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A Carmichael number \ldots | According to Howe, 17 · 31 · 41 · 43 · 89 · 97 · 167 · 331 is an order 2 Carmichael number. This product is equal to 443,372,888,629,441. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A Carmichael number \ldots | In number theory, a Carmichael number is a composite number n {\displaystyle n} , which in modular arithmetic satisfies the congruence relation: b n ≡ b ( mod n ) {\displaystyle b^{n}\equiv b{\pmod {n}}} for all integers b {\displaystyle b} . The relation may also be expressed in the form: b n − 1 ≡ 1 ( mod n ) {\displaystyle b^{n-1}\equiv 1{\pmod {n}}} .for all integers b {\displaystyle b} which are relatively prime to n {\displaystyle n} . Carmichael numbers are named after American mathematician Robert Carmichael, the term having been introduced by Nicolaas Beeger in 1950 (Øystein Ore had referred to them in 1948 as numbers with the "Fermat property", or "F numbers" for short). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement. The discrete logarithm | Select y ~ ∈ { 1 , . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement. The discrete logarithm | which was arrived at partly by "trial and a table of logarithms". The answer is not so accurate as the number of digits of precision would suggest. No analytical solution was provided. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which protocol is used for encryption in GSM? | GSM uses several cryptographic algorithms for security. The A5/1, A5/2, and A5/3 stream ciphers are used for ensuring over-the-air voice privacy. A5/1 was developed first and is a stronger algorithm used within Europe and the United States; A5/2 is weaker and used in other countries. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which protocol is used for encryption in GSM? | In 2008 it was reported that a GSM phone's encryption key can be obtained using $1,000 worth of computer hardware and 30 minutes of cryptanalysis performed on signals encrypted using A5/1. However, GSM also supports an export weakened variant of A5/1 called A5/2. This weaker encryption cypher can be cracked in real-time. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Choose the \emph{correct} statement | Note: "..." = to be specified | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Choose the \emph{correct} statement | 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 |
Which is NOT a mobile telephony protocol? | The field of technology available for telephony has broadened with the advent of new communication technologies. Telephony now includes the technologies of Internet services and mobile communication, including video conferencing. The new technologies based on Internet Protocol (IP) concepts are often referred to separately as voice over IP (VoIP) telephony, also commonly referred to as IP telephony or Internet telephony. Unlike traditional phone service, IP telephony service is relatively unregulated by government. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which is NOT a mobile telephony protocol? | Mobile telephony is the provision of telephone services to mobile phones rather than fixed-location phones (landline phones). Telephony is supposed to specifically point to a voice-only service or connection, though sometimes the line may blur. Modern mobile phones connect to a terrestrial cellular network of base stations (cell sites), whereas satellite phones connect to orbiting satellites. Both networks are interconnected to the public switched telephone network (PSTN) to allow any phone in the world to be dialed. In 2010 there were estimated to be five billion mobile cellular subscriptions in the world. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement. Enigma ... | ; a {\displaystyle p?\mathbin {;} a\,\!} zero or more times and then performs ¬ p ? {\displaystyle \neg p?\,\!} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement. Enigma ... | Only tokens are defined in the CFG. Web search engines often use this approach. Boolean. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{incorrect} assertion regarding the Diffie-Hellman key exchange | Diffie–Hellman (RFC 3526) ECDH (RFC 4753) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{incorrect} assertion regarding the Diffie-Hellman key exchange | "Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems". Advances in Cryptology – CRYPTO '96. pp. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} statement regarding $\mathsf{GF}(2^k)$. | In particular G / T = G C / B . {\displaystyle \displaystyle {G/T=G_{\mathbf {C} }/B.}} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} statement regarding $\mathsf{GF}(2^k)$. | The second term g ( T ( x ) | λ ) {\displaystyle g(T(\mathbf {x} )|\lambda )} depends on the sample only through T ( x ) = ∑ i = 1 n x i . {\textstyle T(\mathbf {x} )=\sum _{i=1}^{n}x_{i}.} Thus, T ( x ) {\displaystyle T(\mathbf {x} )} is sufficient. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Kerckhoffs principle states that the security of a cryptosystem should rely on the secrecy of\dots | 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 states that the security of a cryptosystem should rely on the secrecy of\dots | Since the key protects the confidentiality and integrity of the system, it is important to be kept secret from unauthorized parties. With public key cryptography, only the private key must be kept secret, but with symmetric cryptography, it is important to maintain the confidentiality of the key. Kerckhoff's principle states that the entire security of the cryptographic system relies on the secrecy of the key. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Tonelli algorithm is | The Tonelli–Shanks algorithm requires (on average over all possible input (quadratic residues and quadratic nonresidues)) 2 m + 2 k + S ( S − 1 ) 4 + 1 2 S − 1 − 9 {\displaystyle 2m+2k+{\frac {S(S-1)}{4}}+{\frac {1}{2^{S-1}}}-9} modular multiplications, where m {\displaystyle m} is the number of digits in the binary representation of p {\displaystyle p} and k {\displaystyle k} is the number of ones in the binary representation of p {\displaystyle p} . If the required quadratic nonresidue z {\displaystyle z} is to be found by checking if a randomly taken number y {\displaystyle y} is a quadratic nonresidue, it requires (on average) 2 {\displaystyle 2} computations of the Legendre symbol. The average of two computations of the Legendre symbol are explained as follows: y {\displaystyle y} is a quadratic residue with chance p + 1 2 p = 1 + 1 p 2 {\displaystyle {\tfrac {\tfrac {p+1}{2}}{p}}={\tfrac {1+{\tfrac {1}{p}}}{2}}} , which is smaller than 1 {\displaystyle 1} but ≥ 1 2 {\displaystyle \geq {\tfrac {1}{2}}} , so we will on average need to check if a y {\displaystyle y} is a quadratic residue two times. This shows essentially that the Tonelli–Shanks algorithm works very well if the modulus p {\displaystyle p} is random, that is, if S {\displaystyle S} is not particularly large with respect to the number of digits in the binary representation of p {\displaystyle p} . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Tonelli algorithm is | The Tonelli–Shanks algorithm can (naturally) be used for any process in which square roots modulo a prime are necessary. For example, it can be used for finding points on elliptic curves. It is also useful for the computations in the Rabin cryptosystem and in the sieving step of the quadratic sieve. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following cryptographic primitives have a security level that is significantly lower than 80 bits? | 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 of the following cryptographic primitives have a security level that is significantly lower than 80 bits? | Cryptographic primitives, on their own, are quite limited. They cannot be considered, properly, to be a cryptographic system. For instance, a bare encryption algorithm will provide no authentication mechanism, nor any explicit message integrity checking. Only when combined in security protocols, can more than one security requirement be addressed. | 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{preimage attacks} of $2^{256}?$ | 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 |
What should the minimal length of the output of a hash function be to provide security against \emph{preimage 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-and-paste attacks, and also cannot be parallelized. As a result, modern hash functions are built on wide-pipe constructions that have a larger internal state size – which range from tweaks of the Merkle–Damgård construction to new constructions such as the sponge construction and HAIFA construction. None of the entrants in the NIST hash function competition use a classical Merkle–Damgård construction.Meanwhile, truncating the output of a longer hash, such as used in SHA-512/256, also defeats many of these attacks. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
How is data integrity ensured in WEP? | Data integrity. Updates by concurrent local and remote users are not lost because of conflicts. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
How is data integrity ensured in WEP? | Integrity in cloud computing implies data integrity as well as computing integrity. Such integrity means that data has to be stored correctly on cloud servers and, in case of failures or incorrect computing, that problems have to be detected. Data integrity can be affected by malicious events or from administration errors (e.g. during backup and restore, data migration, or changing memberships in P2P systems).Integrity is easy to achieve using cryptography (typically through message-authentication code, or MACs, on data blocks).There exist checking mechanisms that effect data integrity. For instance: HAIL (High-Availability and Integrity Layer) is a distributed cryptographic system that allows a set of servers to prove to a client that a stored file is intact and retrievable. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{non-commutative} operation. | Some noncommutative binary operations: | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{non-commutative} operation. | Converse nonimplication is notated p ↚ q {\textstyle p\nleftarrow q} , which is the left arrow from converse implication ( ← {\textstyle \leftarrow } ), negated with a stroke (/). Alternatives include p ⊄ q {\textstyle p\not \subset q} , which combines converse implication's ⊂ {\displaystyle \subset } , negated with a stroke (/). p ← ~ q {\textstyle p{\tilde {\leftarrow }}q} , which combines converse implication's left arrow ( ← {\textstyle \leftarrow } ) with negation's tilde ( ∼ {\textstyle \sim } ). Mpq, in Bocheński notation | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $H$ be a hash function. Collision resistance means that \dots | Collision resistance prevents an attacker from creating two distinct documents with the same hash. A function meeting these criteria may still have undesirable properties. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $H$ be a hash function. Collision resistance means that \dots | This property is sometimes referred to as strong collision resistance. It requires a hash value at least twice as long as what is required for pre-image resistance, otherwise collisions may be found by a birthday attack. Pseudo-randomness: it should be hard to distinguish the pseudo-random number generator based on the hash function from a random number generator, e.g., it passes usual randomness tests. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select \emph{incorrect} statement. The exhaustive search | "Fast text searching with errors." Technical Report TR-91-11. Department of Computer Science, University of Arizona, Tucson, June 1991. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select \emph{incorrect} statement. The exhaustive search | The trailing ";" is customarily quoted with a leading "\", but could just as effectively be enclosed in single quotes. Note that the command itself should not be quoted; otherwise you get error messages like which means that find is trying to run a file called 'echo "mv ./3bfn rel071204"' and failing. If you will be executing over many results, it is more efficient to use a variant of the exec primary that collects filenames up to ARG_MAX and then executes COMMAND with a list of filenames. This will ensure that filenames with whitespaces are passed to the executed COMMAND without being split up by the shell. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Choose the \emph{incorrect} statement. | Make a decisive statement about each. If the subject agrees – says, 'That's right', or 'That describes me all right', or similar – leave it immediately. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Choose the \emph{incorrect} statement. | | | !! Correct Acceptors notice error and choose | X<>X<>X------>|->| Accepted(N,I,V) - BROADCAST |<-------------------X--X Response(V) | | | ! | | | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A Carmichael number is | According to Howe, 17 · 31 · 41 · 43 · 89 · 97 · 167 · 331 is an order 2 Carmichael number. This product is equal to 443,372,888,629,441. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A Carmichael number is | In number theory, a Carmichael number is a composite number n {\displaystyle n} , which in modular arithmetic satisfies the congruence relation: b n ≡ b ( mod n ) {\displaystyle b^{n}\equiv b{\pmod {n}}} for all integers b {\displaystyle b} . The relation may also be expressed in the form: b n − 1 ≡ 1 ( mod n ) {\displaystyle b^{n-1}\equiv 1{\pmod {n}}} .for all integers b {\displaystyle b} which are relatively prime to n {\displaystyle n} . Carmichael numbers are named after American mathematician Robert Carmichael, the term having been introduced by Nicolaas Beeger in 1950 (Øystein Ore had referred to them in 1948 as numbers with the "Fermat property", or "F numbers" for short). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
We want to generate a $\ell$-bit prime. The complexity is roughly\dots | 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 be shown to be expected polynomial time for all but a small fraction of primes, and this fraction exponentially decreases with the size of the primes. Consequently, it's well-suited to generating certified large random primes, an application that is important in cryptography applications such as generating provably valid RSA keys. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
We want to generate a $\ell$-bit prime. The complexity is roughly\dots | Agrawal and Biswas use a more sophisticated technique, which divides P n {\displaystyle {\mathcal {P}}_{n}} by a random monic polynomial of small degree. Prime numbers are used in a number of applications such as hash table sizing, pseudorandom number generators and in key generation for cryptography. Therefore, finding very large prime numbers (on the order of (at least) 10 350 ≈ 2 1024 {\displaystyle 10^{350}\approx 2^{1024}} ) becomes very important and efficient primality testing algorithms are required. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The ElGamal cryptosystem is based on\dots | For the ElGamal encryption we suppose now that Alice is the owner of the XTR public key data ( p , q , T r ( g ) ) {\displaystyle (p,q,Tr(g))} and that she has selected a secret integer k {\displaystyle k} , computed T r ( g k ) {\displaystyle Tr(g^{k})} and published the result. Given Alice's XTR public key data ( p , q , T r ( g ) , T r ( g k ) ) {\displaystyle \left(p,q,Tr(g),Tr(g^{k})\right)} , Bob can encrypt a message M {\displaystyle M} , intended for Alice, using the following XTR version of the ElGamal encryption: Bob selects randomly a b ∈ Z {\displaystyle b\in \mathbb {Z} } with 1 < b < q − 2 {\displaystyle 1 | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The ElGamal cryptosystem is based on\dots | The GM cryptosystem is semantically secure based on the assumed intractability of the quadratic residuosity problem modulo a composite N = pq where p, q are large primes. This assumption states that given (x, N) it is difficult to determine whether x is a quadratic residue modulo N (i.e., x = y2 mod N for some y), when the Jacobi symbol for x is +1. The quadratic residue problem is easily solved given the factorization of N, while new quadratic residues may be generated by any party, even without knowledge of this factorization. The GM cryptosystem leverages this asymmetry by encrypting individual plaintext bits as either random quadratic residues or non-residues modulo N, all with quadratic residue symbol +1. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $E$ be an elliptic curve. Solving which of the following problems would help you to break Elliptic Curve Diffie-Hellman (ECDH) over $E$? | 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 used to encrypt subsequent communications using a symmetric-key cipher. It is a variant of the Diffie–Hellman protocol using elliptic-curve cryptography. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $E$ be an elliptic curve. Solving which of the following problems would help you to break Elliptic Curve Diffie-Hellman (ECDH) over $E$? | The external Diffie–Hellman (XDH) assumption is a computational hardness assumption used in elliptic curve cryptography. The XDH assumption holds that there exist certain subgroups of elliptic curves which have useful properties for cryptography. Specifically, XDH implies the existence of two distinct groups ⟨ G 1 , G 2 ⟩ {\displaystyle \langle {\mathbb {G} }_{1},{\mathbb {G} }_{2}\rangle } with the following properties: The discrete logarithm problem (DLP), the computational Diffie–Hellman problem (CDH), and the computational co-Diffie–Hellman problem are all intractable in G 1 {\displaystyle {\mathbb {G} }_{1}} and G 2 {\displaystyle {\mathbb {G} }_{2}} . There exists an efficiently computable bilinear map (pairing) e ( ⋅ , ⋅ ): G 1 × G 2 → G T {\displaystyle e(\cdot ,\cdot ):{\mathbb {G} }_{1}\times {\mathbb {G} }_{2}\rightarrow {\mathbb {G} }_{T}} . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What is the encryption of the word ``SECRECY'' under the Vigen\`ere cipher using the key ``ZAB''? | It is byte-oriented, with variable block size, typically 2 to 6 bytes. The key size is only 64 bits. Both of these are unusually small for a modern cipher. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What is the encryption of the word ``SECRECY'' under the Vigen\`ere cipher using the key ``ZAB''? | The following Python code can be used to encrypt text with the affine cipher: | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A passive adversary can \ldots | Using the theorem prover SPASS it has been shown that this protocol can be attacked. This attack and two more from are outlined in . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A passive adversary can \ldots | In the computationally bounded adversary model the channel – the adversary – is restricted to only being able to perform a reasonable amount of computation to decide which bits of the code word need to change. In other words, this model does not need to consider how many errors can possibly be handled, but only how many errors could possibly be introduced given a reasonable amount of computing power on the part of the adversary. Once the channel has been given this restriction it becomes possible to construct codes that are both faster to encode and decode compared to previous methods that can also handle a large number of errors. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $n$ be a positive integer. The Fermat test most likely outputs ``prime'' \dots | Let us say we want to investigate if n = 31697 is a probable prime (PRP). We pick base a = 3 and, inspired by Fermat's little theorem, calculate: 3 31696 ≡ 1 ( mod 31697 ) {\displaystyle 3^{31696}\equiv 1{\pmod {31697}}} This shows 31697 is a Fermat PRP (base 3), so we may suspect it is a prime. We now repeatedly halve the exponent: 3 15848 ≡ 1 ( mod 31697 ) {\displaystyle 3^{15848}\equiv 1{\pmod {31697}}} 3 7924 ≡ 1 ( mod 31697 ) {\displaystyle 3^{7924}\equiv 1{\pmod {31697}}} 3 3962 ≡ 28419 ( mod 31697 ) {\displaystyle 3^{3962}\equiv 28419{\pmod {31697}}} The first couple of times do not yield anything interesting (the result was still 1 modulo 31697), but at exponent 3962 we see a result that is neither 1 nor minus 1 (i.e. 31696) modulo 31697. This proves 31697 is in fact composite (it equals 29×1093). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $n$ be a positive integer. The Fermat test most likely outputs ``prime'' \dots | Let F n = 2 2 n + 1 {\displaystyle F_{n}=2^{2^{n}}+1} be the nth Fermat number. Pépin's test states that for n > 0, F n {\displaystyle F_{n}} is prime if and only if 3 ( F n − 1 ) / 2 ≡ − 1 ( mod F n ) . {\displaystyle 3^{(F_{n}-1)/2}\equiv -1{\pmod {F_{n}}}.} The expression 3 ( F n − 1 ) / 2 {\displaystyle 3^{(F_{n}-1)/2}} can be evaluated modulo F n {\displaystyle F_{n}} by repeated squaring. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
When designing a cryptosystem that follows the rules of modern cryptography, we \dots | Practical Cryptography, Wiley, ISBN 0-471-22357-3. A cryptosystem design consideration primer. Covers both algorithms and protocols. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
When designing a cryptosystem that follows the rules of modern cryptography, we \dots | Modern cryptography is heavily based on mathematical theory and computer science practice; cryptographic algorithms are designed around computational hardness assumptions, making such algorithms hard to break in actual practice by any adversary. While it is theoretically possible to break into a well-designed system, it is infeasible in actual practice to do so. Such schemes, if well designed, are therefore termed "computationally secure". | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which one of these digital signature schemes is \emph{not} based on the Discrete Log problem? | Digital Signature Standard (DSS), based on the Digital Signature Algorithm (DSA) RSA Elliptic Curve DSA | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which one of these digital signature schemes is \emph{not} based on the Discrete Log problem? | Digital signatures schemes are among the most important cryptographic primitives. They can be obtained by using the one-way functions based on the worst-case hardness of lattice problems. However, they are impractical. A number of new digital signature schemes based on learning with errors, ring learning with errors and trapdoor lattices have been developed since the learning with errors problem was applied in a cryptographic context. | 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 |
The result of $2^{2015} \bmod{9}$ is $\ldots$ | !^{2}} given by 2 k ( 2 k − 1 ) ! ! 2 ( p − 1 2 ) ! | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The result of $2^{2015} \bmod{9}$ is $\ldots$ | As with the proof by infinite descent, we obtain a 2 = 2 b 2 {\displaystyle a^{2}=2b^{2}} . Being the same quantity, each side has the same prime factorization by the fundamental theorem of arithmetic, and in particular, would have to have the factor 2 occur the same number of times. However, the factor 2 appears an odd number of times on the right, but an even number of times on the left—a contradiction. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The complexities of the encryption and decryption in RSA with a modulus of $s$ bits are respectively within the order of magnitude \ldots | This RSA modulus is made public together with the encryption exponent e. N and e form the public key pair (e, N). By making this information public, anyone can encrypt messages to Bob. The decryption exponent d satisfies e d = 1 mod λ ( N ) {\displaystyle ed=1{\bmod {\lambda }}(N)} , where λ ( N ) {\displaystyle \lambda (N)} denotes the Carmichael function, though sometimes φ ( N ) {\displaystyle \varphi (N)} , the Euler’s phi function, is used (note: this is the order of the multiplicative group Z N ∗ {\displaystyle \mathbb {Z} _{N}^{*}} , which is not necessarily a cyclic group). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The complexities of the encryption and decryption in RSA with a modulus of $s$ bits are respectively within the order of magnitude \ldots | Developments in quantum computing over the past decade and the optimistic prospects for real quantum computers within 20 years have begun to threaten the basic cryptography that secures the internet. A relatively small quantum computer capable of processing only ten thousand of bits of information would easily break all of the widely used public key cryptography algorithms used to protect privacy and digitally sign information on the internet.One of the most widely used public key algorithm used to create digital signatures is known as RSA. Its security is based on the classical difficulty of factoring the product of two large and unknown primes into the constituent primes. The integer factorization problem is believed to be intractable on any conventional computer if the primes are chosen at random and are sufficiently large. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{false} assumption. | The following is the two-sentence version: Assume (D1) is true. Then (D2) is true. This would mean that (D1) is false. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{false} assumption. | For example, given the statement L = {\displaystyle L=} "all swans are white", we can deduce Q = {\displaystyle Q=} "the specific swan here is white", but if what is observed is ¬ Q = {\displaystyle \neg Q=} "the specific swan here is not white" (say black), then "all swans are white" is false. More accurately, the statement Q {\displaystyle Q} that can be deduced is broken into an initial condition and a prediction as in C ⇒ P {\displaystyle C\Rightarrow P} in which C = {\displaystyle C=} "the thing here is a swan" and P = {\displaystyle P=} "the thing here is a white swan". If what is observed is C being true while P is false (formally, C ∧ ¬ P {\displaystyle C\wedge \neg P} ), we can infer that the law is false. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A simple substitution cipher can be broken \dots | Permutation box Substitution box Permutation cipher Substitution cipher Transposition cipher | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A simple substitution cipher can be broken \dots | The following is an implementation of the cipher in Python. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which one of the following notions means that ``the information should make clear who the author of it is''? | In some publications, the author responsible for new names and nomenclatural acts is not stated directly in the original source, but can sometimes be inferred from reliable external evidence. Recommendation 51D of the Code states: "...if the authorship is known or inferred from external evidence, the name of the author, if cited, should be enclosed in square brackets to show the original anonymity". | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which one of the following notions means that ``the information should make clear who the author of it is''? | In an automated story, there is often confusion about who should be credited as the author. Several participants of a study on algorithmic authorship attributed the credit to the programmer; others perceived the news organization as the author, emphasizing the collaborative nature of the work. There is also no way for the reader to verify whether an article was written by a robot or human, which raises issues of transparency although such issues also arise with respect to authorship attribution between human authors too. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Stream ciphers often use a nonce to \dots | 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 |
Stream ciphers often use a nonce to \dots | In cryptography, a nonce is an arbitrary number that can be used just once in a cryptographic communication. It is often a random or pseudo-random number issued in an authentication protocol to ensure that old communications cannot be reused in replay attacks. They can also be useful as initialization vectors and in cryptographic hash functions. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Choose the \emph{correct} statement. | Make a decisive statement about each. If the subject agrees – says, 'That's right', or 'That describes me all right', or similar – leave it immediately. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Choose the \emph{correct} statement. | 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 |
The group $\mathbb{Z}_{60}^*$ has \ldots | The partial group algebra C par ( Z 4 ) {\displaystyle \mathbb {C} _{\text{par}}\left(\mathbb {Z} _{4}\right)} is isomorphic to the direct sum: C ⊕ C ⊕ C ⊕ C ⊕ C ⊕ C ⊕ C ⊕ M 2 ( C ) ⊕ M 3 ( C ) {\displaystyle \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus M_{2}\left(\mathbb {C} \right)\oplus M_{3}\left(\mathbb {C} \right)} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The group $\mathbb{Z}_{60}^*$ has \ldots | The main fact about these groups is that they are discrete subgroups and they have finite covolume for the Haar measure on P S L 2 ( R ) . {\displaystyle \mathrm {PSL} _{2}(\mathbb {R} ).} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following integers has the square roots $\{2,3\}$ when taken modulo $5$ \textbf{and} the square roots $\{3,10\}$ when taken modulo $13$. | For q = 13, the field Fq is just integer arithmetic modulo 13. The numbers with square roots mod 13 are: ±1 (square roots ±1 for +1, ±5 for −1) ±3 (square roots ±4 for +3, ±6 for −3) ±4 (square roots ±2 for +4, ±3 for −4).Thus, in the Paley graph, we form a vertex for each of the integers in the range , and connect each such integer x to six neighbors: x ± 1 (mod 13), x ± 3 (mod 13), and x ± 4 (mod 13). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following integers has the square roots $\{2,3\}$ when taken modulo $5$ \textbf{and} the square roots $\{3,10\}$ when taken modulo $13$. | {\displaystyle 5=1^{2}+2^{2},\quad 13=2^{2}+3^{2},\quad 17=1^{2}+4^{2},\quad 29=2^{2}+5^{2},\quad 37=1^{2}+6^{2},\quad 41=4^{2}+5^{2}.} On the other hand, the primes 3, 7, 11, 19, 23 and 31 are all congruent to 3 modulo 4, and none of them can be expressed as the sum of two squares. This is the easier part of the theorem, and follows immediately from the observation that all squares are congruent to 0 or 1 modulo 4. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pick the \emph{false} statement. | . . VERIFY-SELECTION . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pick the \emph{false} statement. | P2 can choose any clause. Then P1 chooses the literal that is true. And because it is true, its adjacent node in the left vertical node has already been selected, so P2 has no moves to make and loses. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Moore's 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 |
Moore's Law ... | Moore's law is the observation that the number of transistors in an integrated circuit (IC) doubles about every two years. Moore's law is an observation and projection of a historical trend. Rather than a law of physics, it is an empirical relationship linked to gains from experience in production. The observation is named after Gordon Moore, the co-founder of Fairchild Semiconductor and Intel (and former CEO of the latter), who in 1965 posited a doubling every year in the number of components per integrated circuit, and projected this rate of growth would continue for at least another decade. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{false} assertion. The index of coincidence | falsehood-preserving: The interpretation under which all variables are assigned a truth value of "false" produces a truth value of "false" as a result of material nonimplication. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{false} assertion. The index of coincidence | falsehood-preserving: The interpretation under which all variables are assigned a truth value of 'false' produces a truth value of 'false' as a result of converse nonimplication | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement. Pedersen Commitment is | . . VERIFY-SELECTION . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement. Pedersen Commitment is | returns metadata that includes a commitment statement from the current service provider. The ARK and its inflections ('?' and '??') | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select a correct statement | Choice or Select. U.S. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select a correct statement | The SQL SELECT statement returns a result set of records, from one or more tables.A SELECT statement retrieves zero or more rows from one or more database tables or database views. In most applications, SELECT is the most commonly used data manipulation language (DML) command. As SQL is a declarative programming language, SELECT queries specify a result set, but do not specify how to calculate it. The database translates the query into a "query plan" which may vary between executions, database versions and database software. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $p$ be a prime number. What is the cardinality of $\mathbf{Z}_p$? | However, they have an ideal generated by the image of the prime number p under the canonical map Z → Zp. The quotient Zp/pZp is again the finite field of p elements. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $p$ be a prime number. What is the cardinality of $\mathbf{Z}_p$? | Let p be a prime number. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Due to the birthday paradox, a collision search in a hash function with $n$-bit output has complexity\dots | For this hash, an attack was eventually discovered with a time complexity close to 2 n / 2 {\displaystyle 2^{n/2}} . This beat by far the birthday bound and ideal pre-image complexities which are 2 3 n / 2 {\displaystyle 2^{3n/2}} and 2 3 n {\displaystyle 2^{3n}} for the Zémor-Tillich hash function. As the attacks include a birthday search in a reduced set of size 2 n {\displaystyle 2n} they indeed do not destroy the idea of provable security or invalidate the scheme but rather suggest that the initial parameters were too small. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Due to the birthday paradox, a collision search in a hash function with $n$-bit output has complexity\dots | It is proposed that the puzzle in Equihash be solved by a variation of Wagner's algorithm for the generalized birthday problem. (Note that the underlying problem is not exactly the Generalized Birthday Problem as defined by Wagner, since it uses a single list rather than multiple lists.) The proposed algorithm makes k {\displaystyle k} iterations over a large list. For every factor of 1 q {\displaystyle {\frac {1}{q}}} fewer entries per list, computational complexity of the algorithm scales proportional to q k 2 {\displaystyle q^{\frac {k}{2}}} for memory-efficient implementations. Alcock and Ren refute Equihash’s security claims, concluding that no tradeoff-resistance bound is in fact known for Equihash. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Using a block cipher, we can build \ldots | Before starting off the symmetric encryption process, the input message M ∈ B ∗ {\displaystyle M\in B^{\ast }} is divided into blocks M 1 , . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Using a block cipher, we can build \ldots | Let P = P ‖ P ‖ P ‖ P {\displaystyle P=P\|P\|P\|P} be a 128-bit block of plaintext and C = C ‖ C ‖ C ‖ C {\displaystyle C=C\|C\|C\|C} be a 128-bit block of ciphertext, where P {\displaystyle P} and C {\displaystyle C} ( 0 ≤ i < 4 {\displaystyle 0\leq i<4} ) are 32-bit blocks. Let K i = K i ‖ K i ‖ K i ‖ K i ‖ K i ‖ K i {\displaystyle K_{i}=K_{i}\|K_{i}\|K_{i}\|K_{i}\|K_{i}\|K_{i}} ( 0 ≤ i < N r {\displaystyle 0\leq i | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What is the length in bits of the input and output of a DES S-Box respectively? | The S-boxes accept a four-bit input and produce a four-bit output. The S-box substitution in the round function consists of eight 4 × 4 S-boxes. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What is the length in bits of the input and output of a DES S-Box respectively? | This table lists the eight S-boxes used in DES. Each S-box replaces a 6-bit input with a 4-bit output. Given a 6-bit input, the 4-bit output is found by selecting the row using the outer two bits, and the column using the inner four bits. For example, an input "011011" has outer bits "01" and inner bits "1101"; noting that the first row is "00" and the first column is "0000", the corresponding output for S-box S5 would be "1001" (=9), the value in the second row, 14th column. (See S-box). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{minimal} assumption on the required channel to exchange the key of a Message Authentication Code (MAC): | A Message authentication code (MAC) is a cryptography method that uses a secret key to digitally sign a message. This method outputs a MAC value that can be decrypted by the receiver, using the same secret key used by the sender. The Message Authentication Code protects both a message's data integrity as well as its authenticity. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{minimal} assumption on the required channel to exchange the key of a Message Authentication Code (MAC): | In cryptography, a message authentication code (MAC), sometimes known as an authentication tag, is a short piece of information used for authenticating a message. In other words, to confirm that the message came from the stated sender (its authenticity) and has not been changed. The MAC value protects a message's data integrity, as well as its authenticity, by allowing verifiers (who also possess the secret key) to detect any changes to the message content. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{true} assertion among the followings: | 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{true} assertion among the followings: | asserts that if p {\displaystyle p\,\!} is valid then so is q {\displaystyle q\,\!} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following is well preserved by 2G? | In Japan the ubiquitous system was Personal Digital Cellular (PDC) though another, Personal Handy-phone System (PHS), also existed.Three primary benefits of 2G networks over their 1G predecessors were: Digitally encrypted phone conversations, at least between the mobile phone and the cellular base station but not necessarily in the rest of the network. Significantly more efficient use of the radio frequency spectrum enabling more users per frequency band. Data services for mobile, starting with SMS text messages then expanding to Multimedia Messaging Service (MMS).With General Packet Radio Service (GPRS), 2G offers a theoretical maximum transfer speed of 40 kbit/s (5 kB/s). With EDGE (Enhanced Data Rates for GSM Evolution), there is a theoretical maximum transfer speed of 384 kbit/s (48 kB/s). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following is well preserved by 2G? | Originally 2G networks were voice centric or even voice only digital cellular systems (as opposed to the analog 1G networks). Typical 2G standards include GSM and IS-95 with extensions via GPRS, EDGE and 1xRTT, providing Internet access to users of originally voice centric 2G networks. Both EDGE and 1xRTT are 3G standards, as defined by the ITU, but are usually marketed as 2.9G due to their comparatively low speeds and high delays when compared to true 3G technologies. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The collision resistance property of a hash function $H$ means that it is infeasible to\dots | Collision resistance prevents an attacker from creating two distinct documents with the same hash. A function meeting these criteria may still have undesirable properties. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The collision resistance property of a hash function $H$ means that it is infeasible to\dots | Krohn, Freedman and Mazieres proposed a theory in 2004 that if we have a hash function H: V ⟶ G {\displaystyle H:V\longrightarrow G} such that: H {\displaystyle H} is collision resistant – it is hard to find x {\displaystyle x} and y {\displaystyle y} such that H ( x ) = H ( y ) {\displaystyle H(x)=H(y)} ; H {\displaystyle H} is a homomorphism – H ( x + y ) = H ( x ) + H ( y ) {\displaystyle H(x+y)=H(x)+H(y)} .Then server can securely distribute H ( v i ) {\displaystyle H(v_{i})} to each receiver, and to check if y = ∑ 1 ≤ i ≤ k ( α i v i ) {\displaystyle y=\sum _{1\leq i\leq k}(\alpha _{i}v_{i})} we can check whether H ( y ) = ∑ 1 ≤ i ≤ k ( α i H ( v i ) ) {\displaystyle H(y)=\sum _{1\leq i\leq k}(\alpha _{i}H(v_{i}))} The problem with this method is that the server needs to transfer secure information to each of the receivers. The hash functions H {\displaystyle H} needs to be transmitted to all the nodes in the network through a separate secure channel. H {\displaystyle H} is expensive to compute and secure transmission of H {\displaystyle H} is not economical either. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Compared to the plain RSA cryptosystem and for equivalent key sizes, the plain Elgamal cryptosystem has\dots | For this reason, RSA is commonly used together with padding methods such as OAEP or PKCS1. In the ElGamal cryptosystem, a plaintext m {\displaystyle m} is encrypted as E ( m ) = ( g b , m A b ) {\displaystyle E(m)=(g^{b},mA^{b})} , where ( g , A ) {\displaystyle (g,A)} is the public key. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Compared to the plain RSA cryptosystem and for equivalent key sizes, the plain Elgamal cryptosystem has\dots | An analysis comparing millions of RSA public keys gathered from the Internet was announced in 2012 by Lenstra, Hughes, Augier, Bos, Kleinjung, and Wachter. They were able to factor 0.2% of the keys using only Euclid's algorithm. They exploited a weakness unique to cryptosystems based on integer factorization. If n = pq is one public key and n′ = p′q′ is another, then if by chance p = p′, then a simple computation of gcd(n,n′) = p factors both n and n′, totally compromising both keys. Nadia Heninger, part of a group that did a similar experiment, said that the bad keys occurred almost entirely in embedded applications, and explains that the one-shared-prime problem uncovered by the two groups results from situations where the pseudorandom number generator is poorly seeded initially and then reseeded between the generation of the first and second primes. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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