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If Alice receives a message proven to be coming from Bob, we say that the message is\dots | When Bob receives the newly enciphered message, he believes it came from Alice. Alice sends a message to Bob, which is intercepted by Mallory: Alice "Hi Bob, it's Alice. Give me your key." | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
If Alice receives a message proven to be coming from Bob, we say that the message is\dots | → Mallory Bob Mallory relays this message to Bob; Bob cannot tell it is not really from Alice: Alice Mallory "Hi Bob, it's Alice. Give me your key." → Bob Bob responds with his encryption key: Alice Mallory ← Bob Mallory replaces Bob's key with her own, and relays this to Alice, claiming that it is Bob's key: Alice ← Mallory Bob Alice encrypts a message with what she believes to be Bob's key, thinking that only Bob can read it: Alice "Meet me at the bus stop!" | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which cryptographic primitive(s) is (are) used in S/Key - OTP ? | Cryptographic primitives are well-established, low-level cryptographic algorithms that are frequently used to build cryptographic protocols for computer security systems. These routines include, but are not limited to, one-way hash functions and encryption functions. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which cryptographic primitive(s) is (are) used in S/Key - OTP ? | In this regard, it is similar to storing unsalted 64-bit hashes of strong, unique passwords. The S/KEY protocol can loop. If such a loop were created in the S/KEY chain, an attacker could use user's key without finding the original value, and possibly without tipping off the valid user. The pathological case of this would be an OTP that hashes to itself. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $(e,N)$ be the public parameters of the RSA cryptosystem. What is the advantage of taking a \emph{small} value for $e$? | Choose an integer e such that 2 < e < λ(n) and gcd(e, λ(n)) = 1; that is, e and λ(n) are coprime. e having a short bit-length and small Hamming weight results in more efficient encryption – the most commonly chosen value for e is 216 + 1 = 65537. The smallest (and fastest) possible value for e is 3, but such a small value for e has been shown to be less secure in some settings. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $(e,N)$ be the public parameters of the RSA cryptosystem. What is the advantage of taking a \emph{small} value for $e$? | In order to reduce encryption or signature verification time, it is useful to use a small public exponent ( e {\displaystyle e} ). In practice, common choices for e {\displaystyle e} are 3, 17 and 65537 ( 2 16 + 1 ) {\displaystyle (2^{16}+1)} . These values for e are Fermat primes, sometimes referred to as F 0 , F 2 {\displaystyle F_{0},F_{2}} and F 4 {\displaystyle F_{4}} respectively ( F x = 2 2 x + 1 ) {\displaystyle (F_{x}=2^{2^{x}}+1)} . They are chosen because they make the modular exponentiation operation faster. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $p$ and $q$ be two distinct prime numbers and let $x \in \mathbf{Z}_{pq}^*$. Which of the following assertion is always true in $\mathbf{Z}_{pq}^*$? | We claim that in fact this is so for one prime number only. Suppose per contra that p and q are two distinct primes with absolute value strictly less than 1. Let k be a positive integer such that | p | ∗ k {\displaystyle |p|_{*}^{k}} and | q | ∗ k {\displaystyle |q|_{*}^{k}} are smaller than 1 / 2 {\displaystyle 1/2} . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $p$ and $q$ be two distinct prime numbers and let $x \in \mathbf{Z}_{pq}^*$. Which of the following assertion is always true in $\mathbf{Z}_{pq}^*$? | This yields a contradiction, as 1 = | 1 | ∗ ≤ | a | ∗ | p | ∗ k + | b | ∗ | q | ∗ k < | a | ∗ + | b | ∗ 2 ≤ 1. {\displaystyle 1=|1|_{*}\leq |a|_{*}|p|_{*}^{k}+|b|_{*}|q|_{*}^{k}<{\frac {|a|_{*}+|b|_{*}}{2}}\leq 1.} This means that there exists a unique prime p such that | p | ∗ < 1 {\displaystyle |p|_{*}<1} and that for all other prime q, one has | q | ∗ = 1 {\displaystyle |q|_{*}=1} (from the hypothesis of this second case). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $h$ be a cryptographic hash function based on the Merkle-Damg{\aa}rd scheme. The Merkle-Damg{\aa}rd Theorem states that\dots | Benaloh and de Mare define a one-way hash function as a family of functions h ℓ: X ℓ × Y ℓ → Z ℓ {\displaystyle h_{\ell }:X_{\ell }\times Y_{\ell }\to Z_{\ell }} which satisfy the following three properties: For all ℓ ∈ Z , x ∈ X ℓ , y ∈ Y ℓ {\displaystyle \ell \in \mathbb {Z} ,x\in X_{\ell },y\in Y_{\ell }} , one can compute h ℓ ( x , y ) {\displaystyle h_{\ell }(x,y)} in time poly ( ℓ , | x | , | y | ) {\displaystyle {\text{poly}}(\ell ,|x|,|y|)} . (Here the "poly" symbol refers to an unspecified, but fixed, polynomial.) No probabilistic polynomial-time algorithm will, for sufficiently large ℓ {\displaystyle \ell } , map the inputs ℓ ∈ Z , ( x , y ) ∈ X ℓ × Y ℓ , y ′ ∈ Y ℓ {\displaystyle \ell \in \mathbb {Z} ,(x,y)\in X_{\ell }\times Y_{\ell },y'\in Y_{\ell }} , find a value x ′ ∈ X ℓ {\displaystyle x'\in X_{\ell }} such that h ℓ ( x , y ) = h ℓ ( x ′ , y ′ ) {\displaystyle h_{\ell }(x,y)=h_{\ell }(x',y')} with more than negligible probability. For all ℓ ∈ Z , x ∈ X ℓ , y 1 , y 2 ∈ Y ℓ {\displaystyle \ell \in \mathbb {Z} ,x\in X_{\ell },y_{1},y_{2}\in Y_{\ell }} , one has h ( h ( x , y 1 ) , y 2 ) = h ( h ( x , y 2 ) , y 1 ) {\displaystyle h(h(x,y_{1}),y_{2})=h(h(x,y_{2}),y_{1})} . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $h$ be a cryptographic hash function based on the Merkle-Damg{\aa}rd scheme. The Merkle-Damg{\aa}rd Theorem states that\dots | Let h: S × X → { 0 , 1 } m {\textstyle h\colon {\mathcal {S}}\times {\mathcal {X}}\rightarrow \{0,\,1\}^{m}} be a 2-universal hash function. If m ≤ H ∞ ( X ) − 2 log ( 1 ε ) {\textstyle m\leq H_{\infty }(X)-2\log \left({\frac {1}{\varepsilon }}\right)} then for S uniform over S {\displaystyle {\mathcal {S}}} and independent of X, we have: δ ≤ ε . {\textstyle \delta \left\leq \varepsilon .} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
$\mathbb{Z}_{37}^*$ denotes ... | Both Z p {\displaystyle \mathbb {Z} _{p}} and Q p {\displaystyle \mathbb {Q} _{p}} are uncountable and have the cardinality of the continuum. For Z p , {\displaystyle \mathbb {Z} _{p},} this results from the p-adic representation, which defines a bijection of Z p {\displaystyle \mathbb {Z} _{p}} on the power set { 0 , … , p − 1 } N . {\displaystyle \{0,\ldots ,p-1\}^{\mathbb {N} }.} For Q p {\displaystyle \mathbb {Q} _{p}} this results from its expression as a countably infinite union of copies of Z p {\displaystyle \mathbb {Z} _{p}}: Q p = ⋃ i = 0 ∞ 1 p i Z p . {\displaystyle \mathbb {Q} _{p}=\bigcup _{i=0}^{\infty }{\frac {1}{p^{i}}}\mathbb {Z} _{p}.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
$\mathbb{Z}_{37}^*$ denotes ... | Here, Z {\displaystyle \mathbb {Z} } is the set of integers, and N {\displaystyle \mathbb {N} } is the set of non-negative integers. Here, all letters represent integers. We say that a map T: N k → N {\displaystyle T:\mathbb {N} ^{k}\rightarrow \mathbb {N} } is piecewise linear if T {\displaystyle T} can be defined by various affine functions with integer coefficients on each of finitely many pieces, where each piece is defined by a finite set of linear inequalities with integer coefficients. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Visual cryptography is a nice visual application of \ldots | (2014). An Introduction to Mathematical Cryptography (2nd ed.). doi:10.1007/978-1-4939-1711-2. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Visual cryptography is a nice visual application of \ldots | Visual cryptography is a cryptographic technique which allows visual information (pictures, text, etc.) to be encrypted in such a way that the decrypted information appears as a visual image. One of the best-known techniques has been credited to Moni Naor and Adi Shamir, who developed it in 1994. They demonstrated a visual secret sharing scheme, where an image was broken up into n shares so that only someone with all n shares could decrypt the image, while any n − 1 shares revealed no information about the original image. Each share was printed on a separate transparency, and decryption was performed by overlaying the shares. | 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 one of these is a closed set? | Some sets are both open and closed and are called clopen sets. The ray [ 1 , + ∞ ) {\displaystyle [1,+\infty )} is closed. The Cantor set is an unusual closed set in the sense that it consists entirely of boundary points and is nowhere dense. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which one of these is a closed set? | The sum of a compact set and a closed set is closed. However, the sum of two closed subsets may fail to be closed (see this footnote for examples). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{incorrect} assertion. | "Fl." for flashing, "F." for fixed. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{incorrect} 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 |
Select the \emph{correct} statement. The Plain RSA Signature scheme | . . VERIFY-SELECTION . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{correct} statement. The Plain RSA Signature scheme | One can verify that a signature ( r , s ) {\displaystyle \left(r,s\right)} is a valid signature for a message m {\displaystyle m} as follows: Verify that 0 < r < q {\displaystyle 0 | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following is an element of $\mathbb{Z}_{60}^*$? | The number 60 is a unitary perfect number, because 1, 3, 4, 5, 12, 15, and 20 are its proper unitary divisors, and 1 + 3 + 4 + 5 + 12 + 15 + 20 = 60. The first five, and only known, unitary perfect numbers are 6 = 2 × 3 {\displaystyle 6=2\times 3} , 60 = 2 2 × 3 × 5 {\displaystyle 60=2^{2}\times 3\times 5} , 90 = 2 × 3 2 × 5 {\displaystyle 90=2\times 3^{2}\times 5} , 87360 = 2 6 × 3 × 5 × 7 × 13 {\displaystyle 87360=2^{6}\times 3\times 5\times 7\times 13} , and 146361946186458562560000 = 2 18 × 3 × 5 4 × 7 × 11 × 13 × 19 × 37 × 79 × 109 × 157 × 313 {\displaystyle 146361946186458562560000=2^{18}\times 3\times 5^{4}\times 7\times 11\times 13\times 19\times 37\times 79\times 109\times 157\times 313} (sequence A002827 in the OEIS). The respective sums of their proper unitary divisors are as follows: 6 = 1 + 2 + 3 60 = 1 + 3 + 4 + 5 + 12 + 15 + 20 90 = 1 + 2 + 5 + 9 + 10 + 18 + 45 87360 = 1 + 3 + 5 + 7 + 13 + 15 + 21 + 35 + 39 + 64 + 65 + 91 + 105 + 192 + 195 + 273 + 320 + 448 + 455 + 832 + 960 + 1344 + 1365 + 2240 + 2496 + 4160 + 5824 + 6720 + 12480 + 17472 + 29120 146361946186458562560000 = 1 + 3 + 7 + 11 + ... + 13305631471496232960000 + 20908849455208366080000 + 48787315395486187520000 (4095 divisors in the sum) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following is an element of $\mathbb{Z}_{60}^*$? | 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 roots modulo 15. Indeed, λ(15) = 4, where λ is the Carmichael function. (sequence A002322 in the OEIS) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following algorithms is \emph{not} a hash function? | Selected schemes for the purpose of hashing: SWIFFT. Lattice Based Hash Function (LASH). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following algorithms is \emph{not} a hash function? | h {\displaystyle h}: a collision resistant hash function with |q|-bit digests. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{correct} answer. | Select y ~ ∈ { 1 , . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{correct} answer. | If it returns "yes", then return "yes". Otherwise, run WSO(K,y,d/3). If it returns "yes", then return "yes". Otherwise, return "no"; see: 52 for proof of correctness. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{false} assertion. Given a ring $R$, $R^\star$ is\ldots | If R is an associative ring, then R can be given the bracket product = xy − yx. Of course then xy = yx if and only if = 0. If we denote the set R with the bracket product as LR, then clearly the ring centralizer of S in R is equal to the Lie ring centralizer of S in LR. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{false} assertion. Given a ring $R$, $R^\star$ is\ldots | In a model of the ring R {\displaystyle {\mathbb {R} }} , one can define a non-trivial positivity predicate 0 < x {\displaystyle 0 | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement. Bluetooth is | Several open-source implementations of the JSR-82 specification are available: AvetanaBluetooth Implementation BlueCove: Java Library for Bluetooth | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement. Bluetooth is | . . VERIFY-SELECTION . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which cipher is AES? | Secretary of Commerce. AES is available in many different encryption packages, and is the first (and only) publicly accessible cipher approved by the U.S. National Security Agency (NSA) for top secret information when used in an NSA approved cryptographic module. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which cipher is AES? | AES encryption: 128-bit block encryption cipher operating in CTR mode with user-selectable 128, 192 or 256-bit key. Slow-speed side channel for short and repeated data transfers, e.g. GNSS position data or telemetry. Text messaging. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following algorithms is 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 is dependent on the current state of the cipher, it is also known as state cipher. In practice, a digit is typically a bit and the combining operation is an exclusive-or (XOR). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following algorithms is a stream cipher? | The table below shows the support of various stream ciphers. Stream ciphers are defined as using plain text digits that are combined with a pseudorandom cipher digit stream. Stream ciphers are typically faster than block ciphers and may have lower hardware complexity, but may be more susceptible to attacks. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a public key cryptosystem. The channel used to transmit the public key has to be\dots | Suppose Bob wishes to send a message, m, to Alice whose public key is (Hpub, t): Bob encodes the message, m, as a binary string em' of length n and weight at most t. Bob computes the ciphertext as c = HpubeT. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a public key cryptosystem. The channel used to transmit the public key has to be\dots | It is also possible to use Diffie–Hellman as part of a public key infrastructure, allowing Bob to encrypt a message so that only Alice will be able to decrypt it, with no prior communication between them other than Bob having trusted knowledge of Alice's public key. Alice's public key is ( g a mod p , g , p ) {\displaystyle (g^{a}{\bmod {p}},g,p)} . To send her a message, Bob chooses a random b and then sends Alice g b mod p {\displaystyle g^{b}{\bmod {p}}} (unencrypted) together with the message encrypted with symmetric key ( g a ) b mod p {\displaystyle (g^{a})^{b}{\bmod {p}}} . Only Alice can determine the symmetric key and hence decrypt the message because only she has a (the private key). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
KEM/DEM refers to\dots | PM's dots are used in a manner similar to parentheses. Each dot (or multiple dot) represents either a left or right parenthesis or the logical symbol ∧. More than one dot indicates the "depth" of the parentheses, for example, ". ", ":" or ":. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
KEM/DEM refers to\dots | This is done with a naming convention of "Dxx.x" or "Kxx.x". Example: Input Data Bits: ABCDEFGH Data is split: ABC DEFGH Data is shuffled: DEFGH ABCNow these bits are converted to decimal in the way they are paired. Input data C3 (HEX) = 11000011 = 110 00011 = 00011 110 = 3 6 E 8B/10B = D03.6 | 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_{1}\lor v_{2}).} With B 1 {\displaystyle B_{1}} , the algorithm can select v 1 = true {\displaystyle v_{1}={\text{true}}} , so to satisfy the second clause, the algorithm will need to set v 3 = false {\displaystyle v_{3}={\text{false}}} , and resultantly to satisfy the first clause, the algorithm will set v 2 = false {\displaystyle v_{2}={\text{false}}} . If the algorithm tries to satisfy B 2 {\displaystyle B_{2}} in the same way it tried to solve B 1 {\displaystyle B_{1}} , then the third clause will remain unsatisfied. This will cause the algorithm to backtrack and set v 1 = false {\displaystyle v_{1}={\text{false}}} and continue assigning variables further. | 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 |
Select \emph{incorrect} statement. The brute force technique against a cipher with key $256$ bits is | The very simple key schedule makes IDEA subject to a class of weak keys; some keys containing a large number of 0 bits produce weak encryption. These are of little concern in practice, being sufficiently rare that they are unnecessary to avoid explicitly when generating keys randomly. A simple fix was proposed: XORing each subkey with a 16-bit constant, such as 0x0DAE.Larger classes of weak keys were found in 2002.This is still of negligible probability to be a concern to a randomly chosen key, and some of the problems are fixed by the constant XOR proposed earlier, but the paper is not certain if all of them are. A more comprehensive redesign of the IDEA key schedule may be desirable. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select \emph{incorrect} statement. The brute force technique against a cipher with key $256$ bits is | The challenger selects a bit b ∈ {\displaystyle \scriptstyle \in } {0, 1} uniformly at random, and sends the challenge ciphertext C = E(PK, M b {\displaystyle \scriptstyle M_{b}} ) back to the adversary. The adversary is free to perform any number of additional computations or encryptions. Finally, the adversary outputs a guess for the value of b.A cryptosystem is indistinguishable under chosen plaintext attack if every probabilistic polynomial time adversary has only a negligible "advantage" over random guessing. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{weakest} algorithm. | Then a random selection is made similar to how the roulette wheel is rotated. While candidate solutions with a higher fitness will be less likely to be eliminated, there is still a chance that they may be eliminated because their probability of selection is less than 1 (or 100%). Contrast this with a less sophisticated selection algorithm, such as truncation selection, which will eliminate a fixed percentage of the weakest candidates. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{weakest} algorithm. | Algorithm selection (sometimes also called per-instance algorithm selection or offline algorithm selection) is a meta-algorithmic technique to choose an algorithm from a portfolio on an instance-by-instance basis. It is motivated by the observation that on many practical problems, different algorithms have different performance characteristics. That is, while one algorithm performs well in some scenarios, it performs poorly in others and vice versa for another algorithm. If we can identify when to use which algorithm, we can optimize for each scenario and improve overall performance. This is what algorithm selection aims to do. The only prerequisite for applying algorithm selection techniques is that there exists (or that there can be constructed) a set of complementary algorithms. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textit{incorrect} assertion. | "I made an error in this transmission. Transmission will continue with the last word correctly sent." | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textit{incorrect} assertion. | (/ indicates line break; some word breaks are uncertain) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Moore law | Moore's law, named after Gordon Moore, is the observation and projection via historical trend that the number of transistors in integrated circuits, and therefore processors by extension, doubles every two years. The progress of processors has followed Moore's law closely. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Moore law | For this reason, many scientists believe that Moore’s Law will not hold forever and will soon reach a peak, since Moore's law is largely predicated on computational gains caused by improvements in micro-lithographic etching technologies. In producing these nanocircuits, there are many aspects involved. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement. The Bluetooth project aims for | . . VERIFY-SELECTION . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement. The Bluetooth project aims for | - 囗 + お/頁 + selector 4 = 馘 | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{false} assertion. The ambiguity issue in the decryption algorithm of the Rabin cryptosystem can be solved by\dots | Tentatively making these assumptions, the following partial decrypted message is obtained. heVeTCSWPeYVaWHaVSReQMthaYVaOeaWHRtatePFaMVaWHKVSTYhtZetheKeetPeJVSZaYPaRRGaReM WQhMGhMtQaReWGPSReHMtQaRaKeaTtMJTPRGaVaKaeTRaWHatthattMZeTWAWSQWtSWatTVaPMRtRSJ GSTVReaYVeatCVMUeMWaRGMeWtMJMGCSMWtSJOMeQtheVeQeVetQSVSTWHKPaGARCStRWeaVSWeeBtV eZMtFSJtheKaGAaWHaPSWYSWeWeaVtheStheVtheRGaPeRQeVeeBGeeHMWYPFhaVHaWHYPSRRFQMtha PPtheaCCeaVaWGeSJKTVWMRheHYSPHtheQeMYhtSJtheMWReGtQaROeVFVeZaVAaKPeaWHtaAMWYaPP thMWYRMWtSGSWRMHeVatMSWMGSTPHhaVHPFKPaZeNTCMteVJSVhMRSCMWMSWVeRCeGtMWYMt Using these initial guesses, Eve can spot patterns that confirm her choices, such as "that". | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{false} assertion. The ambiguity issue in the decryption algorithm of the Rabin cryptosystem can be solved by\dots | Decrypting produces three false results in addition to the correct one, so that the correct result must be guessed. This is the major disadvantage of the Rabin cryptosystem and one of the factors which have prevented it from finding widespread practical use. If the plaintext is intended to represent a text message, guessing is not difficult; however, if the plaintext is intended to represent a numerical value, this issue becomes a problem that must be resolved by some kind of disambiguation scheme. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What is the order of $2^{124}$ in $(\mathbb{Z}_{2^{128}},+)$? | The twelfth root of two (21/12 or 12√2 ≈ 1.059463...), using "standard notation": 2 12 = 1 + 1 12 + 11 2 + 13 36 + 23 2 + 25 60 + 35 2 + 37 84 + 47 2 + ⋱ = 1 + 2 ⋅ 1 36 − 1 − 11 ⋅ 13 108 − 23 ⋅ 25 180 − 35 ⋅ 37 252 − 47 ⋅ 49 324 − ⋱ . {\displaystyle {\sqrt{2}}=1+{\cfrac {1}{12+{\cfrac {11}{2+{\cfrac {13}{36+{\cfrac {23}{2+{\cfrac {25}{60+{\cfrac {35}{2+{\cfrac {37}{84+{\cfrac {47}{2+\ddots }}}}}}}}}}}}}}}}=1+{\cfrac {2\cdot 1}{36-1-{\cfrac {11\cdot 13}{108-{\cfrac {23\cdot 25}{180-{\cfrac {35\cdot 37}{252-{\cfrac {47\cdot 49}{324-\ddots }}}}}}}}}}.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What is the order of $2^{124}$ in $(\mathbb{Z}_{2^{128}},+)$? | It is trivial if n is even. If n is 1 mod 4 it has order 1 or 2; in particular it has order 1 if n is 1, 5, 13, 29, or 61, and William Browder (1969) proved that it has order 2 if n = 1 {\displaystyle n=1} mod 4 is not of the form 2 k − 3 {\displaystyle 2^{k}-3} . It follows from the now almost completely resolved Kervaire invariant problem that it has order 2 for all n bigger than 126; the case n = 126 {\displaystyle n=126} is still open. The order of b P 4 k {\displaystyle bP_{4k}} for k ≥ 2 {\displaystyle k\geq 2} is 2 2 k − 2 ( 2 2 k − 1 − 1 ) B , {\displaystyle 2^{2k-2}(2^{2k-1}-1)B,} where B is the numerator of 4 B 2 k / k {\displaystyle 4B_{2k}/k} , and B 2 k {\displaystyle B_{2k}} is a Bernoulli number. (The formula in the topological literature differs slightly because topologists use a different convention for naming Bernoulli numbers; this article uses the number theorists' convention.) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which problem in communication is \emph{not} treated by cryptography? | Yet, it has been shown that even quantum communication does not allow the secure implementation of many other two-party cryptographic tasks. These all form instances of secure function evaluation. An example is oblivious transfer. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which problem in communication is \emph{not} treated by cryptography? | A commonly cited sufficient condition for the existence of unbreakable encryption is the existence of one-way functions, but it is conceivable that some physical means might also achieve it. On top of this, they also showed that the graph nonisomorphism problem, the complement of the graph isomorphism problem, has a zero-knowledge proof. This problem is in co-NP, but is not currently known to be in either NP or any practical class. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What are the complexities for the single-target dictionary attacks, when there are $N$ keys? | Attacks that allow distinguishing ciphertext from random data. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What are the complexities for the single-target dictionary attacks, when there are $N$ keys? | A polynomial-time attack, for Ω ( n ) {\displaystyle \Omega (n)} concurrent executions, was shown in 2020 by Benhamouda, Lepoint, Raykova, and Orrù. Schnorr also suggested enhancements for securing blind signatures schemes based on discrete logarithm problem. == References == | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{incorrect} assertion. The Diffie-Hellman key agreement protocol \ldots | Diffie–Hellman (RFC 3526) ECDH (RFC 4753) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{incorrect} assertion. The Diffie-Hellman key agreement protocol \ldots | The Syslog Protocol. RFC 5424. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of these components was not part of the Enigma machine? | Like other rotor machines, the Enigma machine is a combination of mechanical and electrical subsystems. The mechanical subsystem consists of a keyboard; a set of rotating disks called rotors arranged adjacently along a spindle; one of various stepping components to turn at least one rotor with each key press, and a series of lamps, one for each letter. These design features are the reason that the Enigma machine was originally referred to as the rotor-based cipher machine during its intellectual inception in 1915. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of these components was not part of the Enigma machine? | This assembly acted similarly to other rotor machines, such as the Enigma; when a plaintext letter was entered, a signal would enter one side of the bank and exit the other, denoting the ciphertext letter. Unlike the Enigma, there was no reflector. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider password-based access control. Tick the \textit{incorrect} assertion. | Password Management System A console based password management program | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider password-based access control. Tick the \textit{incorrect} assertion. | Another security consideration is the ability of malicious software to spoof dialogs that look like legitimate security confirmation requests. If the user were to input credentials into a fake dialog, thinking the dialog was legitimate, the malicious software would then know the user's password. If the Secure Desktop or similar feature were disabled, the malicious software could use that password to gain higher privileges. Though it is not the default behavior for usability reasons, UAC may be configured to require the user to press Ctrl+Alt+Del (known as the secure attention sequence) as part of the authentication process. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement. In ElGamal signature | . . VERIFY-SELECTION . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement. In ElGamal signature | One can verify that a signature ( r , s ) {\displaystyle \left(r,s\right)} is a valid signature for a message m {\displaystyle m} as follows: Verify that 0 < r < q {\displaystyle 0 | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
You are given the task of choosing the parameters of a hash function. What value of the output will you recommend in order to be minimal and secure against second preimage attacks? | The computational infeasibility of a first preimage attack on an ideal hash function assumes that the set of possible hash inputs is too large for a brute force search. However if a given hash value is known to have been produced from a set of inputs that is relatively small or is ordered by likelihood in some way, then a brute force search may be effective. Practicality depends on the input set size and the speed or cost of computing the hash function. A common example is the use of hashes to store password validation data for authentication. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
You are given the task of choosing the parameters of a hash function. What value of the output will you recommend in order to be minimal and secure against second preimage attacks? | By definition, an ideal hash function is such that the fastest way to compute a first or second preimage is through a brute-force attack. For an n-bit hash, this attack has a time complexity 2n, which is considered too high for a typical output size of n = 128 bits. If such complexity is the best that can be achieved by an adversary, then the hash function is considered preimage-resistant. However, there is a general result that quantum computers perform a structured preimage attack in 2 n = 2 n 2 {\displaystyle {\sqrt {2^{n}}}=2^{\frac {n}{2}}} , which also implies second preimage and thus a collision attack. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
$\mathrm{GF}(2^k)$ is represented by the set of\dots | Let X n {\displaystyle X^{n}} be an n-dimensional vector space over the finite field G F ( q N ) {\displaystyle GF\left({q^{N}}\right)} , where q {\displaystyle q} is a power of a prime and N {\displaystyle N} is a positive integer. Let ( u 1 , u 2 , … , u N ) {\displaystyle \left(u_{1},u_{2},\dots ,u_{N}\right)} , with u i ∈ G F ( q N ) {\displaystyle u_{i}\in GF(q^{N})} , be a base of G F ( q N ) {\displaystyle GF\left({q^{N}}\right)} as a vector space over the field G F ( q ) {\displaystyle GF\left({q}\right)} . Every element x i ∈ G F ( q N ) {\displaystyle x_{i}\in GF\left({q^{N}}\right)} can be represented as x i = a 1 i u 1 + a 2 i u 2 + ⋯ + a N i u N {\displaystyle x_{i}=a_{1i}u_{1}+a_{2i}u_{2}+\dots +a_{Ni}u_{N}} . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
$\mathrm{GF}(2^k)$ is represented by the set of\dots | Roughly it asserts that the matrix coefficients for G, suitably renormalized, are an orthonormal basis of L2(G). In particular, L 2 ( G ) {\displaystyle L^{2}(G)} decomposes into an orthogonal direct sum of all the irreducible unitary representations, in which the multiplicity of each irreducible representation is equal to its degree (that is, the dimension of the underlying space of the representation). Thus, L 2 ( G ) = ⨁ ^ π ∈ Σ E π ⊕ dim E π {\displaystyle L^{2}(G)={\underset {\pi \in \Sigma }{\widehat {\bigoplus }}}E_{\pi }^{\oplus \dim E_{\pi }}} where Σ denotes the set of (isomorphism classes of) irreducible unitary representations of G, and the summation denotes the closure of the direct sum of the total spaces Eπ of the representations π. We may also regard L 2 ( G ) {\displaystyle L^{2}(G)} as a representation of the direct product group G × G {\displaystyle G\times G} , with the two factors acting by translation on the left and the right, respectively. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thick the \emph{incorrect} assertion. | asserts that if p {\displaystyle p\,\!} is valid then so is q {\displaystyle q\,\!} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Thick the \emph{incorrect} assertion. | Squeeze { '__'e.1 = ; s.A e.1 = s.A ; = ; }; | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
According to the Kerckhoffs Principle: | Kerckhoffs's principle (also called Kerckhoffs's desideratum, assumption, axiom, doctrine or law) of cryptography was stated by Dutch-born cryptographer Auguste Kerckhoffs in the 19th century. The principle holds that a cryptosystem should be secure, even if everything about the system, except the key, is public knowledge. This concept is widely embraced by cryptographers, in contrast to security through obscurity, which is not. Kerckhoffs's principle was phrased by American mathematician Claude Shannon as "the enemy knows the system", i.e., "one ought to design systems under the assumption that the enemy will immediately gain full familiarity with them". | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
According to the Kerckhoffs Principle: | A generalization some make from Kerckhoffs's principle is: "The fewer and simpler the secrets that one must keep to ensure system security, the easier it is to maintain system security." Bruce Schneier ties it in with a belief that all security systems must be designed to fail as gracefully as possible: principle applies beyond codes and ciphers to security systems in general: every secret creates a potential failure point. Secrecy, in other words, is a prime cause of brittleness—and therefore something likely to make a system prone to catastrophic collapse. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
KEM \dots | Ket, a Yeniseian language (split-S) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
KEM \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 |
Tick the \emph{false} assertion. Two-keys triple DES\dots | Squeeze { '__'e.1 = ; s.A e.1 = s.A ; = ; }; | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{false} assertion. Two-keys triple DES\dots | asserts that if p {\displaystyle p\,\!} is valid then so is q {\displaystyle q\,\!} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} statement regarding $\mathbb{Z}_p^*$, where $p$ is an arbitrary prime number. | This formulation is from Tenenbaum. : 302 Other formulations are in Narkiewicz: 243 and in Cojocaru & Murty. : 45–46 Suppose f is an additive complex-valued arithmetic function, and write p for an arbitrary prime and ν for an arbitrary positive integer. Write A ( x ) = ∑ p ν ≤ x f ( p ν ) p − ν ( 1 − p − 1 ) {\displaystyle A(x)=\sum _{p^{\nu }\leq x}f(p^{\nu })p^{-\nu }(1-p^{-1})} and B ( x ) 2 = ∑ p ν ≤ x | f ( p ν ) | 2 p − ν . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} statement regarding $\mathbb{Z}_p^*$, where $p$ is an arbitrary prime number. | When Carl Friedrich Gauss first introduced the notion of complex integers Z, he observed that the ordinary prime numbers may factor further in this new set of integers. In fact, if a prime p is congruent to 1 mod 4, then it factors into a product of two distinct prime gaussian integers, or "splits completely"; if p is congruent to 3 mod 4, then it remains prime, or is "inert"; and if p is 2 then it becomes a product of the square of the prime (1+i) and the invertible gaussian integer -i; we say that 2 "ramifies". For instance, 5 = ( 1 + 2 i ) ( 1 − 2 i ) {\displaystyle 5=(1+2i)(1-2i)} splits completely; 3 {\displaystyle 3} is inert; 2 = − i ( 1 + i ) 2 {\displaystyle 2=-i(1+i)^{2}} ramifies.From this description, it appears that as one considers larger and larger primes, the frequency of a prime splitting completely approaches 1/2, and likewise for the primes that remain primes in Z. Dirichlet's theorem on arithmetic progressions demonstrates that this is indeed the case. Even though the prime numbers themselves appear rather erratically, splitting of the primes in the extension Z ⊂ Z {\displaystyle \mathbb {Z} \subset \mathbb {Z} } follows a simple statistical law. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement regarding the DES round function. | One then has F = d A . {\displaystyle {\textbf {F}}=d{\textbf {A}}.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement regarding the DES round function. | . 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 |
Which of the following ciphers is based on arithmetics over the finite field $\mathrm{GF}(2^8)$? | The elements of GF(2n), i.e. a finite field whose order is a power of two, are usually represented as polynomials in GF(2). Multiplication of two such field elements consists of multiplication of the corresponding polynomials, followed by a reduction with respect to some irreducible polynomial which is taken from the construction of the field. If the polynomials are encoded as binary numbers, carry-less multiplication can be used to perform the first step of this computation. Such fields have applications in cryptography and for some checksum algorithms. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following ciphers is based on arithmetics over the finite field $\mathrm{GF}(2^8)$? | These spaces can also be augmented with a multiplication operation that makes them into a field GF(2n), but the multiplication operation cannot be a bitwise operation. When n is itself a power of two, the multiplication operation can be nim-multiplication; alternatively, for any n, one can use multiplication of polynomials over GF(2) modulo a irreducible polynomial (as for instance for the field GF(28) in the description of the Advanced Encryption Standard cipher). Vector spaces and polynomial rings over GF(2) are widely used in coding theory, and in particular in error correcting codes and modern cryptography. For example, many common error correcting codes (such as BCH codes) are linear codes over GF(2) (codes defined from vector spaces over GF(2)), or polynomial codes (codes defined as quotients of polynomial rings over GF(2)). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ensuring the information integrity means that\dots | Data integrity demands maintaining and assuring the accuracy and completeness of data. A data owner always expects that her or his data in a cloud can be stored correctly and trustworthy. It means that the data should not be illegally tampered with, improperly modified, deliberately deleted, or maliciously fabricated. If any undesirable operations corrupt or delete the data, the owner should be able to detect the corruption or loss. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ensuring the information integrity means that\dots | The Clark–Wilson integrity model provides a foundation for specifying and analyzing an integrity policy for a computing system. The model is primarily concerned with formalizing the notion of information integrity. Information integrity is maintained by preventing corruption of data items in a system due to either error or malicious intent. An integrity policy describes how the data items in the system should be kept valid from one state of the system to the next and specifies the capabilities of various principals in the system. The model uses security labels to grant access to objects via transformation procedures and a restricted interface model. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Given an odd prime $p$, for any $a \in \mathbb{Z}_p$ the equation | Again, the result is trivial for p = 2, so suppose p is an odd prime, p ≥ 3. Consider the polynomial g ( x ) = ( x − 1 ) ( x − 2 ) ⋯ ( x − ( p − 1 ) ) . {\displaystyle g(x)=(x-1)(x-2)\cdots (x-(p-1)).} g has degree p − 1, leading term xp − 1, and constant term (p − 1)!. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Given an odd prime $p$, for any $a \in \mathbb{Z}_p$ the equation | Let p {\displaystyle p} be an odd prime number. Consider the polynomial f ( x ) = a 0 + a 1 x + ⋯ + a n x n {\textstyle f(x)=a_{0}+a_{1}x+\cdots +a_{n}x^{n}} over the field Z p {\displaystyle \mathbb {Z} _{p}} of remainders modulo p {\displaystyle p} . The algorithm should find all λ {\displaystyle \lambda } in Z p {\displaystyle \mathbb {Z} _{p}} such that f ( λ ) = 0 {\textstyle f(\lambda )=0} in Z p {\displaystyle \mathbb {Z} _{p}} . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which one of the following notions is not in the fundamental trilogy of cryptography? | Supplanted by Cryptography Engineering. Smart, Nigel (2004). Cryptography: An introduction ISBN 0-07-709987-7. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which one of the following notions is not in the fundamental trilogy of cryptography? | Equivalent to Applied Cryptography in many ways, but somewhat more mathematical. For the technically inclined. Covers few meta-cryptographic topics, such as crypto system design. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a mobile station (MS) with a SIM card associated to a home network (HN). The MS tries to connect to a visited network (VN). In the GSM authentication, who knows the key $K_i$? | The current cellular location of the phone (i.e., which BTS it is at) is entered into the VLR record and will be used during a process called paging when the GSM network wishes to locate the mobile phone. Every SIM card contains a secret key, called the Ki, which is used to provide authentication and encryption services. This is useful to prevent theft of service, and also to prevent "over the air" snooping of a user's activity. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a mobile station (MS) with a SIM card associated to a home network (HN). The MS tries to connect to a visited network (VN). In the GSM authentication, who knows the key $K_i$? | GSM 02.09 defines the following security features on Um: authentication of subscribers by the network, encryption on the channel, anonymization of transactions (at least partially)Um also supports frequency hopping (GSM 05.01 Section 6), which is not specifically intended as a security feature but has the practical effect of adding significant complexity to passive interception of the Um link. Authentication and encryption both rely on a secret key, Ki, that is unique to the subscriber. Copies of Ki are held in the SIM and in the Authentication Center (AuC), a component of the HLR. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select \emph{incorrect} statement. Brithday paradox | Select y ~ ∈ { 1 , . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select \emph{incorrect} statement. Brithday paradox | Statements are separated by one semicolon (;) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Kerckhoffs principle says: | Kerckhoffs's principle (also called Kerckhoffs's desideratum, assumption, axiom, doctrine or law) of cryptography was stated by Dutch-born cryptographer Auguste Kerckhoffs in the 19th century. The principle holds that a cryptosystem should be secure, even if everything about the system, except the key, is public knowledge. This concept is widely embraced by cryptographers, in contrast to security through obscurity, which is not. Kerckhoffs's principle was phrased by American mathematician Claude Shannon as "the enemy knows the system", i.e., "one ought to design systems under the assumption that the enemy will immediately gain full familiarity with them". | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Kerckhoffs principle says: | A generalization some make from Kerckhoffs's principle is: "The fewer and simpler the secrets that one must keep to ensure system security, the easier it is to maintain system security." Bruce Schneier ties it in with a belief that all security systems must be designed to fail as gracefully as possible: principle applies beyond codes and ciphers to security systems in general: every secret creates a potential failure point. Secrecy, in other words, is a prime cause of brittleness—and therefore something likely to make a system prone to catastrophic collapse. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{correct} assertion. The Vernam cipher provides \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 |
Tick the \emph{correct} assertion. The Vernam cipher provides \dots | . ) {\displaystyle \,\vert \psi '\rangle \langle \psi '\vert +(...)} , where the dots denote components of ρ out {\displaystyle \rho _{\operatorname {out} }} resulting from errors not properly corrected by the protocol. It follows that This fidelity is to be compared with the corresponding fidelity obtained when no error-correcting protocol is used, which was shown before to equal 1 − p {\displaystyle {1-p}} . A little algebra then shows that the fidelity after error correction is greater than the one without for p < 1 / 2 {\displaystyle p<1/2} . Note that this is consistent with the working assumption that was made while deriving the protocol (of p {\displaystyle p} being small enough). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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