→ {0, 1}m such that the...
متن کاملDeterministic Extractors for Additive Sources
We propose a new model of a weakly random source that admits randomness extraction. Our model of additive sources includes such natural sources as uniform distributions on arithmetic progressions (APs), generalized arithmetic progressions (GAPs), and Bohr sets, each of which generalizes affine sources. We give an explicit extractor for additive sources with linear minentropy over both Zp and Z ...
متن کاملDeterministic Extractors for Bit-Fixing Sources and Exposure-Resilient Cryptography
We give an efficient deterministic algorithm that extracts Ω(n2γ) almost-random bits from sources where n 1 2 +γ of the n bits are uniformly random and the rest are fixed in advance. This improves upon previous constructions, which required that at least n/2 of the bits be random in order to extract many bits. Our construction also has applications in exposure-resilient cryptography, giving exp...
متن کاملDeterministic Extractors - Lecture Notes
Randomness is used in many places in our daily lives. Some examples are gambling, statistics, algorithms, cryptography etc. For such applications one typically assumes a supply of completely unbiased and independent randim bits. This raises the problem of where to get these assumed random bits from. We could try and use natural sources of randomness such as sun spots, the stock market or the we...
متن کاملExtractors for Turing-Machine Sources
We obtain the first deterministic randomness extractors for n-bit sources with minentropy ≥ n1−α generated (or sampled) by single-tape Turing machines running in time n2−16α, for all sufficiently small α > 0. We also show that such machines cannot sample a uniform n-bit input to the Inner Product function together with the output. The proofs combine a variant of the crossing-sequence technique ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 2011
ISSN: 0022-0000
DOI: 10.1016/j.jcss.2010.06.014