Universal OWF and Hardcore predicates
نویسندگان
چکیده
Proof: The proof of this lemma uses a technique called as Padding which has has its roots in complexity theory. Let fk : {0, 1} → {0, 1} be one-way. From the property of one-way functions (efficient evaluation) there exists a specific polynomial p(·) such that for all k ∈ N, fk can be evaluated in time p(n(k)). We now define a function gk : {0, 1} → {0, 1}m(k)+p(n(k))−n(k) such that gk(x||w) = f(x)||w where |x| = n(k) and |w| = p(n(k))− n(k). We first claim that {gk}k is one-way.
منابع مشابه
Goldreich-Levin Theorem, Hardcore Predicates and Probabilistic Public-Key Encryption
Error Correcting Codes and Hardcore Predicates Error correcting codes (ECC) play an important role in both complexity theory and cryptography. For our purposes let an ECC be a mapping C : {0, 1} → {0, 1} (more generally the source and target alphabets can be arbitrary finite sets), such that if a string y which is close to a valid encoding C(x) is given, then it is possible to reconstruct the m...
متن کاملLearning Noisy Characters, Multiplication Codes, and Cryptographic Hardcore Predicates
We present results in cryptography, coding theory and sublinear algorithms. In cryptography, we introduce a unifying framework for proving that a Boolean predicate is hardcore for a one-way function and apply it to a broad family of functions and predicates, showing new hardcore predicates for well known one-way function candidates such as RSA and discrete-log as well as reproving old results i...
متن کاملA Cookbook for Black-Box Separations and a Recipe for UOWHFs
We present a new framework for proving fully black-box separations and lower bounds. We prove a general theorem that facilitates the proofs of fully black-box lower bounds from a one-way function (OWF). Loosely speaking, our theorem says that in order to prove that a fully black-box construction does not securely construct a cryptographic primitive Q (e.g., a pseudo-random generator or a univer...
متن کاملExtending application of the 'hardcore' definition to smokeless tobacco use: estimates from a nationally representative population in India and its implications.
BACKGROUND The term 'hardcore' has been applied to use of smoking tobacco and generally referred to as the inability or unwillingness of regular smokers to quit. The component constructs of hardcore except nicotine dependence are product neutral. With the use of 'time to first chew' as a measure of nicotine dependence, hardcore definition can be extended to characterize smokeless tobacco users....
متن کاملG22.3033-003 Introduction to Cryptography
This lecture begins with a discussion on secret-key and public-key cryptography, and then discusses One-Way Functions (OWF), and their importance in cryptography. Essentially, an OWF is easy to compute, but difficult to invert. A One-Way Permutation (OWP) is an OWF that permutes elements from a set. A Trap-Door Permutation (TDP) is essentially an OWP with certain information, that if disclosed,...
متن کامل