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The Advanced Encryption Standard (AES) is based on arithmetics on\dots | The Advanced Encryption Standard (AES), also known by its original name Rijndael (Dutch pronunciation: ), is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001.AES is a variant of the Rijndael block cipher developed by two Belgian ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Advanced Encryption Standard (AES) is based on arithmetics on\dots | The estimated strength of the encryption corresponds to about 60–80 bits for common symmetrical ciphers. Cryptographically, this effective key length is quite low, but appropriate in that the protocol was not designed as a secure transport protocol but rather as a fast and efficient obfuscation method. AES was proposed... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{incorrect} assertion. In \emph{all} finite Abelian groups $(G,+)$ \ldots | Consider a finite abelian group G = ⊕i Cdi , where the d1 | d2 | ... | dr are invariant factors. Then D ( G ) ≥ M ( G ) = 1 − r + ∑ i d i . {\displaystyle D(G)\geq M(G)=1-r+\sum _{i}{d_{i}}.} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{incorrect} assertion. In \emph{all} finite Abelian groups $(G,+)$ \ldots | The finite group G {\displaystyle G} is abelian if and only if p ( G ) = 1 {\displaystyle p(G)=1} . One has p ( G ) = k ( G ) # G {\displaystyle p(G)={\frac {k(G)}{\#G}}} where k ( G ) {\displaystyle k(G)} is the number of conjugacy classes of G {\displaystyle G} .If G {\displaystyle G} is not abelian then p ( G ) ≤ 5 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The needed number of DES operations to attack DES is about ... | 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 needed number of DES operations to attack DES is about ... | An attack can be plausibly carried out. A wounded primitive has an attack taking between 280 and around 2100 operations. An attack is not possible right now, but future improvements are likely to make it possible. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which algorithm can be typically used in order to generate a prime number? | In computational number theory, a variety of algorithms make it possible to generate prime numbers efficiently. These are used in various applications, for example hashing, public-key cryptography, and search of prime factors in large numbers. For relatively small numbers, it is possible to just apply trial division to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which algorithm can be typically used in order to generate a prime number? | 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, findin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{correct} assertion. In RSA with public key $(e,N)$ and private key $(d,N)$ \ldots | Given block size r, a public/private key pair is generated as follows: Choose large primes p and q such that r | ( p − 1 ) , gcd ( r , ( p − 1 ) / r ) = 1 , {\displaystyle r\vert (p-1),\operatorname {gcd} (r,(p-1)/r)=1,} and gcd ( r , ( q − 1 ) ) = 1 {\displaystyle \operatorname {gcd} (r,(q-1))=1} Set n = p q , ϕ =... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{correct} assertion. In RSA with public key $(e,N)$ and private key $(d,N)$ \ldots | Bob does not want Alice to know which one he receives. Alice generates an RSA key pair, comprising the modulus N {\displaystyle N} , the public exponent e {\displaystyle e} and the private exponent d {\displaystyle d} . She also generates two random values, x 0 , x 1 {\displaystyle x_{0},x_{1}} and sends them to Bob al... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{correct} assertion concerning WPA2 | A tool to automatize WEP cracking and logging of WPA handshakes. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{correct} assertion concerning WPA2 | WS-ReliableMessaging WS-Reliability WS-RM Policy Assertion | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement regarding Kerckhoffs' principle. | 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} statement regarding Kerckhoffs' principle. | Suppose we are given a Boolean expressions: B 1 = ( v 3 ∨ ¬ v 2 ) ∧ ( ¬ v 1 ∨ ¬ v 3 ) {\displaystyle B_{1}=(v_{3}\lor \neg v_{2})\wedge (\neg v_{1}\lor \neg v_{3})} B 2 = ( v 3 ∨ ¬ v 2 ) ∧ ( ¬ v 1 ∨ ¬ v 3 ) ∧ ( ¬ v 1 ∨ v 2 ) . {\displaystyle B_{2}=(v_{3}\lor \neg v_{2})\wedge (\neg v_{1}\lor \neg v_{3})\wedge (\neg v_{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $H$ be a hash function based on the Merkle-Damg{\aa}rd construction. The Merkle-Damg{\aa}rd theorem says 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 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $H$ be a hash function based on the Merkle-Damg{\aa}rd construction. The Merkle-Damg{\aa}rd theorem says 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 inde... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a blockcipher $\mathsf{B}:\mathcal{K}\times\{0,1\}^n \rightarrow \{0,1\}^n$ with $|\mathcal{K}|=N$ for which we choose a secret key $K\in\mathcal{K}$ uniformly at random. Tick the \textit{correct} assertion. | Let k {\displaystyle k} be a positive integer and let P = { 0 , 1 } k {\displaystyle P=\{0,1\}^{k}} be the set of messages. Let f: Y → Z {\displaystyle f:\,Y\rightarrow Z} be a one-way function. For 1 ≤ i ≤ k {\displaystyle 1\leq i\leq k} and j ∈ { 0 , 1 } {\displaystyle j\in \{0,1\}} the signer chooses y i , j ∈ Y {\d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a blockcipher $\mathsf{B}:\mathcal{K}\times\{0,1\}^n \rightarrow \{0,1\}^n$ with $|\mathcal{K}|=N$ for which we choose a secret key $K\in\mathcal{K}$ uniformly at random. Tick the \textit{correct} assertion. | Even if k-1 players collude to generate the number r*, as long as the kth player truthfully generates a random r ′ {\displaystyle r'} , the sum r = r ∗ + r ′ {\displaystyle r=r*+r'} is still uniformly random in {0, 51}. Measured in terms of the number of single-agent encryptions, the algorithm in is optimal when no co... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The $n^2$ problem ... | For n ∈ { 1 , 2 , . . . } | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The $n^2$ problem ... | . . , n M ) x 2 ∗ ( n 1 , . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A passive adversary\dots | (Each of these q interactions is a query.) The attacker guesses how the coin landed. He wins if his guess is correct.The attacker, which we can model as an algorithm, is called an adversary. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A passive adversary\dots | Unlike traditional cryptographic applications, such as encryption or signature, one must assume that the adversary in an MPC protocol is one of the players engaged in the system (or controlling internal parties). That corrupted party or parties may collude in order to breach the security of the protocol. Let n {\displa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} statement regarding RSA Cryptosystem. | RSA-400 has 400 decimal digits (1,327 bits), and has not been factored so far. RSA-400 = 2014096878945207511726700485783442547915321782072704356103039129009966793396 1419850865094551022604032086955587930913903404388675137661234189428453016032 6191193056768564862615321256630010268346471747836597131398943140685464051631 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{true} statement regarding RSA Cryptosystem. | In the random oracle model, if RSA is ( t ′ , ϵ ′ ) {\displaystyle (t',\epsilon ')} -secure, then the full domain hash RSA signature scheme is ( t , ϵ ) {\displaystyle (t,\epsilon )} -secure where, t = t ′ − ( q hash + q sig + 1 ) ⋅ O ( k 3 ) ϵ = ( 1 + 1 q sig ) q sig + 1 ⋅ q sig ⋅ ϵ ′ {\displaystyle {\begin{aligned}t&... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Vernam cipher\dots | (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 |
The Vernam cipher\dots | Goldreich, Oded (2001 and 2004). Foundations of Cryptography. Cambridge University Press. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which protocol does \emph{not} use RC4. | RFC 7366: "Encrypt-then-MAC for Transport Layer Security (TLS) and Datagram Transport Layer Security (DTLS)". RFC 7465: "Prohibiting RC4 Cipher Suites". | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which protocol does \emph{not} use RC4. | WEP TKIP (default algorithm for WPA, but can be configured to use AES-CCMP instead of RC4) BitTorrent protocol encryption Microsoft Office XP (insecure implementation since nonce remains unchanged when documents get modified) Microsoft Point-to-Point Encryption Transport Layer Security / Secure Sockets Layer (was optio... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following is a mode of operation for blockciphers that requires a non-repeating IV (a nonce) to be secure? | Some cryptographic primitives require the IV only to be non-repeating, and the required randomness is derived internally. In this case, the IV is commonly called a nonce (a number used only once), and the primitives (e.g. CBC) are considered stateful rather than randomized. This is because an IV need not be explicitly ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following is a mode of operation for blockciphers that requires a non-repeating IV (a nonce) to be secure? | Furthermore, it does not suffer from the short-cycle problem that can affect OFB.If the IV/nonce is random, then they can be combined with the counter using any invertible operation (concatenation, addition, or XOR) to produce the actual unique counter block for encryption. In case of a non-random nonce (such as a pack... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
How many generators are there in $\mathbb{Z}_n$? | (Z/pZ)n is generated by n elements, and n is the least possible number of generators. In particular, the set {e1, ..., en} , where ei has a 1 in the ith component and 0 elsewhere, is a minimal generating set. Every elementary abelian group has a fairly simple finite presentation. ( Z / p Z ) n ≅ ⟨ e 1 , … , e n ∣ e i p... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
How many generators are there in $\mathbb{Z}_n$? | The basic generator set G 0 {\displaystyle {\mathcal {G}}_{0}} has n − k {\displaystyle n-k} Pauli sequences of finite support: G 0 = { G i ∈ F ( Π Z + ): 1 ≤ i ≤ n − k } . {\displaystyle {\mathcal {G}}_{0}=\left\{\mathbf {G} _{i}\in F(\Pi ^{\mathbb {Z} ^{+}}):1\leq i\leq n-k\right\}.} The constraint length ν {\display... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Using salt for UNIX passwords \ldots | Earlier versions of Unix used a password file /etc/passwd to store the hashes of salted passwords (passwords prefixed with two-character random salts). In these older versions of Unix, the salt was also stored in the passwd file (as cleartext) together with the hash of the salted password. The password file was publicl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Using salt for UNIX passwords \ldots | The security of passwords is therefore protected only by the one-way functions (enciphering or hashing) used for the purpose. Early Unix implementations limited passwords to eight characters and used a 12-bit salt, which allowed for 4,096 possible salt values. This was an appropriate balance for 1970s computational and... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
One can find a collision in a hash function $h\colon \{0,1\}^* \rightarrow \{0,1\}^n$ with expected time complexity\dots | In this approach, we base the security of hash function on some hard mathematical problem and we prove that finding collisions of the hash functions is as hard as breaking the underlying problem. This gives a somewhat stronger notion of security than just relying on complex mixing of bits as in the classical approach. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
One can find a collision in a hash function $h\colon \{0,1\}^* \rightarrow \{0,1\}^n$ with expected time complexity\dots | Since m {\displaystyle m} is a constant, hashing requires time O ( n log n log log n ) {\displaystyle O(n\log n\log \log n)} . They proved that the hash function family is collision resistant by showing that if there is a polynomial-time algorithm that succeeds with non-negligible probability in finding b ≠ b ′ ∈... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement regarding the Enigma machine. | Tentatively making these assumptions, the following partial decrypted message is obtained. heVeTCSWPeYVaWHaVSReQMthaYVaOeaWHRtatePFaMVaWHKVSTYhtZetheKeetPeJVSZaYPaRRGaReM WQhMGhMtQaReWGPSReHMtQaRaKeaTtMJTPRGaVaKaeTRaWHatthattMZeTWAWSQWtSWatTVaPMRtRSJ GSTVReaYVeatCVMUeMWaRGMeWtMJMGCSMWtSJOMeQtheVeQeVetQSVSTWHKPaGARCStRW... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement regarding the Enigma machine. | On the other hand, if A paid, she announces ¬ ( 1 ⊕ 0 ) = 0 {\displaystyle \lnot (1\oplus 0)=0} . The three public announcements combined reveal the answer to their question. One simply computes the XOR of the three bits announced. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
One of the following ciphers is a \emph{block} cipher. Which one? | In cryptography, a block cipher is a deterministic algorithm that operates on fixed-length groups of bits, called blocks. Block ciphers are the elementary building blocks of many cryptographic protocols. They are ubiquitous in the storage and exchange of data, where such data is secured and authenticated via encryption... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
One of the following ciphers is a \emph{block} cipher. Which one? | A block cipher is one of the most basic primitives in cryptography, and frequently used for data encryption. However, by itself, it can only be used to encode a data block of a predefined size, called the block size. For example, a single invocation of the AES algorithm transforms a 128-bit plaintext block into a ciphe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Compute $\phi(90)$. | There are several formulae for computing φ(n). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Compute $\phi(90)$. | })=\phi (m)^{i!}} . Since N is finite, for i great enough, ϕ ( m ) i ! | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $p$ and $q$ be two prime numbers and $n=pq$. Let $K_p=(e,n)$ and $K_s=(d,n)$ be the RSA public and private keys respectively. Recall that the encryption of a message $m$ is $c=m^e \bmod{n}$ and the decryption is $m=c^d \bmod{n}$. Which assertion is \emph{always true}? | On the other hand, if n = pq is the product of two distinct prime numbers, then φ(n) = (p − 1)(q − 1). In this case, finding f from n and e is as difficult as computing φ(n) (this has not been proven, but no algorithm is known for computing f without knowing φ(n)). Knowing only n, the computation of φ(n) has essentiall... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $p$ and $q$ be two prime numbers and $n=pq$. Let $K_p=(e,n)$ and $K_s=(d,n)$ be the RSA public and private keys respectively. Recall that the encryption of a message $m$ is $c=m^e \bmod{n}$ and the decryption is $m=c^d \bmod{n}$. Which assertion is \emph{always true}? | 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 \lambd... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the non-associative operation. | Note that this operation is in general not associative. The main difficulty is how to choose the map r e d {\displaystyle red} . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the non-associative operation. | A partial operation is associative if x ∗ ( y ∗ z ) = ( x ∗ y ) ∗ z {\displaystyle x*(y*z)=(x*y)*z} for every x, y, z in X for which one of the members of the equality is defined; the equality means that the other member of the equality must also be defined. Examples of non-total associative operations are multiplicati... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
MD5 is | MD5 is a hash function producing a 128-bit hash value. Apache Avro uses a 128-bit random number as synchronization marker for efficient splitting of data files. == References == | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
MD5 is | The MD5 message-digest algorithm is a widely used hash function producing a 128-bit hash value. MD5 was designed by Ronald Rivest in 1991 to replace an earlier hash function MD4, and was specified in 1992 as RFC 1321. MD5 can be used as a checksum to verify data integrity against unintentional corruption. Historically ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $N=3\cdot5\cdot13$. Then a quadratic residue in $\mathbb{Z}_N^*$ has | Take p = 97 {\displaystyle p=97} . A possible quadratic non-residue for 97 is 13, since 13 97 − 1 2 ≡ − 1 ( mod 97 ) {\displaystyle 13^{\frac {97-1}{2}}\equiv -1{\pmod {97}}} . so we let x = 13 97 − 1 4 = 22 ( mod 97 ) {\displaystyle x=13^{\frac {97-1}{4}}=22{\pmod {97}}} . The Euclidean algorithm applied to 97 and 22 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $N=3\cdot5\cdot13$. Then a quadratic residue in $\mathbb{Z}_N^*$ has | The first thing to notice when working within the ring Z of integers is that if the prime number q is ≡ 3 (mod 4) then a residue r is a quadratic residue (mod q) if and only if it is a biquadratic residue (mod q). Indeed, the first supplement of quadratic reciprocity states that −1 is a quadratic nonresidue (mod q), so... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{incorrect} assertion regarding WEP and WPA2. | A tool to automatize WEP cracking and logging of WPA handshakes. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{incorrect} assertion regarding WEP and WPA2. | WEP WPA (TKIP in hardware) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Plain RSA (with an $\ell$-bit modulus) \dots | The proof of the correctness of RSA is based on Fermat's little theorem, stating that ap − 1 ≡ 1 (mod p) for any integer a and prime p, not dividing a.We want to show that for every integer m when p and q are distinct prime numbers and e and d are positive integers satisfying ed ≡ 1 (mod λ(pq)). Since λ(pq) = lcm(p − 1... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Plain RSA (with an $\ell$-bit modulus) \dots | In this example, an RSA modulus purporting to be of the form n = pq is actually of the form n = pqr, for primes p, q, and r. Calculation shows that exactly one extra bit can be hidden in the digitally signed message. The cure for this was found by cryptologists at the Centrum Wiskunde & Informatica in Amsterdam, who de... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Pick 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 |
Pick the \emph{correct} statement. | . . VERIFY-SELECTION . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following elements belong to $\mathbf{Z}_{35}^*$? | ( z − α 4 ) ! ( β 1 − z ) ! ( β 2 − z ) ! | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of the following elements belong to $\mathbf{Z}_{35}^*$? | The elements of Z {\displaystyle \mathbb {Z} } ×15 are the congruence classes {1, 2, 4, 7, 8, 11, 13, 14}; there are φ(15) = 8 of them. x x, x2, x3, ... (mod 15) 1: 1 2: 2, 4, 8, 1 4: 4, 1 7: 7, 4, 13, 1 8: 8, 4, 2, 1 11: 11, 1 13: 13, 4, 7, 1 14: 14, 1 Since there is no number whose order is 8, there are no primitive ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
When using the plain ElGamal cryptosystem over the group $\mathbb{Z}_p^*$ with a fixed $\ell$-bit prime $p$ and a fixed generator $g\in\mathbb{Z}_p^*$, the \textit{tightest} complexity of generating a new key-pair is\ldots | Regev proposed a public-key cryptosystem based on the hardness of the LWE problem. The cryptosystem as well as the proof of security and correctness are completely classical. The system is characterized by m , q {\displaystyle m,q} and a probability distribution χ {\displaystyle \chi } on T {\displaystyle \mathbb {T} }... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
When using the plain ElGamal cryptosystem over the group $\mathbb{Z}_p^*$ with a fixed $\ell$-bit prime $p$ and a fixed generator $g\in\mathbb{Z}_p^*$, the \textit{tightest} complexity of generating a new key-pair is\ldots | Shahram Khazaei, Simon Fischer, and Willi Meier give a cryptanalysis of the ASG allowing various tradeoffs between time complexity and the amount of output needed to mount the attack, e.g. with asymptotic complexity O ( L 2 .2 2 L / 3 ) {\displaystyle O(L^{2}.2^{2L/3})} and O ( 2 2 L / 3 ) {\displaystyle O(2^{2L/3})} b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
We represent $GF(2^8)$ as $\mathbb{Z}_2[X]/P(X)$ where $P(X) = X^8 + X^4+X^3+X+1$. Then, $(X^7+X^6)\times (X + 1)=$\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)} , wit... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
We represent $GF(2^8)$ as $\mathbb{Z}_2[X]/P(X)$ where $P(X) = X^8 + X^4+X^3+X+1$. Then, $(X^7+X^6)\times (X + 1)=$\dots | Such a g − a {\textstyle g-a} has a nontrivial factor in common with f ( x ) {\textstyle f(x)} , which can be computed via the gcd. As p {\textstyle p} is small, we can cycle through all possible a {\textstyle a} . For the case of large primes, which are necessarily odd, one can exploit the fact that a random nonzero e... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textit{wrong} 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{wrong} assertion. | (/ indicates line break; some word breaks are uncertain) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement: hash functions can be used to construct | Select y ~ ∈ { 1 , . . . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Select the \emph{incorrect} statement: hash functions can be used to construct | Selected schemes for the purpose of hashing: SWIFFT. Lattice Based Hash Function (LASH). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{false} assertion about Diffie and Hellman. | Diffie–Hellman (RFC 3526) ECDH (RFC 4753) | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{false} assertion about Diffie and Hellman. | "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 |
A hash function $h$ is collision-resistant if\dots | h {\displaystyle h}: a collision resistant hash function with |q|-bit digests. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A hash function $h$ is collision-resistant if\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 |
Tick the \textbf{false} statement. Bluetooth 2.0 Pairing is secure when ... | Current mobile software generally must allow a connection using a temporary state initiated by the user in order to be 'paired' with another device to copy content. There seem to have been, in the past, available reports of phones being Bluesnarfed without pairing being explicitly allowed. After the disclosure of this ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement. Bluetooth 2.0 Pairing is secure when ... | Pairing mechanisms changed significantly with the introduction of Secure Simple Pairing in Bluetooth v2.1. The following summarizes the pairing mechanisms: Legacy pairing: This is the only method available in Bluetooth v2.0 and before. Each device must enter a PIN code; pairing is only successful if both devices enter ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bluetooth pairing v2.0 is based on\dots | updated Bluetooth stack that opens up even more tethered connectivity options | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bluetooth pairing v2.0 is based on\dots | Pairing mechanisms changed significantly with the introduction of Secure Simple Pairing in Bluetooth v2.1. The following summarizes the pairing mechanisms: Legacy pairing: This is the only method available in Bluetooth v2.0 and before. Each device must enter a PIN code; pairing is only successful if both devices enter ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Kerckhoffs principle says that | 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 knowle... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Kerckhoffs principle says that | 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 appli... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A MAC forgery is\dots | The problem is that the MAC is only authenticating a string of bytes, while Alice and Bob need to authenticate the way the message was constructed as well. If not, then it may be possible for an attacker to substitute a message with a valid MAC but a different meaning. Systems can manage this problem by adding metadata... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A MAC forgery is\dots | If the check fails, a short poem is displayed, reading "Your karma check for today: There once was a user that whined, his existing OS was so blind, he'd do better to pirate an OS that ran great, but found his hardware declined. Please don't steal Mac OS! Really, that's way uncool. | 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 encryption in GSM is done by ... | 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-tim... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The encryption in GSM is done by ... | There are flaws in the implementation of the GSM encryption algorithm that allow passive interception. The equipment needed is available to government agencies or can be built from freely available parts.In December 2011, German researcher Karsten Nohl revealed that it was possible to hack into mobile phone voice and t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement. GSM anonymity is broken by ... | The GSM industry has identified a number of potential fraud attacks on mobile operators that can be delivered via abuse of SMS messaging services. The most serious threat is SMS Spoofing, which occurs when a fraudster manipulates address information in order to impersonate a user that has roamed onto a foreign network ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \textbf{false} statement. GSM anonymity is broken by ... | See id. at 1257. Claim 20 is directed to a problem unique to text-message telecommunication between a mobile device and a computer. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{true} assertion related to the ElGamal signature scheme. | 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 \emph{true} assertion related to the ElGamal signature scheme. | One can verify that a signature ( r , s ) {\displaystyle (r,s)} is a valid signature for a message m {\displaystyle m} as follows: Verify that 0 < r < p {\displaystyle 0 | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Kerckhoff's principle is not followed when security requires that \dots | First, a 19th century rule known as Kerckhoffs's principle, later formulated as Shannon's maxim, teaches that "the enemy knows the system" and the secrecy of a cryptosystem algorithm does not provide any advantage. Second, secret methods are not open to public peer review and cryptanalysis, so potential mistakes and in... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
The Kerckhoff's principle is not followed when security requires that \dots | 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 appli... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{correct} assertion about $\mathbf{Z}_{pq}^*$, where $p$ and $q$ are distinct prime numbers \ldots | Let π ( x ) {\displaystyle \pi (x)} , the prime-counting function, denote the number of primes less than or equal to x {\displaystyle x} . If q {\displaystyle q} is a positive integer and a {\displaystyle a} is coprime to q {\displaystyle q} , we let π ( x ; q , a ) {\displaystyle \pi (x;q,a)} denote the number of prim... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Tick the \emph{correct} assertion about $\mathbf{Z}_{pq}^*$, where $p$ and $q$ are distinct prime numbers \ldots | 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 fo... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What is the inverse of 28 in $\mathbf{Z}_{77}$? | With increasing dimension, expressions for the inverse of A get complicated. For n = 4, the Cayley–Hamilton method leads to an expression that is still tractable: A − 1 = 1 det ( A ) ( 1 6 I − 1 2 A + A 2 tr A − A 3 ) . {\displaystyle \mathbf {A} ^{-1}={\frac {1}{\det(\mathbf {A} )}}\left({\frac {1}{6}}\left\mathbf... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What is the inverse of 28 in $\mathbf{Z}_{77}$? | Then for the inverse g ( z ) {\displaystyle g(z)} (satisfying f ( g ( z ) ) ≡ z {\displaystyle f(g(z))\equiv z} ), we have g ( z ) = ∑ n = 1 ∞ z n n ! = ∑ n = 1 ∞ 1 n z n , {\displaystyle {\begin{aligned}g(z)&=\sum _{n=1}^{\infty }\left{\frac {z^{n}}{n! | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What is the time complexity to perfom a left-to-right multiplication of two $\ell$-bit integers? | A fundamental question of longstanding theoretical interest is to prove lower bounds on the complexity and exact operation counts of fast Fourier transforms, and many open problems remain. It is not rigorously proved whether DFTs truly require Ω ( N log N ) {\textstyle \Omega (N\log N)} (i.e., order N log N {\displ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What is the time complexity to perfom a left-to-right multiplication of two $\ell$-bit integers? | There is a trivial lower bound of Ω(n) for multiplying two n-bit numbers on a single processor; no matching algorithm (on conventional machines, that is on Turing equivalent machines) nor any sharper lower bound is known. Multiplication lies outside of AC0 for any prime p, meaning there is no family of constant-depth, ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $X$ and $K$ be two independent random variables in a group $G$ with $n$ elements and where $K$ is uniformly distributed over $G$. Let $Y = X+K$. Then, for any $y\in G$, $\Pr[Y=y]=$\dots | Consider a group G {\displaystyle G} and subgroups G 1 , G 2 , … , G n {\displaystyle G_{1},G_{2},\dots ,G_{n}} of G {\displaystyle G} . Let G I {\displaystyle G_{I}} denote ⋂ i ∈ I G i {\displaystyle \bigcap _{i\in I}G_{i}} for I ⊆ { 1 , … , n } {\displaystyle I\subseteq \{1,\dots ,n\}} ; this is also a subgroup of G ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let $X$ and $K$ be two independent random variables in a group $G$ with $n$ elements and where $K$ is uniformly distributed over $G$. Let $Y = X+K$. Then, for any $y\in G$, $\Pr[Y=y]=$\dots | If the X1, X2, ..., XN are independent, but not identically distributed random variables, where G X i {\displaystyle G_{X_{i}}} denotes the probability generating function of X i {\displaystyle X_{i}} , then G S N ( z ) = ∑ i ≥ 1 f i ∏ k = 1 i G X i ( z ) . {\displaystyle G_{S_{N}}(z)=\sum _{i\geq 1}f_{i}\prod _{k=1}^{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of these primitives can be surely considered insecure today? | 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 secur... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Which of these primitives can be surely considered insecure today? | A computer programmer rarely invents a new programming language while writing a new program; instead, they will use one of the already established programming languages to program in. Cryptographic primitives are one of the building blocks of every crypto system, e.g., TLS, SSL, SSH, etc. Crypto system designers, not b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
If an adversary mounts a chosen plaintext attack, it means he can\dots | Attacks that lead to disclosure of the key or plaintext. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
If an adversary mounts a chosen plaintext attack, it means he can\dots | In a chosen-plaintext attack the adversary can (possibly adaptively) ask for the ciphertexts of arbitrary plaintext messages. This is formalized by allowing the adversary to interact with an encryption oracle, viewed as a black box. The attacker’s goal is to reveal all or a part of the secret encryption key. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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