id
int64 0
134
| question
stringlengths 40
1.55k
| choice
listlengths 4
7
| answer
listlengths 1
3
| label
stringclasses 5
values |
|---|---|---|---|---|
100
|
A cryptographic system needs to compute polynomial operations over a quotient ring $\mathbb{Z}_{17}[x]/\phi(x)$. Without regard to security, which is the best choice of $\phi(x)$ for efficiency?
|
[
"$\\phi(x) = x^8+1$",
"$\\phi(x) = x^8+2$",
"$\\phi(x) = x^8+3$",
"$\\phi(x) = x^8+4$"
] |
[
0
] |
math
|
101
|
Let $n = pq$ be an RSA modulus, where $p$ and $q$ are large primes. Let $e$ and $d$ be the public and private exponents such that $ed \equiv 1 \pmod{k}$. Originally, $k = \phi(n)$. Which alternative choice of $k$ still guarantees correct decryption while potentially allowing for a smaller $d$?
|
[
"$\\mathrm{lcm}(p - 1, q - 1)$",
"$\\gcd(p - 1, q - 1)$",
"$\\mathrm{lcm}(p + 1, q + 1)$",
"$\\gcd(p + 1, q + 1)$",
"None of the above"
] |
[
0
] |
asymmetric
|
102
|
Which of the following statements about the Key Encryption Key (KEK) is \textbf{FALSE}?
|
[
"KDC (Key Distribution Center) shares a unique KEK with each user individually.",
"KDC sends session keys encrypted under KEKs to the users.",
"If KEKs are compromised, an attacker still cannot decrypt previously transmitted messages.",
"Adding a new user only affects the KEK related to that user without impacting others.",
"None of the above"
] |
[
2
] |
misc
|
103
|
For arbitrary inputs $A$ and $B$, which relation does the diffusion operation $D$ in the AES diffusion layer always satisfy?
|
[
"$D(A \\oplus B) \\neq A \\oplus B$",
"$D(A \\oplus B) = A \\oplus B$",
"$D(A \\oplus B) = D(A) \\oplus D(B)$",
"$D(A \\oplus B) \\neq D(A) \\oplus D(B)$",
"None of the above"
] |
[
2
] |
symmetric
|
104
|
Which attack reduces the effective key length of 3-key Triple DES from 168 bits to approximately 112 bits?
|
[
"Meet-in-the-Middle attack",
"Man-in-the-Middle attack",
"Differential attack",
"Linear attack",
"None of the above"
] |
[
0
] |
symmetric
|
105
|
Given an elliptic curve over a prime field $\mathbb{F}_p$, let the number of points on the curve be denoted as $\#E$. Suppose the binary expansions of $p$ and $|p - \#E|$ have $m$ and $n$ bits respectively. Which is the best approximation of the relation between $m$ and $n$?
|
[
"$m = 4n$",
"$m = 2n$",
"$2m = n$",
"$4m = n$",
"None of the above"
] |
[
1
] |
asymmetric
|
106
|
For an RSA implementation, suppose signing using the Chinese Remainder Theorem (CRT) takes time $s$, while signing without CRT takes time $t$. What best approximates the relation between $s$ and $t$? (Consider the complexity of modular multiplication over $\mathbb{Z}_p$ is $\log(p)^2$.)
|
[
"$s = 4t$",
"$s = 2t$",
"$2s = t$",
"$4s = t$",
"None of the above"
] |
[
3
] |
asymmetric
|
107
|
Which of the following systems of congruences does \textbf{NOT} have a solution?
|
[
"$x \\equiv 1 \\pmod{7}, \\quad x \\equiv 3 \\pmod{9}, \\quad x \\equiv 5 \\pmod{11}$",
"$x \\equiv 1 \\pmod{8}, \\quad x \\equiv 3 \\pmod{9}, \\quad x \\equiv 5 \\pmod{11}$",
"$x \\equiv 1 \\pmod{7}, \\quad x \\equiv 3 \\pmod{9}, \\quad x \\equiv 5 \\pmod{12}$",
"$x \\equiv 1 \\pmod{7}, \\quad x \\equiv 3 \\pmod{10}, \\quad x \\equiv 5 \\pmod{12}$",
"None of the above"
] |
[
2
] |
math
|
108
|
Which of the following statements about the Man-in-the-Middle (MITM) attack is \textbf{FALSE}?
|
[
"An attacker can replace the public key of one party with their own key.",
"MITM attacks are applicable to Diffie-Hellman Key Exchange (DHKE) but not to RSA encryption.",
"MITM attacks are possible only if the public keys are not authenticated.",
"Public Key Infrastructure (PKI) is a solution to prevent MITM attacks.",
"None of the above"
] |
[
1
] |
misc
|
109
|
How many generators exist in the cyclic multiplicative group \( \mathbb{Z}_{243}^* \)?
|
[
"81",
"110",
"121",
"162",
"None of the above"
] |
[
1
] |
misc
|
110
|
Alice and Bob are in a country with 50 states. Alice is in state $a \in \{1, \ldots, 50\}$ and Bob is in state $b \in \{1, \ldots, 50\}$. Alice wants to determine if she is in the same state as Bob (i.e., if $a=b$) without revealing her state $a$ to Bob if $a \neq b$. Bob should not learn Alice's state $a$ regardless. They agree on the following cryptographic protocol\begin{enumerate}
\item They fix a public cyclic group $G$ of prime order $p$ with a generator $g \in G$.
\item Alice chooses random exponents $x, y \in \mathbb{Z}_p$. She computes and sends to Bob the triplet$$ (A_0, A_1, A_2) = (g^x, g^y, g^{xy+a}) $$
(Note: $(A_1, A_2)$ can be seen as an ElGamal encryption of $g^a$ under the ephemeral public key $A_0=g^x$, using $y$ as the ephemeral private key, since $A_2 = g^a \cdot (g^x)^y$.)
\item Bob chooses random exponents $r, s \in \mathbb{Z}_p$. He computes and sends back to Alice the pair$$ (B_1, B_2) = (A_1^r \cdot g^s, (A_2 \cdot g^{-b})^r \cdot A_0^s) $$
\end{enumerate}
After receiving $(B_1, B_2)$ from Bob, what check should Alice perform to test if $a=b$?
|
[
"Alice tests if $B_1^x \\cdot B_2 = 1$.",
"Alice tests if $B_2 \\cdot B_1^x = 1$.",
"Alice tests if $B_1 / B_2^x = 1$.",
"Alice tests if $B_2 / B_1^x = 1$.",
"None of the above"
] |
[
3
] |
asymmetric
|
111
|
Which of the following represents the encryption process of the standard 3DES (Triple-DES) scheme with a 112-bit key?
|
[
"$\\mathrm{DES}_{k_3}(\\mathrm{DES}_{k_2}(\\mathrm{DES}_{k_1}(\\cdot)))$, where $k_1 = k_3$",
"$\\mathrm{DES}_{k_3}\\bigl(\\mathrm{DES}_{k_2}^{-1}(\\mathrm{DES}_{k_1}(\\cdot))\\bigr)$, where $k_1 = k_3$",
"$\\mathrm{DES}_{k_3}\\bigl(\\mathrm{DES}_{k_2}^{-1}(\\mathrm{DES}_{k_1}(\\cdot))\\bigr)$, where $k_1 = k_2$",
"$\\mathrm{DES}_{k_3}(\\mathrm{DES}_{k_2}(\\mathrm{DES}_{k_1}(\\cdot)))$, where $k_1 = k_2$",
"None of the above"
] |
[
1
] |
symmetric
|
112
|
Let $M = C = K = \{0, 1, 2, \ldots, 255\}$ and consider the following cipher defined over $(K, M, C)$: $E(k, m) = m + k \pmod{256}$ and $D(k, c) = c - k \pmod{256}$. Does this cipher have perfect secrecy (meaning that the ciphertext conveys no information about the content of the plaintext)?
|
[
"No, only the One Time Pad has perfect secrecy.",
"Yes",
"No, there is a simple attack on this cipher.",
"None of the above"
] |
[
1
] |
misc
|
113
|
Let $N=pq$ be an RSA modulus (where $p$ and $q$ are large distinct primes) and let $e$ be an integer such that $\gcd(e, \phi(N))=1$. Consider a hash function $h$ that processes a message $M$ by first parsing it into two blocks, $M = m_1 \| m_2$. These blocks, $m_1$ and $m_2$, are interpreted as integers. The hash function is then defined as$$h(M) = (m_1 \cdot m_2)^e \pmod N$$
Is this hash function $h$ collision-resistant?
|
[
"Yes, it is collision resistant.",
"No, it is not collision resistant.",
"Collision resistance cannot be determined from the information given.",
"None of the above"
] |
[
1
] |
asymmetric
|
114
|
Given the ciphertext C = eiioqoyldc and the key K = security, what is the original plaintext if the Playfair cipher was used? Assume 'x' is the special character used for padding identical adjacent letters and to complete a final digraph if necessary. Treat 'i' and 'j' as the same character.
|
[
"stalxlings",
"stallings",
"secrettext",
"stollings",
"None of the above"
] |
[
0
] |
classic
|
115
|
Alice encrypts a message using a stream cipher. If she accidentally reuses the same keystream to encrypt a second, different message, what is the MOST likely consequence for an attacker who intercepts both ciphertexts?
|
[
"The attacker can immediately decrypt both messages.",
"The attacker can obtain the XOR of the two original plaintexts, potentially revealing information about both.",
"The security of only the first message is compromised.",
"The stream cipher automatically detects the reuse and becomes secure again for subsequent communications."
] |
[
1
] |
symmetric
|
116
|
For a $n\times n$ Hill cipher over the English alphabet, which is the correct size of its key space?
|
[
"$\\prod_{i=0}^{n-1}\\left((2^n-2^i)\\cdot(13^n-13^i)\\right)$",
"$\\prod_{i=0}^{n-1}(2^n-2^i) \\cdot \\prod_{i=0}^{n-1}(13^{n-1}-13^i)$",
"$\\prod_{i=0}^{n-1}(26^n-26^i)$",
"$\\prod_{i=0}^{n-1}26^i$",
"None of the above"
] |
[
0
] |
classic
|
117
|
For a LWE instance $(A, b)$, where $A \leftarrow \mathcal{U}(\mathbb{Z}_q^{m\times n})$ and $b \equiv As + e \mod q$, which of the following is the most vulnerable parameter setting for algebraic attack (find the correct $s$ from $(A, b)$ through solving equations)? Let $\mathcal{U}(\mathcal{S})$ be the uniform distribution over the set $\mathcal{S}$, and $\mathcal{D}_{\sigma}$ be the discrete Gaussian distribution centered at $0$ with the standard deviation $\sigma$.
|
[
"$s \\leftarrow \\mathcal{D}_{0.5}, e \\leftarrow \\mathcal{U}(\\{0, 1\\}^{n})$",
"$s \\leftarrow \\mathcal{U}(\\{0, 1\\}^{n}), e \\leftarrow \\mathcal{U}(\\{0, 1\\}^{n})$",
"$s \\leftarrow \\mathcal{U}(\\{0, 1\\}^{n}), e \\leftarrow \\mathcal{D}_{0.5}$",
"$s \\leftarrow \\mathcal{D}_{0.5}, e \\leftarrow \\mathcal{D}_{0.5}$",
"None of the above"
] |
[
1
] |
asymmetric
|
118
|
The high strength of a synchronous stream cipher mainly depends on which of the following?
|
[
"The design of the keystream generator",
"The key length",
"The plaintext length",
"The complexity of the key",
"None of the above"
] |
[
0,
1
] |
symmetric
|
119
|
Which of the following cryptosystems are vulnerable to quantum attacks up to date?
|
[
"RSA",
"Rabin",
"AES-256",
"NTRU"
] |
[
0,
1
] |
misc
|
120
|
For a $\lambda$-secure (the time complexity under classic mode is exponential to $\lambda$) RSA instance $(N, p, q, e,d)$, where $gcd(e, \phi(N)) = 1, \, ed\equiv 1 \mod \phi(N)$. Which of the following cases are vulnerable RSA instances?
|
[
"small $d$ such that $N^{1/8} < d < N^{1/4}$",
"approximate $p, q$ such that $|p-q| < poly(\\lambda)$",
"small $e$ such that $N^{1/8} < e < N^{1/4}$",
"the leakage of a past key $(e', d')$ such that $e'\\neq e, e'd'\\equiv 1 \\mod \\phi(N)$"
] |
[
0,
1,
3
] |
asymmetric
|
121
|
Which encryption schemes utilize different keys for encryption and decryption?
|
[
"Shift cipher",
"RSA",
"Advanced Encryption Standard",
"Data Encryption Standard",
"ElGamal scheme",
"Secure Hash Algorithm"
] |
[
1,
4
] |
misc
|
122
|
Factor the polynomial $x^4 + 1$ in GF(2)
|
[
"Cannot be factored in GF(2)",
"Factors as $(x^2 + 1)^2$",
"Factors as $(x + 1)^4$",
"Already in simplest form"
] |
[
1,
2
] |
math
|
123
|
Which statements about block cipher modes are correct?
|
[
"CBC XORs plaintext with previous ciphertext",
"CTR doesn't need IV",
"CBC's last block uses IV",
"CBC hides plaintext patterns"
] |
[
0,
3
] |
symmetric
|
124
|
What is true about public key message encryption?
|
[
"Encrypt with recipient's public key",
"Encrypt with sender's public key",
"Decrypt with sender's public key",
"Decrypt with recipient's private key"
] |
[
0,
3
] |
asymmetric
|
125
|
Which of the following are essential characteristics of a secure cryptographic hash function?
|
[
"Support for revoking keys",
"Resistance to hash collisions",
"Deterministic behavior for any given input",
"Unique one-to-one mapping between inputs and outputs",
"Computational difficulty in finding a preimage for a given hash"
] |
[
1,
2,
4
] |
symmetric
|
126
|
SuperMail wants to ensure that all outgoing emails are authenticated and tamper-proof. Alice wishes to send a message \( M \) to Bob. Let \( K_B \) be Bob's public key and \( K_A^{-1} \) be Alice's private signing key. Based on SuperMail's security goals, which methods are appropriate for ensuring authenticity and integrity?
|
[
"Encrypt \\( M \\) using Bob's public key: \\( E_{K_B}(M) \\)",
"Transmit \\( M \\) along with a digital signature generated with Alice's private key: \\( M, \\text{Sign}_{K_A^{-1}}(M) \\)",
"Generate a symmetric key \\( k \\), send \\( E_{K_B}(k) \\), and send \\( M \\oplus \\text{RC4}(k) \\)",
"Generate a symmetric key \\( k \\), send \\( E_{K_B}(k) \\), and \\( \\text{AES-CBC-Encrypt}_k(M) \\)\n",
"Generate a symmetric key \\( k \\); send \\( M, \\text{MAC}_k(M), E_{K_B}(k), \\text{Sign}_{K_A^{-1}}(E_{K_B}(M) || E_{K_B}(k)) \\)"
] |
[
1,
4
] |
misc
|
127
|
Alice needs to securely send a private email \( M \) to Bob. Let \( K_B \) be Bob's public key and \( K_A^{-1} \) be Alice's private signing key. Which methods protect confidentiality while ensuring authenticity?
|
[
"Send \\( E_{K_B}(M), \\text{Sign}_{K_A^{-1}}(K_B) \\)",
"Send \\( E_{K_B}(M), \\text{Sign}_{K_A^{-1}}(M) \\)",
"Send \\( E_{K_B}(M), \\text{Sign}_{K_A^{-1}}(E_{K_B}(M)) \\)",
"Generate a symmetric key \\( k \\); send \\( E_{K_B}(k), \\text{Sign}_{K_A^{-1}}(E_{K_B}(k)) \\), and then encrypt \\( M \\) with \\( k \\)\n",
"Generate two keys \\( k_1, k_2 \\); send \\( E_{K_B}(k_1||k_2), \\text{Sign}_{K_A^{-1}}(E_{K_B}(k_1||k_2)) \\), $E_{k_1}(M || \\text{MAC}_{k_2}(M))$"
] |
[
2,
4
] |
misc
|
128
|
In the RSA encryption scheme, after selecting two large numbers $p$ and $q$, which of the following must be true about their properties?
|
[
"$p$ and $q$ must be prime numbers",
"$p$/$q$ must yield an integer quotient",
"$p$ and $q$ should divide $\\phi(n)$",
"$p$ and $q$ must be co-prime"
] |
[
0,
3
] |
asymmetric
|
129
|
Differential cryptanalysis is a method of analyzing which type of cipher algorithm?
|
[
"DES",
"AES",
"RSA",
"Rabin"
] |
[
0,
1
] |
symmetric
|
130
|
Let $(E, D)$ be a (one-time) semantically secure cipher where the message and ciphertext space is $\{0,1\}^n$. Which of the following encryption schemes are (one-time) semantically secure? (Select all that apply)
|
[
"Scheme 1: $E'(k, m) = E(0^n, m)$",
"Scheme 2: $E'((k,k'), m) = E(k,m) \\| E(k', m)$, where $k \\neq k'$",
"Scheme 3: $E'(k,m) = E(k,m) \\| \\text{LSB}(m)$",
"Scheme 4: $E'(k,m) = 0 \\| E(k,m)$",
"Scheme 5: $E'(k,m) = E(k,m) \\| k$",
"Scheme 6: $E'(k,m) = \\text{reverse}(E(k,m))$"
] |
[
1,
3,
5
] |
misc
|
131
|
Let $F: \{0,1\}^n \times \{0,1\}^n \to \{0,1\}^n$ be a secure PRF (i.e., a PRF where the key space, input space, and output space are all $\{0,1\}^n$) and say $n = 128$. Which of the following constructions are secure PRFs? (Select all that apply)
|
[
"$F'(k, x) = \\begin{cases} F(k,x) & \\text{when } x \\neq 0^n \\\\ 0^n & \\text{otherwise} \\end{cases}$",
"$F'(k,x) = F(k,x)[0,\\ldots,n-2]$ (i.e., $F'(k,x)$ drops the last bit of $F(k,x)$)",
"$F'((k_1,k_2), x) = F(k_1,x) \\| F(k_2,x)$ (here $\\|$ denotes concatenation, and $k\\neq k'$)",
"$F'(k, x) = k \\oplus x$",
"$F'(k,x) = F(k, x) \\oplus F(k, x \\oplus 1^n)$",
"$F'(k,x) = F(k, x \\oplus 1^n)$"
] |
[
1,
2,
5
] |
symmetric
|
132
|
Let $(S, V)$ be a secure MAC defined over $(K, M, T)$ where $K =\{0, 1\}^{128}, M = \{0,1\}^n$, and $T = \{0,1\}^{128}$. Which of the following constructions are secure MACs? (Select all that apply. $k\in K, m\in M, \, t \in T$)
|
[
"$S'(k,m) = S(k, m \\oplus m)$ and $V'(k,m,t) = V(k, m \\oplus m, t)$",
"$S'(k,m) = S(k,m)$ and $V'(k,m,t) = [V(k, m, t) \\text{ or } V(k, m \\oplus 1^n, t)]$",
"$S'(k,m) = S(k, m[0,\\ldots,n-2] \\| 0)$ and $V'(k,m,t) = V(k, m[0,\\ldots,n-2] \\| 0, t)$",
"\\begin{minipage}[t]{\\linewidth}\n$S'((k_1,k_2), m) = (S(k_1,m), S(k_2,m))$ and \\\\\n$V'((k_1,k_2),m,(t_1,t_2)) = [V(k_1,m,t_1) \\text{ and } V(k_2,m,t_2)]$\n\\end{minipage}",
"$S'(k,m) = S(k, m \\| m)$ and $V'(k,m,t) = V(k, m \\| m, t)$",
"$S'(k,m) = S(k, m \\oplus 1^n)$ and $V'(k,m,t) = V(k, m \\oplus 1^n, t)$"
] |
[
3,
5
] |
misc
|
133
|
Let $H: \{0, 1\}^* \rightarrow \{0, 1\}^l$ be a collision resistant hash function, where $l > 32$. Which of the following constructions are collision resistant?
|
[
"$H'(m) = H(|m|)$ (i.e., hash the length of $m$)",
"$H'(m) = H(0)$",
"$H'(m) = H(m) \\| H(0)$",
"$H'(m) = H(m)[0,\\ldots,31]$ (i.e., output the first 32 bits of the hash)",
"$H'(m) = H(H(m))$",
"$H'(m) = H(m \\| m)$",
"$H'(m) = H(m) \\oplus H(m \\oplus 1^{|m|})$ (where $m \\oplus 1^{|m|}$ is the complement of $m$)"
] |
[
2,
4,
5
] |
symmetric
|
134
|
Let $(E,D)$ be an encryption system with key space $K$, message space $\{0,1\}^n$ and ciphertext space $\{0,1\}^s$. Suppose $(E, D)$ provides authenticated encryption. Which of the following systems provides authenticated encryption?
|
[
"$E'(k,m) = (E(k,m), H(m))$ and $D'(k,(c,h)) = \\begin{cases} D(k,c) & \\text{if } H(D(k,c)) = h \\\\ \\perp & \\text{otherwise} \\end{cases}$ \\\\\n(here $H$ is some collision-resistant hash function.)",
"\\begin{minipage}[t]{\\linewidth}\n$E'((k_1,k_2),m) = E(k_2, E(k_1,m))$ and \\\\\n$D'((k_1,k_2), c) = \\begin{cases} D(k_1,D(k_2,c)) & \\text{if } D(k_2,c) \\neq \\perp \\\\ \\perp & \\text{otherwise} \\end{cases}$\n\\end{minipage}",
"$E'(k,m) = (E(k,m), 0)$ and $D'(k,(c,b)) = D(k,c)$",
"$E'(k,m) = E(k, m \\oplus 1^n)$ and $D'(k,c) = \\begin{cases} D(k,c) \\oplus 1^n & \\text{if } D(k,c) \\neq \\perp \\\\ \\perp & \\text{otherwise} \\end{cases}$"
] |
[
1,
3
] |
misc
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.