Number Theory , OWF Variants Instructor
نویسندگان
چکیده
As a consequence of Algorithm 1 below, there always exist integers x, y ∈ Z such that ax+by = gcd(a, b). We say that a and b are co-prime (or relatively prime) if gcd(a, b) = 1, i.e., ax = 1 mod b. From this, x is the multiplicative inverse of a modulo b, and likewise y is the multiplicative inverse of b modulo a. The following deterministic algorithm shows that gcd(a, b) (and additionally, the integers x and y) can be computed efficiently.
منابع مشابه
The Tale of One-Way Functions
The existence of one-way functions (owf) is arguably the most important problem in computer theory. The article discusses and refines a number of concepts relevant to this problem. For instance, it gives the first combinatorial complete owf, i.e., a function which is one-way if any function is. There are surprisingly many subtleties in basic definitions. Some of these subtleties are discussed o...
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 کاملCryptography in
We study the parallel time-complexity of basic cryptographic primitives such as one-way functions (OWFs) and pseudorandom generators (PRGs). Specifically, we study the possibility of computing instances of these primitives by NC circuits, in which each output bit depends on a constant number of input bits. Despite previous efforts in this direction, there has been no significant theoretical evi...
متن کاملLecture 4 : Strong OWF Instructor : Rachel
Finally, we proved that the hardness of factoring implies that the inverse function (that is to say the multiplication operation or fmult(x, y)) is a weak one way function. This class will combine these definitions together. Particularly, today’s lesson will focus on proving an important theorem which states that if we are able to build a weak one-way function, then we are able to build a stron...
متن کاملCryptography in NC0
We study the parallel time-complexity of basic cryptographic primitives such as one-way functions (OWFs) and pseudorandom generators (PRGs). Specifically, we study the possibility of implementing instances of these primitives by NC functions, namely by functions in which each output bit depends on a constant number of input bits. Despite previous efforts in this direction, there has been no con...
متن کامل