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Consider the exhaustive search of a uniformly distributed key in a set of size $N$. Think of the possible strategies and their complexities. Which of the following is \textbf{not} possible (We assume that memory access is constant.) | Suppose that there are 100 million key texts that might plausibly be used, and that on average each has 11 thousand possible starting positions. To an opponent with a massive collection of possible key texts, this leaves possible a brute force search of the order of 2 40 {\displaystyle 2^{40}} , which by computer crypt... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider the exhaustive search of a uniformly distributed key in a set of size $N$. Think of the possible strategies and their complexities. Which of the following is \textbf{not} possible (We assume that memory access is constant.) | Gasarch, Glenn, and Kruskal have performed a comparison of different computational methods for large subsets of { 1 , … n } {\displaystyle \{1,\dots n\}} with no arithmetic progression. Using these methods they found the exact size of the largest such set for n ≤ 187 {\displaystyle n\leq 187} . Their results include se... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} assertion. | 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} assertion. | {\textsf {T}}\rangle } . The reasoning is as follows. The object booleanWitness has the member T that is assigned the type Boolean as its value. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Pohlig-Hellman algorithm can be used to \dots | Donald Knuth, The Art of Computer Programming, Vol 2: Seminumerical Algorithms, section 3.4.1. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Pohlig-Hellman algorithm can be used to \dots | "Section 2.3.4: The Bellman-Ford-Moore algorithm". Digraphs: Theory, Algorithms and Applications (First ed.). Springer. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} assertion. In a zero-knowledge interactive proof of knowledge, \ldots | A formal definition of zero-knowledge has to use some computational model, the most common one being that of a Turing machine. Let P {\displaystyle P} , V {\displaystyle V} , and S {\displaystyle S} be Turing machines. An interactive proof system with ( P , V ) {\displaystyle (P,V)} for a language L {\displaystyle L} i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} assertion. In a zero-knowledge interactive proof of knowledge, \ldots | As the program of the prover does not necessarily spit out the knowledge itself (as is the case for zero-knowledge proofs) a machine with a different program, called the knowledge extractor is introduced to capture this idea. We are mostly interested in what can be proven by polynomial time bounded machines. In this ca... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} assertion. Let $X,Y$ be two random variables over the same probability space. Then, | Finally, the two random variables X and Y are equal if they are equal as functions on their measurable space: X ( ω ) = Y ( ω ) for all ω . {\displaystyle X(\omega )=Y(\omega )\qquad {\hbox{for all }}\omega .} This notion is typically the least useful in probability theory because in practice and in theory, the underly... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} assertion. Let $X,Y$ be two random variables over the same probability space. Then, | Given two random variables X , Y {\displaystyle X,Y} with values ( 1 , . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} assertion. | 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{false} assertion. | {\textsf {T}}\rangle } . The reasoning is as follows. The object booleanWitness has the member T that is assigned the type Boolean as its value. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} assertion. The advantage of a distinguisher of two distributions $P_0$ and $P_1$ | The truth table of P ↚ Q {\displaystyle P\nleftarrow Q} . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} assertion. The advantage of a distinguisher of two distributions $P_0$ and $P_1$ | Using P ( ¬ B | A ) = 1 − P ( B | A ) {\displaystyle P(\neg B\vert A)=1-P(B\vert A)} twice, one may use Bayes' theorem to also express P ( ¬ B | ¬ A ) {\displaystyle P(\neg B\vert \neg A)} in terms of P ( A | B ) {\displaystyle P(A\vert B)} and without negations: P ( ¬ B | ¬ A ) = 1 − ( 1 − P ( A | B ) ) P ( B ) P ( ¬ ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The number of plaintext/ciphertext pairs required for a linear cryptanalysis is\dots | But this may not be enough assurance; a linear cryptanalysis attack against DES requires 243 known plaintexts (with their corresponding ciphertexts) and approximately 243 DES operations. This is a considerable improvement over brute force attacks. Public-key algorithms are based on the computational difficulty of vario... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The number of plaintext/ciphertext pairs required for a linear cryptanalysis is\dots | A generalization of LC—multiple linear cryptanalysis—was suggested in 1994 (Kaliski and Robshaw), and was further refined by Biryukov and others. (2004); their analysis suggests that multiple linear approximations could be used to reduce the data requirements of the attack by at least a factor of 4 (that is, 241 instea... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{incorrect} assertion. For a cipher $C$, decorrelation theory says that \ldots | In cryptography, decorrelation theory is a system developed by Serge Vaudenay in 1998 for designing block ciphers to be provably secure against differential cryptanalysis, linear cryptanalysis, and even undiscovered cryptanalytic attacks meeting certain broad criteria. Ciphers designed using these principles include CO... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{incorrect} assertion. For a cipher $C$, decorrelation theory says that \ldots | We say that assumption A {\displaystyle A} is stronger than assumption B {\displaystyle B} when A {\displaystyle A} implies B {\displaystyle B} (and the converse is false or not known). In other words, even if assumption A {\displaystyle A} were false, assumption B {\displaystyle B} may still be true, and cryptographic... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Given a function $f:\left\{ 0,1 \right\}^p \rightarrow \left\{ 0,1 \right\}^q$, given $a\in\left\{ 0,1 \right\}^p$ and $b \in \left\{ 0,1 \right\}^q$, we define $DP^{f}(a,b) = \Pr_{X}[f(X \oplus a) = f(X) \oplus b]$. We have that $\ldots$ | f →: P ( X ) → P ( Y ) {\displaystyle f^{\rightarrow }:{\mathcal {P}}(X)\to {\mathcal {P}}(Y)} with f → ( A ) = { f ( a ) | a ∈ A } {\displaystyle f^{\rightarrow }(A)=\{f(a)\;|\;a\in A\}} f ←: P ( Y ) → P ( X ) {\displaystyle f^{\leftarrow }:{\mathcal {P}}(Y)\to {\mathcal {P}}(X)} with f ← ( B ) = { a ∈ X | f ( a ) ∈ B... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Given a function $f:\left\{ 0,1 \right\}^p \rightarrow \left\{ 0,1 \right\}^q$, given $a\in\left\{ 0,1 \right\}^p$ and $b \in \left\{ 0,1 \right\}^q$, we define $DP^{f}(a,b) = \Pr_{X}[f(X \oplus a) = f(X) \oplus b]$. We have that $\ldots$ | Let q = p + ε. Taking a = nq in (1), we obtain: Pr ( 1 n ∑ X i ≥ q ) ≤ inf t > 0 E e t n q = inf t > 0 ( E e t q ) n . {\displaystyle \Pr \left({\frac {1}{n}}\sum X_{i}\geq q\right)\leq \inf _{t>0}{\frac {E\left}{e^{tnq}}}=\inf _{t>0}\left({\frac {E\left}{e^{tq}}}\right)^{n}.} Now, knowing that Pr(Xi = 1) = p, Pr(Xi ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In linear cryptanalysis,\dots | Forking lemma Leftover hash lemma Piling-up lemma (linear cryptanalysis) Yao's XOR lemma | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In linear cryptanalysis,\dots | A generalization of LC—multiple linear cryptanalysis—was suggested in 1994 (Kaliski and Robshaw), and was further refined by Biryukov and others. (2004); their analysis suggests that multiple linear approximations could be used to reduce the data requirements of the attack by at least a factor of 4 (that is, 241 instea... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The worst case complexity of an exaustive search (with memory) against DES is\dots | When top-down parser tries to parse an ambiguous input with respect to an ambiguous CFG, it may need exponential number of steps (with respect to the length of the input) to try all alternatives of the CFG in order to produce all possible parse trees, which eventually would require exponential memory space. The problem... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The worst case complexity of an exaustive search (with memory) against DES is\dots | In the geometric view of the online binary search tree problem, an access sequence x 1 , . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Who invented linear cryptanalysis? | A linear cryptanalysis is a form of cryptanalysis based on finding affine approximations to the action of a cipher. Linear cryptanalysis is one of the two most widely used attacks on block ciphers; the other being differential cryptanalysis.The discovery is attributed to Mitsuru Matsui, who first applied the technique ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Who invented linear cryptanalysis? | In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. Attacks have been developed for block ciphers and stream ciphers. Linear cryptanalysis is one of the two most widely used attacks on block ciphers; the other being differential cryp... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
For a blockcipher $B:\{0,1\}^k\times \{0,1\}^n \rightarrow \{0,1\}^n$ that has decorrelation $Dec^q_{\| \cdot \|_{\infty}}(B,C^*)=d$ (from a perfect cipher $C^*$), the best advantage of \textit{any} distinguisher that makes $q$ queries is \ldots | Suppose a code of 2 n R {\displaystyle 2^{nR}} codewords. Let W be drawn uniformly over this set as an index. Let X n {\displaystyle X^{n}} and Y n {\displaystyle Y^{n}} be the transmitted codewords and received codewords, respectively. n R = H ( W ) = H ( W | Y n ) + I ( W ; Y n ) {\displaystyle nR=H(W)=H(W|Y^{n})+I(W... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
For a blockcipher $B:\{0,1\}^k\times \{0,1\}^n \rightarrow \{0,1\}^n$ that has decorrelation $Dec^q_{\| \cdot \|_{\infty}}(B,C^*)=d$ (from a perfect cipher $C^*$), the best advantage of \textit{any} distinguisher that makes $q$ queries is \ldots | by only comparing the 8 bits of each intermediate value, the authors was able to orchestrate a MITM attack on the cipher, despite there being 20 rounds between the two subciphers. Using partial-matching increased the amount of false positives, but nothing that noticeably increased the complexity of the attack. == Notes... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
I want to send a value to Bob without him knowing which value I sent and such that I cannot change my mind later when I reveal it in clear. I should use \dots | Alice keeps a private. Bob chooses an element b from B and sends wb to Alice. Bob keeps b private. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
I want to send a value to Bob without him knowing which value I sent and such that I cannot change my mind later when I reveal it in clear. I should use \dots | Alice (the sender) wishes to send a value x to Bob (the receiver). The communication channel between Alice and Bob is imperfect, and can introduce errors. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} assertion. | 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{false} assertion. | {\textsf {T}}\rangle } . The reasoning is as follows. The object booleanWitness has the member T that is assigned the type Boolean as its value. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} assertion. $x\in \mathbf{Z}_{n}$ is invertible iff \ldots | We then have X X − 1 = = = I n {\displaystyle \mathbf {X} \mathbf {X} ^{-1}=\left=\left=\mathbf {I} _{n}} , where δ i j {\displaystyle \delta _{i}^{j}} is the Kronecker delta. We also have X − 1 X = = = = I n {\displaystyle \mathbf {X} ^{-1}\mathbf {X} =\left=\left=\left=\mathbf {I} _{n}} , as required. If the vec... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} assertion. $x\in \mathbf{Z}_{n}$ is invertible iff \ldots | {\displaystyle \mathbf {B} ={\begin{pmatrix}-1&{\tfrac {3}{2}}\\1&-1\end{pmatrix}}.} The matrix B {\displaystyle \mathbf {B} } is invertible. To check this, one can compute that det B = − 1 2 {\textstyle \det \mathbf {B} =-{\frac {1}{2}}} , which is non-zero. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following circuits does not change an input difference. | The voltage difference in the low state, where the voltages on the wires are exchanged, is 0 V − V S = − V S {\displaystyle 0\,\mathrm {V} -V_{S}=-V_{S}} . The difference between high and low logic levels is therefore V S − ( − V S ) = 2 V S {\displaystyle V_{S}-(-V_{S})=2V_{S}\,} . This is twice the difference of the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following circuits does not change an input difference. | Examples are the classic transistor emitter-coupled Schmitt trigger, the op-amp inverting Schmitt trigger, etc. Modified input voltage (parallel feedback): when the input voltage crosses the threshold in some direction the circuit changes its input voltage in the same direction (now it adds a part of its output voltage... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which one of these attacks is not a side channel attack? | In computer security, a side-channel attack is any attack based on extra information that can be gathered because of the fundamental way a computer protocol or algorithm is implemented, rather than flaws in the design of the protocol or algorithm itself (e.g. flaws found in a cryptanalysis of a cryptographic algorithm)... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which one of these attacks is not a side channel attack? | Side-channel attacks do not attack the cipher as a black box, and thus are not related to cipher security as defined in the classical context, but are important in practice. They attack implementations of the cipher on hardware or software systems that inadvertently leak data. There are several such known attacks on va... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{correct} assertion. The maximum advantage of an \textbf{adaptive} distinguisher limited to $q$ queries between two random functions $F$ and $F^*$ is always\dots | Sensitivity conjecture for Boolean functions (Hao Huang, 2019) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{correct} assertion. The maximum advantage of an \textbf{adaptive} distinguisher limited to $q$ queries between two random functions $F$ and $F^*$ is always\dots | For a Boolean function f: { 0 , 1 } n → { 0 , 1 } {\displaystyle f:\{0,1\}^{n}\to \{0,1\}} , the sensitivity of f {\displaystyle f} is defined to be the maximum sensitivity of f {\displaystyle f} over all x {\displaystyle x} , where the sensitivity of f {\displaystyle f} at x {\displaystyle x} is the number of single-b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} assertion. A distinguisher can \ldots | 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{false} assertion. A distinguisher can \ldots | asserts that if p {\displaystyle p\,\!} is true then so is q {\displaystyle q\,\!} , the inference p ⊢ q {\displaystyle p\vdash q\,\!} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider any block cipher $C$ and a uniformly distributed random permutation $C^*$ on $\{0,1\}^\ell$. Then, for any $n \ge 1$ we always have\dots | For this case we prove a weaker version of the theorem: One-way permutation → pseudorandom generator A one-way permutation is a one-way function that is also a permutation of the input bits. A pseudorandom generator can be constructed from one-way permutation ƒ as follows: Gl: {0,1}l→{0,1}l+1 = ƒ(x).B(x), where B is ha... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider any block cipher $C$ and a uniformly distributed random permutation $C^*$ on $\{0,1\}^\ell$. Then, for any $n \ge 1$ we always have\dots | The idealized abstraction of a (keyed) block cipher is a truly random permutation on the mappings between plaintext and ciphertext. If a distinguishing algorithm exists that achieves significant advantage with less effort than specified by the block cipher's security parameter (this usually means the effort required sh... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $X$, $Y$, and $K$ be respectively the plaintext, ciphertext, and key distributions. $H$ denotes the Shannon entropy. The consequence of perfect secrecy is \dots | Shannon proved, using information theoretic considerations, that the one-time pad has a property he termed perfect secrecy; that is, the ciphertext C gives absolutely no additional information about the plaintext. This is because (intuitively), given a truly uniformly random key that is used only once, a ciphertext can... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $X$, $Y$, and $K$ be respectively the plaintext, ciphertext, and key distributions. $H$ denotes the Shannon entropy. The consequence of perfect secrecy is \dots | The final output is H t | | G t {\displaystyle H_{t}||G_{t}} . The scheme has the rate R H i r o s e = k − n 2 n {\textstyle R_{Hirose}={\frac {k-n}{2n}}} relative to encrypting the message with the cipher. Hirose also provides a proof in the Ideal Cipher Model. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} assertion. A first preimage attack on a hash function H is \ldots | For a hash function for which L is the number of bits in the message digest, finding a message that corresponds to a given message digest can always be done using a brute force search in approximately 2L evaluations. This is called a preimage attack and may or may not be practical depending on L and the particular comp... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} assertion. A first preimage attack on a hash function H is \ldots | Hence, the Merkle–Damgård hash construction reduces the problem of finding a proper hash function to finding a proper compression function. A second preimage attack (given a message m 1 {\displaystyle m_{1}} an attacker finds another message m 2 {\displaystyle m_{2}} to satisfy hash ( m 1 ) = hash ( m 2 ) {\display... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In an interactive proof system for a language $L$, having $\beta$-soundness means that\dots | Every interactive proof system defines a formal language of strings L {\displaystyle L} . Soundness of the proof system refers to the property that no prover can make the verifier accept for the wrong statement y ∉ L {\displaystyle y\not \in L} except with some small probability. The upper bound of this probability is ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In an interactive proof system for a language $L$, having $\beta$-soundness means that\dots | Most proofs of soundness are trivial. For example, in an axiomatic system, proof of soundness amounts to verifying the validity of the axioms and that the rules of inference preserve validity (or the weaker property, truth). If the system allows Hilbert-style deduction, it requires only verifying the validity of the ax... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A proof system is computational-zero-knowledge if \dots | As the program of the prover does not necessarily spit out the knowledge itself (as is the case for zero-knowledge proofs) a machine with a different program, called the knowledge extractor is introduced to capture this idea. We are mostly interested in what can be proven by polynomial time bounded machines. In this ca... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A proof system is computational-zero-knowledge if \dots | A formal definition of zero-knowledge has to use some computational model, the most common one being that of a Turing machine. Let P {\displaystyle P} , V {\displaystyle V} , and S {\displaystyle S} be Turing machines. An interactive proof system with ( P , V ) {\displaystyle (P,V)} for a language L {\displaystyle L} i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} assertion. Assume that $C$ is a random permutation. | There is a simple randomized polynomial-time algorithm that provides a ( 1 − 1 2 k ) {\displaystyle \textstyle \left(1-{\frac {1}{2^{k}}}\right)} -approximation to MAXEkSAT: independently set each variable to true with probability 1/2, otherwise set it to false. Any given clause c is unsatisfied only if all of its k co... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} assertion. Assume that $C$ is a random permutation. | If x {\displaystyle \mathbf {x} } is a random permutation of the integers 1 , 2 , … , n {\displaystyle 1,2,\ldots ,n} and A n ≡ a s n ( x ) {\displaystyle A_{n}\equiv {\rm {as}}_{n}(\mathbf {x} )} , then it is possible to show that E = 2 n 3 + 1 6 and Var = 8 n 45 − 13 180 . {\displaystyle E={\frac {2n}{3}}+{\frac ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Standard encryption threats do not include: | The encryption features are prohibited. The digital signature features (from SES) are prohibited. The "patched data" features (from PKPatchMaker) are prohibited. Archives may not span multiple volumes or be segmented. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Standard encryption threats do not include: | Recent incidents of terrorism have led to further calls for restrictions on encryption. Even though, in the interest of public safety, there are many proposals to interfere with the free deployment of strong encryption, these proposals do not hold up against close scientific scrutiny. These proposals side-step a more f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} assertion. In Linear Cryptanalysis, the corresponding mask circuit of \ldots | Output: Decrypted message M ∈ B ∗ ∪ R e j e c t {\displaystyle M\in B^{\ast }\cup {Reject}} . Decrypt the ciphertext: If L ( ψ ) < 3 L B ( P ) + 16 {\displaystyle L(\psi )<3L_{B}(P)+16} , then return R e j e c t {\displaystyle Reject} . Compute: note that 0 ≤ u 1 , u 2 , v < 256 l {\displaystyle 0\leq u_{1},u_{2},v<256... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} assertion. In Linear Cryptanalysis, the corresponding mask circuit of \ldots | The Vernam cipher implemented by the Lorenz SZ machines utilizes the Boolean "exclusive or" (XOR) function, symbolised by ⊕ and verbalised as "A or B but not both". This is represented by the following truth table, where x represents "true" and • represents "false". Other names for this function are: exclusive disjunct... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} assertion. In a zero-knowledge interactive proof for $L$, \ldots | "Formalization of Forcing in Isabelle/ZF". Archive of Formal Proofs. arXiv:2001.09715. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} assertion. In a zero-knowledge interactive proof for $L$, \ldots | We explain how the four inference rules are used in proofs, using the proof of ¬ p ≡ p ≡ ⊥ {\textstyle \lnot p\equiv p\equiv \bot } . The logic symbols ⊤ {\textstyle \top } and ⊥ {\textstyle \bot } indicate "true" and "false," respectively, and ¬ {\textstyle \lnot } indicates "not." The theorem numbers refer to theorem... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What is the Squared Euclidean Imbalance? | The imbalance in feature i {\displaystyle i} is: c i = ∑ j = 1 m X j {\displaystyle c_{i}=\sum _{j=1}^{m}{X_{j}}} . Since the X j {\displaystyle X_{j}} are independent random variables, by the Chernoff bound, for every a > 0 {\displaystyle a>0}: P r o b ≤ 2 exp ( − a 2 / 2 m ) {\displaystyle Prob\left\leq 2\exp(-a^{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What is the Squared Euclidean Imbalance? | The squared Euclidean distance is a measure of how "close" two sets are. In particular, if two sets are compact, then their squared Euclidean distance is zero if and only if they are equal. Thus, we may quantify how close to convexity Q {\displaystyle Q} is by upper-bounding d 2 ( C o n v ( Q ) , Q ) . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} assertion. A cipher with a good decorrelation of order 2 protects against \ldots | Verify the ciphertext preamble: If u 1 ≥ P {\displaystyle u_{1}\geq P} or u 2 ≥ P {\displaystyle u_{2}\geq P} or v ≥ P {\displaystyle v\geq P} , then return R e j e c t {\displaystyle Reject} . If u 1 q ≠ 1 r e m P {\displaystyle u_{1}^{q}\neq 1remP} , then return R e j e c t {\displaystyle Reject} . r e j e c t ← 0 {\... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} assertion. A cipher with a good decorrelation of order 2 protects against \ldots | The Vernam cipher implemented by the Lorenz SZ machines utilizes the Boolean "exclusive or" (XOR) function, symbolised by ⊕ and verbalised as "A or B but not both". This is represented by the following truth table, where x represents "true" and • represents "false". Other names for this function are: exclusive disjunct... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
For any function $f:\{0,1\}^p\rightarrow \{0,1\}^q$ and for any $a\in\{0,1\}^p$, we have\ldots | f →: P ( X ) → P ( Y ) {\displaystyle f^{\rightarrow }:{\mathcal {P}}(X)\to {\mathcal {P}}(Y)} with f → ( A ) = { f ( a ) | a ∈ A } {\displaystyle f^{\rightarrow }(A)=\{f(a)\;|\;a\in A\}} f ←: P ( Y ) → P ( X ) {\displaystyle f^{\leftarrow }:{\mathcal {P}}(Y)\to {\mathcal {P}}(X)} with f ← ( B ) = { a ∈ X | f ( a ) ∈ B... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
For any function $f:\{0,1\}^p\rightarrow \{0,1\}^q$ and for any $a\in\{0,1\}^p$, we have\ldots | We show that f() ⊆ . Indeed, for every x ∈ W we have x = f(x) and since w is the least upper bound of W, x ≤ f(w). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{incorrect} assertion regarding plain Rabin, i.e., Rabin without any redundancy. | 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, gue... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{incorrect} assertion regarding plain Rabin, i.e., Rabin without any redundancy. | Patterns may assert that previous text or subsequent text contains a pattern without consuming matched text (zero-width assertion). For example, /\w+(?=\t)/ matches a word followed by a tab, without including the tab itself. Look-behind assertions cannot be of uncertain length though (unlike Perl) each branch can be a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{incorrect} assertion. A cipher $C$ perfectly decorrelated at order 2 implies\dots | Verify the ciphertext preamble: If u 1 ≥ P {\displaystyle u_{1}\geq P} or u 2 ≥ P {\displaystyle u_{2}\geq P} or v ≥ P {\displaystyle v\geq P} , then return R e j e c t {\displaystyle Reject} . If u 1 q ≠ 1 r e m P {\displaystyle u_{1}^{q}\neq 1remP} , then return R e j e c t {\displaystyle Reject} . r e j e c t ← 0 {\... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{incorrect} assertion. A cipher $C$ perfectly decorrelated at order 2 implies\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 err... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} assertion. A distinguisher \ldots | 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{false} assertion. A distinguisher \ldots | asserts that if p {\displaystyle p\,\!} is true then so is q {\displaystyle q\,\!} , the inference p ⊢ q {\displaystyle p\vdash q\,\!} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{incorrect} assertion regarding the security of the Diffie-Hellman key exchange over a subgroup $\langle g \rangle \subset \mathbb{Z}_p^*$. | G F ( p t ) {\displaystyle GF\left(p^{t}\right)} Let now ⟨ γ ⟩ {\displaystyle \langle \gamma \rangle } be a multiplicative group of order ω {\displaystyle \omega } . The security of the Diffie–Hellman protocol in ⟨ γ ⟩ {\displaystyle \langle \gamma \rangle } relies on the Diffie–Hellman (DH) problem of computing γ x y ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{incorrect} assertion regarding the security of the Diffie-Hellman key exchange over a subgroup $\langle g \rangle \subset \mathbb{Z}_p^*$. | The group G satisfies the requisite condition for secure communication as long as there is no efficient algorithm for determining gab given g, ga, and gb. For example, the elliptic curve Diffie–Hellman protocol is a variant that represents an element of G as a point on an elliptic curve instead of as an integer modulo ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} assertion. In Differential Cryptanalysis, the corresponding differential circuit of \ldots | Higher-order differential cryptanalysis Truncated differential cryptanalysis Impossible differential cryptanalysis Boomerang attack | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} assertion. In Differential Cryptanalysis, the corresponding differential circuit of \ldots | The Vernam cipher implemented by the Lorenz SZ machines utilizes the Boolean "exclusive or" (XOR) function, symbolised by ⊕ and verbalised as "A or B but not both". This is represented by the following truth table, where x represents "true" and • represents "false". Other names for this function are: exclusive disjunct... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{correct} assertion. Linear cryptanalysis \ldots | In order for the whole system to work, one has to postulate that: ∀ m ∈ M , I D ∈ { 0 , 1 } ∗: D e c r y p t ( E x t r a c t ( P , K m , I D ) , P , E n c r y p t ( P , m , I D ) ) = m {\displaystyle \forall m\in {\mathcal {M}},ID\in \left\{0,1\right\}^{*}:\mathrm {Decrypt} \left(\mathrm {Extract} \left({\mathcal {P}},... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{correct} assertion. Linear cryptanalysis \ldots | Verify the ciphertext preamble: If u 1 ≥ P {\displaystyle u_{1}\geq P} or u 2 ≥ P {\displaystyle u_{2}\geq P} or v ≥ P {\displaystyle v\geq P} , then return R e j e c t {\displaystyle Reject} . If u 1 q ≠ 1 r e m P {\displaystyle u_{1}^{q}\neq 1remP} , then return R e j e c t {\displaystyle Reject} . r e j e c t ← 0 {\... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $p>2$ be a prime. Then \dots | Let p be a prime number. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $p>2$ be a prime. Then \dots | If p is an odd prime, then every prime q that divides 2p − 1 must be 1 plus a multiple of 2p. This holds even when 2p − 1 is prime. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which assertion has not been proven? | It is based on the premise that there is no proof for a certain claim. From this premise, the conclusion is drawn that this claim must therefore be false. For example, "Nobody has ever proved to me there's a God, so I know there is no God". | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which assertion has not been proven? | It is based on the premise that there is no proof for a certain claim. From this premise, the conclusion is drawn that this claim must therefore be false. For example, "Nobody has ever proved to me there's a God, so I know there is no God". | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{incorrect} assertion. In hypothesis testing \ldots | asserts that if p {\displaystyle p\,\!} is true then so is q {\displaystyle q\,\!} , the inference p ⊢ q {\displaystyle p\vdash q\,\!} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{incorrect} assertion. In hypothesis testing \ldots | The method proposed in Section 8.7 of Duda, Hart & Stork (2001) suggests successively guessing grammar rules (productions) and testing them against positive and negative observations. The rule set is expanded so as to be able to generate each positive example, but if a given rule set also generates a negative example, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider the cipher defined using the key $K\in \{0,1\}^{64} $ by $$\begin{array}{llll} C : & \{0,1\}^{64} & \rightarrow & \{0,1\}^{64} \\ & x & \mapsto & C(x)=x \oplus K \\ \end{array} $$ Let $x=1\dots 11$, the value $\mathsf{LP}^{C_K}(x,x)$ is equal to | For RC5P, analysis was conducted modulo 3. It was observed that the operations in the cipher (rotation and addition, both on 32-bit words) were somewhat biased over congruence classes mod 3. To illustrate the approach, consider left rotation by a single bit: X ⋘ 1 = { 2 X , if X < 2 31 2 X + 1 − 2 32 , if X ≥ 2 31 {\di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider the cipher defined using the key $K\in \{0,1\}^{64} $ by $$\begin{array}{llll} C : & \{0,1\}^{64} & \rightarrow & \{0,1\}^{64} \\ & x & \mapsto & C(x)=x \oplus K \\ \end{array} $$ Let $x=1\dots 11$, the value $\mathsf{LP}^{C_K}(x,x)$ is equal to | Decryption of a ciphertext ( R n + 1 , L n + 1 ) {\displaystyle (R_{n+1},L_{n+1})} is accomplished by computing for i = n , n − 1 , … , 0 {\displaystyle i=n,n-1,\ldots ,0} R i = L i + 1 , {\displaystyle R_{i}=L_{i+1},} L i = R i + 1 ⊕ F ( L i + 1 , K i ) . {\displaystyle L_{i}=R_{i+1}\oplus \operatorname {F} (L_{i+1}... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{incorrect} assertion. Let $H:\left\{ 0,1 \right\}^*\rightarrow\left\{ 0,1 \right\}^n$ be a hash function. | If this hash value equals the hash value of the pattern, it performs a full comparison at that position. In order for this to work well, the hash function should be selected randomly from a family of hash functions that are unlikely to produce many false positives, that is, positions of the text which have the same has... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{incorrect} assertion. Let $H:\left\{ 0,1 \right\}^*\rightarrow\left\{ 0,1 \right\}^n$ be a hash function. | , h ( k , y ) } {\displaystyle \left\{h(0,x),...,h(k,x)\right\}=\left\{h(0,y),...,h(k,y)\right\}} are identical. This makes a collision twice as likely as the hoped-for 1 / | T | 2 {\displaystyle 1/|T|^{2}} . There are additionally a significant number of mostly-overlapping hash sets; if h 2 ( y ) = h 2 ( x ) {\display... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In which group is the discrete logarithm problem believed to be hard? | There exist groups for which computing discrete logarithms is apparently difficult. In some cases (e.g. large prime order subgroups of groups (Zp)×) there is not only no efficient algorithm known for the worst case, but the average-case complexity can be shown to be about as hard as the worst case using random self-red... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In which group is the discrete logarithm problem believed to be hard? | The discrete logarithm problem is considered to be computationally intractable. That is, no efficient classical algorithm is known for computing discrete logarithms in general. A general algorithm for computing logb a in finite groups G is to raise b to larger and larger powers k until the desired a is found. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider two distributions $P_0,P_1$ with the same supports and a distinguisher $\mathcal{A}$ that makes $q$ queries. Tick the \textit{incorrect} assertion. | Consider two uniform distributions, with the support of p = {\displaystyle p=} enclosed within q = {\displaystyle q=} ( C ≤ A < B ≤ D {\displaystyle C\leq A | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider two distributions $P_0,P_1$ with the same supports and a distinguisher $\mathcal{A}$ that makes $q$ queries. Tick the \textit{incorrect} assertion. | Consider two probability distributions P {\displaystyle P} and Q {\displaystyle Q} . Usually, P {\displaystyle P} represents the data, the observations, or a measured probability distribution. Distribution Q {\displaystyle Q} represents instead a theory, a model, a description or an approximation of P {\displaystyle P}... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What is the complexity of prime number generation for a prime of length $\ell$? | To derive a certificate from this theorem, we first encode Mx, My, A, B, and q, then recursively encode the proof of primality for q < n, continuing until we reach a known prime. This certificate has size O((log n)2) and can be verified in O((log n)4) time. Moreover, the algorithm that generates these certificates can ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What is the complexity of prime number generation for a prime of length $\ell$? | Let π ( x ) {\displaystyle \pi (x)} be the number of primes smaller than x ∃ c 1 , c 2 > 0: π ( x + x ) − π ( x ) ≥ c 2 x log c 1 x {\displaystyle \exists c_{1},c_{2}>0:\pi (x+{\sqrt {x}})-\pi (x)\geq {\frac {c_{2}{\sqrt {x}}}{\log ^{c_{1}}x}}} for sufficiently large x. If one accepts this conjecture then the Goldwas... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In ElGamal signature scheme, if we avoid checking that $0 \leq r < p$ then \ldots | When A attempts to forge on a message m, we consider the output of A to be (J, y) where y is the forgery, and J is such that m was the Jth unique query to the random oracle (it may be assumed that A will query m at some point, if A is to be successful with non-negligible probability). (If A outputs an incorrect forgery... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
In ElGamal signature scheme, if we avoid checking that $0 \leq r < p$ then \ldots | The ElGamal signature scheme is a digital signature scheme based on the algebraic properties of modular exponentiation, together with the discrete logarithm problem. The algorithm uses a key pair consisting of a public key and a private key. The private key is used to generate a digital signature for a message, and suc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} assertion. MAC is \ldots | DEBUG gdb DDT, a PDP-10 debugger from DEC used as a command shell for the MIT Incompatible Timesharing System Firebug/Chromebug, a JavaScript shell and debugging environment as a Firefox plugin | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} assertion. MAC is \ldots | COBOL On-Line debugger. APL. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
For $K$ a field, $a,b\in K$ with $4a^3+27b^2 \neq 0$, $E_{a,b}(K)$ is | Let K be any field of characteristic not 2. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
For $K$ a field, $a,b\in K$ with $4a^3+27b^2 \neq 0$, $E_{a,b}(K)$ is | {\displaystyle N_{B/A}(xB)=N_{L/K}(x)A.} Let L / K {\displaystyle L/K} be a Galois extension of number fields with rings of integers O K ⊂ O L {\displaystyle {\mathcal {O}}_{K}\subset {\mathcal {O}}_{L}} . Then the preceding applies with A = O K , B = O L {\displaystyle A={\mathcal {O}}_{K},B={\mathcal {O}}_{L}} , and ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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