equicontinuous
... Let X be a topological space, (Y, d) a metric space and C(X, Y ) the set of continuous functions X → Y . Let F be a subset of C(X, Y ). A function f ∈ F is continuous at a point x0 when given > 0 there is a neighbourhood U of x0 such that d(f (x), f (x0 )) < for every x ∈ U . When the same neigh ...
... Let X be a topological space, (Y, d) a metric space and C(X, Y ) the set of continuous functions X → Y . Let F be a subset of C(X, Y ). A function f ∈ F is continuous at a point x0 when given > 0 there is a neighbourhood U of x0 such that d(f (x), f (x0 )) < for every x ∈ U . When the same neigh ...
String-Matching Problem
... Rabin-Karp Algorithm Correctness: T is a string of
characters over an alphabet of size d, P
is string of characters over an alphabet of
size d and |P| <= |T|, d is the size of the
alphabet and q is a prime number
...
... Rabin-Karp Algorithm Correctness
Implementing Security for Electronic Commerce
... Encodes messages by using two mathematicallyrelated numeric keys: a public key and a private key. The public key is freely available to anyone (public) who wants to communicate with the holder of both keys. It is used to encrypt messages. ...
... Encodes messages by using two mathematicallyrelated numeric keys: a public key and a private key. The public key is freely available to anyone (public) who wants to communicate with the holder of both keys. It is used to encrypt messages. ...
security
... Hash functions • Produce fixed-length hash (~32 bits) from variable-length message – It is computationally infeasible to find a message with that hash; in fact one can't determine any usable information about a message with that hash, not even a single bit. – Biometrics usually work the same way! ...
... Hash functions • Produce fixed-length hash (~32 bits) from variable-length message – It is computationally infeasible to find a message with that hash; in fact one can't determine any usable information about a message with that hash, not even a single bit. – Biometrics usually work the same way! ...
Jensen3
... – Traitor tracing algorithm needs to identify at least one traitor and reduce possibilities of a false positives. – For a k-resilient open user scheme the hash function needs to satisfy. ...
... – Traitor tracing algorithm needs to identify at least one traitor and reduce possibilities of a false positives. – For a k-resilient open user scheme the hash function needs to satisfy. ...
Design and Implementation of a High
... • network links are getting faster and faster • but many clients still connected by fairly slow links • 56K and cell modems, USB, cable, DSL, 802.11 • bandwidth also a problem in P2P systems (large data) • how can we deal with such slow links in ways that are transparent to the user? ...
... • network links are getting faster and faster • but many clients still connected by fairly slow links • 56K and cell modems, USB, cable, DSL, 802.11 • bandwidth also a problem in P2P systems (large data) • how can we deal with such slow links in ways that are transparent to the user? ...
The Mathematics Behind the Birthday Attack
... I have presented to you how message integrity is maintained in a nutshell (actually the above is a very basic model and there is more but delving too deep into different types of Message Authentication Codes would be a digression). An important concept here is that when a tag is generated, it involve ...
... I have presented to you how message integrity is maintained in a nutshell (actually the above is a very basic model and there is more but delving too deep into different types of Message Authentication Codes would be a digression). An important concept here is that when a tag is generated, it involve ...
Blue Border - Courant Institute of Mathematical Sciences
... Collision-Resistant Hash Functions Digital Signatures Identification Schemes (Minicrypt) ...
... Collision-Resistant Hash Functions Digital Signatures Identification Schemes (Minicrypt) ...
Split-Ordered Lists: Lock-Free Extensible Hash Tables
... The key to success lies in the correct ordering of the list items. To simplify, the authors assume a modulo 2i hash function and a hash table size of 2i . For example, given a table of size 4, this means that key 13 will be in bucket 13 modulo 4 = 1. Note that this is equivalent to saying that the i ...
... The key to success lies in the correct ordering of the list items. To simplify, the authors assume a modulo 2i hash function and a hash table size of 2i . For example, given a table of size 4, this means that key 13 will be in bucket 13 modulo 4 = 1. Note that this is equivalent to saying that the i ...
Cryptographic hashing - comp
... Consider that Alice sends a message to Bob and wants to authenticate it by sending h(K||m), where K is a secret shared by Alice and Bob. Now an attacker can append text to m, and update the hash value without knowing K. ...
... Consider that Alice sends a message to Bob and wants to authenticate it by sending h(K||m), where K is a secret shared by Alice and Bob. Now an attacker can append text to m, and update the hash value without knowing K. ...
Current Issues in Maintaining a Secure System
... κρυπτός kryptós "hidden," and γράφειν gráfein "to write") is a discipline of mathematics concerned with information security and related issues, particularly encryption, authentication, and access control. Its purpose is to hide the meaning of a message rather than its existence. In modern times, it ...
... κρυπτός kryptós "hidden," and γράφειν gráfein "to write") is a discipline of mathematics concerned with information security and related issues, particularly encryption, authentication, and access control. Its purpose is to hide the meaning of a message rather than its existence. In modern times, it ...
U.C. Berkeley — CS270: Algorithms Lectures 13, 14 Scribe: Anupam
... The algorithm is run for O(log 1/δ) independent iterations and the output is ‘yes’ if the fraction of yes answers is more than 5/16. Applying the claim for the yes and no cases, it follows that the correct answer is obtained with probability at least 1 − δ. The number of distinct items N can be appr ...
... The algorithm is run for O(log 1/δ) independent iterations and the output is ‘yes’ if the fraction of yes answers is more than 5/16. Applying the claim for the yes and no cases, it follows that the correct answer is obtained with probability at least 1 − δ. The number of distinct items N can be appr ...
Heap Sort
... that the key is also the index to the array that stores the entries, searching and inserting items would be very fast ► Example: empdata[1000] index = employee ID number ► Search ...
... that the key is also the index to the array that stores the entries, searching and inserting items would be very fast ► Example: empdata[1000] index = employee ID number ► Search ...
Hashing
... Perfect hashing Goal: worst-case O(1) search space used O(m) static set of elements n = m2 ...
... Perfect hashing Goal: worst-case O(1) search space used O(m) static set of elements n = m2 ...
Untersuchungen zur MAC Address Translation (MAT)
... Hash functions have a search complexity of ideally O(1) and memory demand of O(N) Problem when using (hardware) hash functions: High performance for different key sets Low hardware costs for a hardware implementation ...
... Hash functions have a search complexity of ideally O(1) and memory demand of O(N) Problem when using (hardware) hash functions: High performance for different key sets Low hardware costs for a hardware implementation ...
Homework 1
... Repeat the above calculations when we randomly throw n log n balls into n bins. §2 The simplest model for a random graph consists of n vertices, and tossing a random fair coin for each pair {i, j} to decide whether this edge should be present in the graph. For each k compute the expected number of k ...
... Repeat the above calculations when we randomly throw n log n balls into n bins. §2 The simplest model for a random graph consists of n vertices, and tossing a random fair coin for each pair {i, j} to decide whether this edge should be present in the graph. For each k compute the expected number of k ...
Cryptographic hash function
A cryptographic hash function is a hash function which is considered practically impossible to invert, that is, to recreate the input data from its hash value alone. These one-way hash functions have been called ""the workhorses of modern cryptography"". The input data is often called the message, and the hash value is often called the message digest or simply the digest.The ideal cryptographic hash function has four main properties: it is easy to compute the hash value for any given message it is infeasible to generate a message from its hash it is infeasible to modify a message without changing the hash it is infeasible to find two different messages with the same hash.Cryptographic hash functions have many information security applications, notably in digital signatures, message authentication codes (MACs), and other forms of authentication. They can also be used as ordinary hash functions, to index data in hash tables, for fingerprinting, to detect duplicate data or uniquely identify files, and as checksums to detect accidental data corruption. Indeed, in information security contexts, cryptographic hash values are sometimes called (digital) fingerprints, checksums, or just hash values, even though all these terms stand for more general functions with rather different properties and purposes.