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Design a one-pass (streaming) algorithm that, for a stream that possesses a majority element (appearing more than $m/2$ times), terminates with this element. Prove the correctness of your algorithm. | If a second pass is not performed and there is no majority the algorithm will not detect that no majority exists. In the case that no strict majority exists, the returned element can be arbitrary; it is not guaranteed to be the element that occurs most often (the mode of the sequence). It is not possible for a streamin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Design a one-pass (streaming) algorithm that, for a stream that possesses a majority element (appearing more than $m/2$ times), terminates with this element. Prove the correctness of your algorithm. | In computing, a one-pass algorithm or single-pass algorithm is a streaming algorithm which reads its input exactly once. It does so by processing items in order, without unbounded buffering; it reads a block into an input buffer, processes it, and moves the result into an output buffer for each step in the process. A o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $f\colon \mathbb{R}\rightarrow \mathbb{R}$ and $g\colon\mathbb{R}\rightarrow \mathbb{R}$ are two functions defined on all $\mathbb{R}$. If $f\circ g$ is injective, then $g$ is injective. | If f {\displaystyle f} and g {\displaystyle g} are both injective then f ∘ g {\displaystyle f\circ g} is injective. If g ∘ f {\displaystyle g\circ f} is injective, then f {\displaystyle f} is injective (but g {\displaystyle g} need not be). f: X → Y {\displaystyle f:X\to Y} is injective if and only if, given any functi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $f\colon \mathbb{R}\rightarrow \mathbb{R}$ and $g\colon\mathbb{R}\rightarrow \mathbb{R}$ are two functions defined on all $\mathbb{R}$. If $f\circ g$ is injective, then $g$ is injective. | Let f: A → B {\displaystyle f:A\to B} and g: B → A {\displaystyle g:B\to A} be the two injective functions. Then define the sets: C 0 = A ∖ g ( B ) {\displaystyle C_{0}=A\setminus g(B)\quad } and C k + 1 = g ( f ( C k ) ) {\displaystyle \quad C_{k+1}=g(f(C_{k}))} for k ∈ { 0 , 1 , 2 , 3 , . . . } | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Suppose that you are given an insertion only stream of items. For every $k\geq 1$, give an algorithm that at each point in the stream maintains $k$ uniformly random elements from the prefix of the stream sampled without replacement. Your algorithm must use $O(k\log n)$ space. | If we associate with each item of the input a uniformly generated random number, the k items with the largest (or, equivalently, smallest) associated values form a simple random sample. A simple reservoir-sampling thus maintains the k items with the currently largest associated values in a priority queue. The expected ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Suppose that you are given an insertion only stream of items. For every $k\geq 1$, give an algorithm that at each point in the stream maintains $k$ uniformly random elements from the prefix of the stream sampled without replacement. Your algorithm must use $O(k\log n)$ space. | A k_insert operation assigns the elements uniformly random to the processors which insert the elements into their local queues. Note that single elements can still be inserted into the queue. Using this strategy the global smallest elements are in the union of the local smallest elements of every processor with high pr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider the problem of finding a maximum cardinality set packing in the semi-streaming model. An instance of this problem consists of a known universe $U$ of $n$ elements and sets $S \subseteq U$ are streamed one-by-one. The goal is to select a family $\mathcal{T}$ of pairwise disjoint sets (i.e., $S\cap S' = \emptys... | The problem is clearly in NP since, given t {\displaystyle t} subsets, we can easily verify that they are pairwise disjoint in polynomial time. The optimization version of the problem, maximum set packing, asks for the maximum number of pairwise disjoint sets in the list. It is a maximization problem that can be formul... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider the problem of finding a maximum cardinality set packing in the semi-streaming model. An instance of this problem consists of a known universe $U$ of $n$ elements and sets $S \subseteq U$ are streamed one-by-one. The goal is to select a family $\mathcal{T}$ of pairwise disjoint sets (i.e., $S\cap S' = \emptys... | Set packing is a classical NP-complete problem in computational complexity theory and combinatorics, and was one of Karp's 21 NP-complete problems. Suppose one has a finite set S and a list of subsets of S. Then, the set packing problem asks if some k subsets in the list are pairwise disjoint (in other words, no two of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In this problem, we consider a generalization of the min-cost perfect matching problem. The generalization is called the \emph{min-cost perfect $b$-matching problem} and is defined as follows: \begin{description} \item[Input:] A graph $G = (V,E)$ with edge costs $c: E \rightarrow \mathbb{R}$ and degree bounds $b: V \ri... | The algorithm can equivalently be described by formulating the problem using a bipartite graph. We have a complete bipartite graph G = ( S , T ; E ) {\displaystyle G=(S,T;E)} with n worker vertices (S) and n job vertices (T), and the edges (E) each have a nonnegative cost c ( i , j ) {\displaystyle c(i,j)} . We want to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In this problem, we consider a generalization of the min-cost perfect matching problem. The generalization is called the \emph{min-cost perfect $b$-matching problem} and is defined as follows: \begin{description} \item[Input:] A graph $G = (V,E)$ with edge costs $c: E \rightarrow \mathbb{R}$ and degree bounds $b: V \ri... | Let G′ = (V′ = A ∪ B, E′ = E). Assign the capacity of all the edges in E′ to 1. Add a source vertex s and connect it to all the vertices in A′ and add a sink vertex t and connect all vertices inside group B′ to this vertex. The capacity of all the new edges is 1 and their costs is 0. It is proved that there is minimum ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Two excellent students, Alice from EPFL and Bob from MIT, have both built their own spam filters. A spam filter is an algorithm that takes as input an email and outputs $1$ if the email is spam and $0$ otherwise. Alice and Bob now want to compare their two spam filters. To perform the comparison, they both download t... | Statistics show that the current probability of any message being spam is 80%, at the very least: Pr ( S ) = 0.8 ; Pr ( H ) = 0.2 {\displaystyle \Pr(S)=0.8;\Pr(H)=0.2} However, most bayesian spam detection software makes the assumption that there is no a priori reason for any incoming message to be spam rather than ham... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Two excellent students, Alice from EPFL and Bob from MIT, have both built their own spam filters. A spam filter is an algorithm that takes as input an email and outputs $1$ if the email is spam and $0$ otherwise. Alice and Bob now want to compare their two spam filters. To perform the comparison, they both download t... | The question asked to the program is: "what is the probability for a given text to be spam knowing which words appear and don't appear in this text?" It can be formalized by: P ( Spam ∣ w 0 ∧ ⋯ ∧ w N − 1 ) {\displaystyle P({\text{Spam}}\mid w_{0}\wedge \cdots \wedge w_{N-1})} which can be computed as follows: P ( Spam ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider the following algorithm that takes as input an undirected graph $G=(V,E)$: \begin{center} \begin{boxedminipage}[t]{0.85\textwidth} \begin{minipage}{14cm} \begin{verse} \textsc{SimpleCut}$(G=(V,E))$: \\[2mm] 1. Let $\mathcal{H}$ be a $2$-universal family of hash functions $h: V \to \{0,1\}$. \\[1mm] 2. Select ... | Since m {\displaystyle m} is a constant, hashing requires time O ( n log n log log n ) {\displaystyle O(n\log n\log \log n)} . They proved that the hash function family is collision resistant by showing that if there is a polynomial-time algorithm that succeeds with non-negligible probability in finding b ≠ b ′ ∈... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider the following algorithm that takes as input an undirected graph $G=(V,E)$: \begin{center} \begin{boxedminipage}[t]{0.85\textwidth} \begin{minipage}{14cm} \begin{verse} \textsc{SimpleCut}$(G=(V,E))$: \\[2mm] 1. Let $\mathcal{H}$ be a $2$-universal family of hash functions $h: V \to \{0,1\}$. \\[1mm] 2. Select ... | As a result, the statistical distance to a uniform family is O ( m / p ) {\displaystyle O(m/p)} , which becomes negligible when p ≫ m {\displaystyle p\gg m} . The family of simpler hash functions h a ( x ) = ( a x mod p ) mod m {\displaystyle h_{a}(x)=(ax~{\bmod {~}}p)~{\bmod {~}}m} is only approximately universal: Pr ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Church booleans are a representation of booleans in the lambda calculus. The Church encoding of true and false are functions of two parameters: Church encoding of tru: t => f => t Church encoding of fls: t => f => f What does the following function implement? b => c => b (not c) c | Church Booleans are the Church encoding of the Boolean values true and false. Some programming languages use these as an implementation model for Boolean arithmetic; examples are Smalltalk and Pico. Boolean logic may be considered as a choice. The Church encoding of true and false are functions of two parameters: true ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Church booleans are a representation of booleans in the lambda calculus. The Church encoding of true and false are functions of two parameters: Church encoding of tru: t => f => t Church encoding of fls: t => f => f What does the following function implement? b => c => b (not c) c | false chooses the second parameter.The two definitions are known as Church Booleans: true ≡ λ a . λ b . a false ≡ λ a . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A leftist min heap is a tree that satisfies the following properties:
P.1 Min heap: For any given node C, if P is a parent node of C, then the value of P is less than or equal
to the value of C.
P.2 Leftist heap: For any given node C, if L is a left child of C and R is a right child of C, then the rank
of R is less tha... | In computer science, a leftist tree or leftist heap is a priority queue implemented with a variant of a binary heap. Every node x has an s-value which is the distance to the nearest leaf in subtree rooted at x. In contrast to a binary heap, a leftist tree attempts to be very unbalanced. In addition to the heap property... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A leftist min heap is a tree that satisfies the following properties:
P.1 Min heap: For any given node C, if P is a parent node of C, then the value of P is less than or equal
to the value of C.
P.2 Leftist heap: For any given node C, if L is a left child of C and R is a right child of C, then the rank
of R is less tha... | A weak heap is most easily understood as a heap-ordered multi-way tree stored as a binary tree using the "right-child left-sibling" convention. (This is equivalent to, but reversed from, the usual left-child right-sibling binary tree.) In the multi-way tree, and assuming a max-heap, each parent's key is greater than or... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Remember that monoids can be represented by the following type class:
1 trait SemiGroup[T]:
2 extension (x: T) def combine (y: T): T
3
4 trait Monoid[T] extends SemiGroup[T]:
5 def unit: T
Additionally the three following laws should hold for all Monoid[M] and all a, b, c: M:
(Associativity) a.combine(b).combine(c) ===... | In particular, when an identity element is required by the type of structure, the identity element of the first structure must be mapped to the corresponding identity element of the second structure. For example: A semigroup homomorphism is a map between semigroups that preserves the semigroup operation. A monoid homom... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Remember that monoids can be represented by the following type class:
1 trait SemiGroup[T]:
2 extension (x: T) def combine (y: T): T
3
4 trait Monoid[T] extends SemiGroup[T]:
5 def unit: T
Additionally the three following laws should hold for all Monoid[M] and all a, b, c: M:
(Associativity) a.combine(b).combine(c) ===... | Some authors regard "semigroup" and "monoid" as synonyms. Here a semigroup need not have an identity element; a monoid is a semigroup with an identity element (also called "unit"). Since the notion of functions acting on a set always includes the notion of an identity function, which when applied to the set does nothin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The little Fermat theorem states that for a prime $n$ and any $b\in \mathbb{Z}_n ^\star$ we have\dots | An analogue of Fermat's little theorem is true in Z {\displaystyle \mathbb {Z} }: if α {\displaystyle \alpha } is not divisible by a prime π {\displaystyle \pi } , α N ( π ) − 1 ≡ 1 mod π . {\displaystyle \alpha ^{N(\pi )-1}\equiv 1{\bmod {\pi }}.} Now assume that N ( π ) ≠ 3 {\displaystyle N(\pi )\neq 3} so that N ( ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The little Fermat theorem states that for a prime $n$ and any $b\in \mathbb{Z}_n ^\star$ we have\dots | This article collects together a variety of proofs of Fermat's little theorem, which states that a p ≡ a ( mod p ) {\displaystyle a^{p}\equiv a{\pmod {p}}} for every prime number p and every integer a (see modular arithmetic). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The number of permutations on a set of $n$ elements | A k-element combination of an n-set S is a k element subset of S, the elements of which are not ordered. By taking all the k element subsets of S and ordering each of them in all possible ways, we obtain all the k-permutations of S. The number of k-combinations of an n-set, C(n,k), is therefore related to the number of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The number of permutations on a set of $n$ elements | (n − k)! permutations, and in each of them the image of the first k elements of U is exactly S. Each permutation may only be associated with a single set in A, for if two prefixes of a permutation both formed sets in A then one would be a subset of the other. Therefore, the number of permutations that can be generated ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select \emph{incorrect} statement. Complexity analysis of an attack consideres | (The overall complexity is additionally quadratic to the number of characters left to match.) Git/Rsync's wildmatch ABORT also covers invalid inputs. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select \emph{incorrect} statement. Complexity analysis of an attack consideres | On 24 April 2019 a paper by Gaëtan Leurent and Thomas Peyrin presented at Eurocrypt 2019 described an enhancement to the previously best chosen-prefix attack in Merkle–Damgård–like digest functions based on Davies–Meyer block ciphers. With these improvements, this method is capable of finding chosen-prefix collisions i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which one of these is \emph{not} a stream cipher? | The keystream is now pseudorandom and so is not truly random. The proof of security associated with the one-time pad no longer holds. It is quite possible for a stream cipher to be completely insecure. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which one of these is \emph{not} a stream cipher? | A stream cipher is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream (keystream). In a stream cipher, each plaintext digit is encrypted one at a time with the corresponding digit of the keystream, to give a digit of the ciphertext stream. Since encryption of each digit i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{correct} assertion regarding GSM. | WS-ReliableMessaging WS-Reliability WS-RM Policy Assertion | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{correct} assertion regarding GSM. | doi:10.1090/gsm/077. ISBN 978-0-8218-4231-7. Morgan, John W.; Fong, Frederick Tsz-Ho (2010). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{wrong} assertion concerning 3G. | EST, but the message's codeword, "HATEFULNESS" again, was incorrect. A cancellation message with the correct codeword, "IMPISH", was not sent until 10:13 a.m. EST. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{wrong} assertion concerning 3G. | 3GPP TS 23.060 V13.4.0 (2015-09) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement. | Suppose we are given a Boolean expressions: B 1 = ( v 3 ∨ ¬ v 2 ) ∧ ( ¬ v 1 ∨ ¬ v 3 ) {\displaystyle B_{1}=(v_{3}\lor \neg v_{2})\wedge (\neg v_{1}\lor \neg v_{3})} B 2 = ( v 3 ∨ ¬ v 2 ) ∧ ( ¬ v 1 ∨ ¬ v 3 ) ∧ ( ¬ v 1 ∨ v 2 ) . {\displaystyle B_{2}=(v_{3}\lor \neg v_{2})\wedge (\neg v_{1}\lor \neg v_{3})\wedge (\neg v_{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement. | . In particular, if v i = ∑ j = 1 d i v i j e i j {\displaystyle {\textbf {v}}_{i}=\sum _{j=1}^{d_{i}}v_{ij}{\textbf {e}}_{ij}\!} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Why do block ciphers use modes of operation? | In cryptography, a block cipher mode of operation is an algorithm that uses a block cipher to provide information security such as confidentiality or authenticity. A block cipher by itself is only suitable for the secure cryptographic transformation (encryption or decryption) of one fixed-length group of bits called a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Why do block ciphers use modes of operation? | They are generally used in modes of operation similar to the block modes described here. As with all protocols, to be cryptographically secure, care must be taken to design these modes of operation correctly. There are several schemes which use a block cipher to build a cryptographic hash function. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
If we pick independent random numbers in $\{1, 2, \dots, N\}$ with uniform distribution, $\theta \sqrt{N}$ times, we get at least one number twice with probability\dots | Generalizing this idea for the other phases we have for each 1 ≤ i ≤ n if f ~ i − 1 ( r 1 , … , r i − 1 ) ≠ f i − 1 ( r 1 , … , r i − 1 ) , {\displaystyle {\tilde {f}}_{i-1}(r_{1},\dots ,r_{i-1})\neq f_{i-1}(r_{1},\dots ,r_{i-1}),} then for ri chosen randomly from F, Pr ≤ 1 n 2 . {\displaystyle \Pr \left\leq {\tfrac {... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
If we pick independent random numbers in $\{1, 2, \dots, N\}$ with uniform distribution, $\theta \sqrt{N}$ times, we get at least one number twice with probability\dots | More precisely, consider equidistribution in n-dimensional ball. Choose N independent random vectors from a ball (they are independent and identically distributed). Let θ be a small positive number. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In practice, what is the typical size of an RSA modulus? | In the U.S., the recommended RSA may extend to 500 feet (150 m) in width, and 1,000 feet (300 m) beyond each runway end (according to U.S. Federal Aviation Administration recommendations; 1000 feet is equivalent to the international ICAO-RESA of 240m plus 60m strip). The standard dimensions have increased over time to ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In practice, what is the typical size of an RSA modulus? | As of 2020, the largest publicly known factored RSA number had 829 bits (250 decimal digits, RSA-250). Its factorization, by a state-of-the-art distributed implementation, took about 2,700 CPU-years. In practice, RSA keys are typically 1024 to 4096 bits long. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The one-time pad is\dots | The poem code was ultimately replaced with the one-time pad, specifically the letter one-time pad (LOP). In LOP, the agent was provided with a string of letters and a substitution square. The plaintext was written under the string on the pad. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The one-time pad is\dots | The one-time pad is, in most cases, impractical as it requires that the key material be as long as the plaintext, actually random, used once and only once, and kept entirely secret from all except the sender and intended receiver. When these conditions are violated, even marginally, the one-time pad is no longer unbrea... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement. | Suppose we are given a Boolean expressions: B 1 = ( v 3 ∨ ¬ v 2 ) ∧ ( ¬ v 1 ∨ ¬ v 3 ) {\displaystyle B_{1}=(v_{3}\lor \neg v_{2})\wedge (\neg v_{1}\lor \neg v_{3})} B 2 = ( v 3 ∨ ¬ v 2 ) ∧ ( ¬ v 1 ∨ ¬ v 3 ) ∧ ( ¬ v 1 ∨ v 2 ) . {\displaystyle B_{2}=(v_{3}\lor \neg v_{2})\wedge (\neg v_{1}\lor \neg v_{3})\wedge (\neg v_{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement. | . In particular, if v i = ∑ j = 1 d i v i j e i j {\displaystyle {\textbf {v}}_{i}=\sum _{j=1}^{d_{i}}v_{ij}{\textbf {e}}_{ij}\!} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Diffie-Hellman refers to \ldots | Diffie–Hellman (RFC 3526) ECDH (RFC 4753) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Diffie-Hellman refers to \ldots | Elliptic-curve Diffie–Hellman (ECDH) is a key agreement protocol that allows two parties, each having an elliptic-curve public–private key pair, to establish a shared secret over an insecure channel. This shared secret may be directly used as a key, or to derive another key. The key, or the derived key, can then be use... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider the Rabin cryptosystem using a modulus $N=pq$ where $p$ and $q$ are both $\ell$-bit primes. What is the tightest complexity of the encryption algorithm? | This problem is believed to be computationally difficult. Several cryptographic methods rely on its hardness, see § Applications. An efficient algorithm for the quadratic residuosity problem immediately implies efficient algorithms for other number theoretic problems, such as deciding whether a composite N {\displaysty... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider the Rabin cryptosystem using a modulus $N=pq$ where $p$ and $q$ are both $\ell$-bit primes. What is the tightest complexity of the encryption algorithm? | Regev proposed a public-key cryptosystem based on the hardness of the LWE problem. The cryptosystem as well as the proof of security and correctness are completely classical. The system is characterized by m , q {\displaystyle m,q} and a probability distribution χ {\displaystyle \chi } on T {\displaystyle \mathbb {T} }... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement. | Select y ~ ∈ { 1 , . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement. | . . VERIFY-SELECTION . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which mode of operation is similar to a stream cipher? | Stream ciphers represent a different approach to symmetric encryption from block ciphers. Block ciphers operate on large blocks of digits with a fixed, unvarying transformation. This distinction is not always clear-cut: in some modes of operation, a block cipher primitive is used in such a way that it acts effectively ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which mode of operation is similar to a stream cipher? | A stream cipher is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream (keystream). In a stream cipher, each plaintext digit is encrypted one at a time with the corresponding digit of the keystream, to give a digit of the ciphertext stream. Since encryption of each digit i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement. | Select y ~ ∈ { 1 , . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement. | . . VERIFY-SELECTION . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In Bluetooth, the link key $K_{link}$ is ... | Users can delete link keys from either device, which removes the bond between the devices—so it is possible for one device to have a stored link key for a device it is no longer paired with. Bluetooth services generally require either encryption or authentication and as such require pairing before they let a remote dev... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In Bluetooth, the link key $K_{link}$ is ... | Bluetooth implements confidentiality, authentication and key derivation with custom algorithms based on the SAFER+ block cipher. Bluetooth key generation is generally based on a Bluetooth PIN, which must be entered into both devices. This procedure might be modified if one of the devices has a fixed PIN (e.g., for head... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $n=pq$ where $p$ and $q$ are prime numbers. We have: | Let p and q be two adjacent prime numbers. Given any n ∈ N {\displaystyle n\in \mathbb {N} } , where p ≤ n < q {\displaystyle p\leq n | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $n=pq$ where $p$ and $q$ are prime numbers. We have: | Let p be a prime number. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following elements belongs to $\mathbb{Z}_{78}^*$? | The elements of Z {\displaystyle \mathbb {Z} } ×15 are the congruence classes {1, 2, 4, 7, 8, 11, 13, 14}; there are φ(15) = 8 of them. x x, x2, x3, ... (mod 15) 1: 1 2: 2, 4, 8, 1 4: 4, 1 7: 7, 4, 13, 1 8: 8, 4, 2, 1 11: 11, 1 13: 13, 4, 7, 1 14: 14, 1 Since there is no number whose order is 8, there are no primitive ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following elements belongs to $\mathbb{Z}_{78}^*$? | For integer values of l {\displaystyle l} , the D-matrix elements with second index equal to zero are proportional to spherical harmonics and associated Legendre polynomials, normalized to unity and with Condon and Shortley phase convention: D m 0 ℓ ( α , β , γ ) = 4 π 2 ℓ + 1 Y ℓ m ∗ ( β , α ) = ( ℓ − m ) ! ( ℓ + m ) ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement. Moore's Law ... | Recent Intel processors include a constant rate TSC (identified by the kern.timecounter.invariant_tsc sysctl on FreeBSD or by the "constant_tsc" flag in Linux's /proc/cpuinfo). With these processors, the TSC ticks at the processor's nominal frequency, regardless of the actual CPU clock frequency due to turbo or power s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement. Moore's Law ... | is (still) false but one more performance of a {\displaystyle a\,\!} could bring about p {\displaystyle p\,\!} . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The elements of $\mathbf{Z}_{14}^*$ are | The elements of Z {\displaystyle \mathbb {Z} } ×15 are the congruence classes {1, 2, 4, 7, 8, 11, 13, 14}; there are φ(15) = 8 of them. x x, x2, x3, ... (mod 15) 1: 1 2: 2, 4, 8, 1 4: 4, 1 7: 7, 4, 13, 1 8: 8, 4, 2, 1 11: 11, 1 13: 13, 4, 7, 1 14: 14, 1 Since there is no number whose order is 8, there are no primitive ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The elements of $\mathbf{Z}_{14}^*$ are | For example, if n = 14 then the elements of Z {\displaystyle \mathbb {Z} } ×n are the congruence classes {1, 3, 5, 9, 11, 13}; there are φ(14) = 6 of them. Here is a table of their powers modulo 14: x x, x2, x3, ... (mod 14) 1: 1 3: 3, 9, 13, 11, 5, 1 5: 5, 11, 13, 9, 3, 1 9: 9, 11, 1 11: 11, 9, 1 13: 13, 1 The order o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement. | Suppose we are given a Boolean expressions: B 1 = ( v 3 ∨ ¬ v 2 ) ∧ ( ¬ v 1 ∨ ¬ v 3 ) {\displaystyle B_{1}=(v_{3}\lor \neg v_{2})\wedge (\neg v_{1}\lor \neg v_{3})} B 2 = ( v 3 ∨ ¬ v 2 ) ∧ ( ¬ v 1 ∨ ¬ v 3 ) ∧ ( ¬ v 1 ∨ v 2 ) . {\displaystyle B_{2}=(v_{3}\lor \neg v_{2})\wedge (\neg v_{1}\lor \neg v_{3})\wedge (\neg v_{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement. | . In particular, if v i = ∑ j = 1 d i v i j e i j {\displaystyle {\textbf {v}}_{i}=\sum _{j=1}^{d_{i}}v_{ij}{\textbf {e}}_{ij}\!} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What is the advantage of using a salt in a password authentication protocol? | However, they remain relevant in multi-server installations which use centralized password management systems to push passwords or password hashes to multiple systems. In such installations, the root account on each individual system may be treated as less trusted than the administrators of the centralized password sys... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What is the advantage of using a salt in a password authentication protocol? | Using the same salt for all passwords is dangerous because a precomputed table which simply accounts for the salt will render the salt useless. Generation of precomputed tables for databases with unique salts for every password is not viable because of the computational cost of doing so. But, if a common salt is used f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select \emph{incorrect} statement. The birthday paradox | Birthday paradox Birthday problem Index of coincidence Bible code Spurious relationship Monty Hall problem | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select \emph{incorrect} statement. The birthday paradox | Select y ~ ∈ { 1 , . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which scheme is the most secure? | The most secure scheme is the global centralized authentication and web application (portal). It is ideal for E-Government use because it allows a wide range of services. It uses a single authentication mechanism involving a minimum of two factors to allow access to required services and the ability to sign documents. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which scheme is the most secure? | Assuming that a deterministic encryption scheme is going to be used, it is important to understand what is the maximum level of security that can be guaranteed. A number of works have focused on this exact problem. The first work to rigorously define security for a deterministic scheme was in CRYPTO 2007. This work pro... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{false} assertion concerning WPA-TKIP. | WEP WPA (TKIP in hardware) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{false} assertion concerning WPA-TKIP. | Second, WPA implements a sequence counter to protect against replay attacks. Packets received out of order will be rejected by the access point. Finally, TKIP implements a 64-bit Message Integrity Check (MIC) and re-initializes the sequence number each time when a new key (Temporal Key) is used.To be able to run on leg... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{correct} assertion. In ElGamal $\ldots$ | A sequent A 1 , … , A m ⊢ B 1 , … , B n {\displaystyle A_{1},\,\dots ,A_{m}\,\vdash \,B_{1},\,\dots ,B_{n}} asserts that, if all the antecedents A 1 , … , A m {\displaystyle A_{1},\,\dots ,A_{m}} are true, then at least one of the consequents B 1 , … , B n {\displaystyle B_{1},\,\dots ,B_{n}} must be true. In the typed... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{correct} assertion. In ElGamal $\ldots$ | asserts that if p {\displaystyle p\,\!} is valid then so is q {\displaystyle q\,\!} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
One-time pad ... | The one-time-pad is the optimum cryptosystem with theoretically perfect secrecy. The one-time-pad is one of the most practical methods of encryption where one or both parties must do all work by hand, without the aid of a computer. This made it important in the pre-computer era, and it could conceivably still be useful... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
One-time pad ... | One-time pads One-time pads are a popular cryptographic method to invoke in advertising, because it is well known that one-time pads, when implemented correctly, are genuinely unbreakable. The problem comes in implementing one-time pads, which is rarely done correctly. Cryptographic systems that claim to be based on on... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Merkle-D{\aa}mgard construction is | The last block processed should also be unambiguously length padded; this is crucial to the security of this construction. This construction is called the Merkle–Damgård construction. Most common classical hash functions, including SHA-1 and MD5, take this form. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Merkle-D{\aa}mgard construction is | We will later use the Merkle–Damgård construction to extend the domain to inputs of arbitrary lengths. The basis of this function consists of a (randomly chosen) binary r × n {\displaystyle r\times n} matrix H {\displaystyle H} which acts on a message of n {\displaystyle n} bits by matrix multiplication. Here we encode... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Fermat Test outputs `maybe prime' with probability which may be high given though $n$ is composite when ... | The simplest probabilistic primality test is the Fermat primality test (actually a compositeness test). It works as follows: Given an integer n, choose some integer a coprime to n and calculate an − 1 modulo n. If the result is different from 1, then n is composite. If it is 1, then n may be prime.If an−1 (modulo n) is... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Fermat Test outputs `maybe prime' with probability which may be high given though $n$ is composite when ... | The error made by the primality test is measured by the probability that a composite number is declared probably prime. The more bases a are tried, the better the accuracy of the test. It can be shown that if n is composite, then at most 1/4 of the bases a are strong liars for n. As a consequence, if n is composite the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What should the minimal length of the output of a hash function be to provide security against \emph{collision attacks} of $2^{256}?$ | A straightforward application of the Merkle–Damgård construction, where the size of hash output is equal to the internal state size (between each compression step), results in a narrow-pipe hash design. This design causes many inherent flaws, including length-extension, multicollisions, long message attacks, generate-a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What should the minimal length of the output of a hash function be to provide security against \emph{collision attacks} of $2^{256}?$ | The aforementioned process achieves a t-bit security level with 4t-bit signatures. For example, a 128-bit security level would require 512-bit (64-byte) signatures. The security is limited by discrete logarithm attacks on the group, which have a complexity of the square-root of the group size. In Schnorr's original 199... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $G$ be a group generated by $g$. What is the discrete logarithm problem? | Given a group G {\displaystyle G} with order p {\displaystyle p} and generator g ∈ G {\displaystyle g\in G} , suppose we know that x = g r ∈ G {\displaystyle x=g^{r}\in G} , for some r ∈ Z p {\displaystyle r\in \mathbb {Z} _{p}} , and we wish to compute r {\displaystyle r} , which is the discrete logarithm: r = log g (... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $G$ be a group generated by $g$. What is the discrete logarithm problem? | In the special case where b is the identity element 1 of the group G, the discrete logarithm logb a is undefined for a other than 1, and every integer k is a discrete logarithm for a = 1. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bluetooth is \dots | updated Bluetooth stack that opens up even more tethered connectivity options | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bluetooth is \dots | Bluetooth is a standard wire-replacement communications protocol primarily designed for low power consumption, with a short range based on low-cost transceiver microchips in each device. Because the devices use a radio (broadcast) communications system, they do not have to be in visual line of sight of each other; howe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{false} answer. In a group, the operation\dots | {\displaystyle (g!)} , players within each group ( s ! ) {\displaystyle (s!)} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{false} answer. In a group, the operation\dots | Note that one can also overcome the problem with containing dots using the \yahnodots command. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a public-key cryptosystem. Let $K_p$, $K_s$, $X$, and $Y$ be respectively the public key, private key, plaintext and ciphertext. Which assertion is \emph{always true}? | Regev proposed a public-key cryptosystem based on the hardness of the LWE problem. The cryptosystem as well as the proof of security and correctness are completely classical. The system is characterized by m , q {\displaystyle m,q} and a probability distribution χ {\displaystyle \chi } on T {\displaystyle \mathbb {T} }... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a public-key cryptosystem. Let $K_p$, $K_s$, $X$, and $Y$ be respectively the public key, private key, plaintext and ciphertext. Which assertion is \emph{always true}? | Limited research on plaintext-aware encryption has been done since Bellare and Rogaway's paper. Although several papers have applied the plaintext-aware technique in proving encryption schemes are chosen-ciphertext secure, only three papers revisit the concept of plaintext-aware encryption itself, both focussed on the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement. Euler Theorem | This second solution is presumably more accurate. Since we have to apply Euler's method twice, the local error is (in the worst case) twice the original error. y n + 1 2 = y n + h 2 f ( t n , y n ) {\displaystyle y_{n+{\frac {1}{2}}}=y_{n}+{\frac {h}{2}}f(t_{n},y_{n})} y n + 1 ( 1 ) = y n + 1 2 + h 2 f ( t n + 1 2 , y ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement. Euler Theorem | Select y ~ ∈ { 1 , . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textit{correct} assertion. | (/ indicates line break; some word breaks are uncertain) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textit{correct} assertion. | If so, attempt to position cursor at that line. If it exists, begin interpretation there; if not, report an error. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $p$ be a prime number and $n$ be an integer. What is the order of $\mathrm{GF}(p^n)$? | Given a prime power q = pn with p prime and n > 1, the field GF(q) may be explicitly constructed in the following way. One first chooses an irreducible polynomial P in GF(p) of degree n (such an irreducible polynomial always exists). Then the quotient ring of the polynomial ring GF(p) by the ideal generated by P is a f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $p$ be a prime number and $n$ be an integer. What is the order of $\mathrm{GF}(p^n)$? | The finite field with pn elements is denoted GF(pn) and is also called the Galois field of order pn, in honor of the founder of finite field theory, Évariste Galois. GF(p), where p is a prime number, is simply the ring of integers modulo p. That is, one can perform operations (addition, subtraction, multiplication) usi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Under which condition is an element $x\in \mathbb{Z}_n$ invertible? | Indeed, we assume that every nonzero element of the ring Z / n Z {\displaystyle \mathbb {Z} /n\mathbb {Z} } is invertible, so that Z / n Z {\displaystyle \mathbb {Z} /n\mathbb {Z} } must be a field. It implies that n {\displaystyle n} must be prime (cf. Bézout's identity). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Under which condition is an element $x\in \mathbb{Z}_n$ invertible? | An element a is invertible if Q(a) is invertible and there exists b such that Q(b) is the inverse of Q(a) and Q(a)b = a: such b is unique and we say that b is the inverse of a. A Jordan division algebra is one in which every non-zero element is invertible. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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