Cryptography Sep 14 , 2006 Lecture 7 : Computational Number Theory III

Introduction to Cryptography September 7 , 2006 Lecture 5 : Existence of OWF and Computational Number Theory

The idea behind the contruction is that fLevin should somehow combine the computations in all efficient functions in such a way that inverting fLevin allows us to invert all other functions. The näıve approach is to interpret the input y to fLevin as a machine-input pair 〈M,x〉, and then let the output of fLevin be M(x). The problem with this approach is that f will not be computable in polynomi...

Computational Number Theory and Applications to Cryptography

• Greatest common divisor (GCD) algorithms. We begin with Euclid’s algorithm, and the extended Euclidean algorithm [2, 12]. We will then discuss variations and improvements such as Lehmer’s algorithm [14], the binary algorithms [12], generalized binary algorithms [20], and FFT-based methods. We will also discuss how to adapt GCD algorithms to compute modular inverses and to compute the Jacobi a...

Randomness in Cryptography April 6 , 2013 Lecture 12 : Computational Key Derivation

In the previous lecture, we discussed methods of key derivation, in particular, how to beat the RT bound for square-friendly applications and defined the notion of unpredictability extractors. In this question, we’ll ask if we can do any better by allowing computational assumptions. Such notions may be helpful for beating information-theoretic bounds for applications that consider only computat...

Quantum Algorithms – Lecture Notes∗– Summer School on Theory and Technology in Quantum Information, Communication, Computation and Cryptography

Cryptography - Wikipedia, the free encyclopedia

Cryptography is an interdisciplinary subject, drawing from several fields. Older forms of cryptography were chiefly concerned with patterns in language. More recently, the emphasis has shifted, and cryptography makes extensive use of mathematics, particularly discrete mathematics, including topics from number theory, information theory, computational complexity, statistics and combinatorics. Cr...