| [ |
| { |
| "id": 0, |
| "question": "The following ciphertext was encoded via Caesar cipher with a fixed shift of three letters. Determine the original plaintext: HQFUBSWHG ZRUG.", |
| "choice": [ |
| "ABANDONED WORD", |
| "ENCRYPTED TEXT", |
| "ABANDONED TEXT", |
| "ENCRYPTED WORD", |
| "None of the above" |
| ], |
| "answer": [ |
| 3 |
| ], |
| "label": "classic" |
| }, |
| { |
| "id": 1, |
| "question": "On Encrypting \"thepepsiisintherefrigerator\" using Vigen\u00e8re Cipher System using the keyword \"HUMOR\" we get cipher text.", |
| "choice": [ |
| "abqqfduugzulqtipaqfraidokvl", |
| "abqdvwmugzulqtipaqfraidokvl", |
| "abqqfsuugzukqtipaqfraidokvl", |
| "abqdvsuugzulqtigaqfraidokvl", |
| "abqdvwmuwjphfvvyyrfznydokvl" |
| ], |
| "answer": [ |
| 4 |
| ], |
| "label": "classic" |
| }, |
| { |
| "id": 2, |
| "question": "In the Triple DES encryption scheme, the total key length is ( ) and the ``meet-in-the-middle'' attack requires ( ) computational tests to breach the cipher.", |
| "choice": [ |
| "${168}$, $2^{111}$", |
| "${192}$, $2^{112}$", |
| "${184}$, $2^{111}$", |
| "${168}$, $2^{112}$", |
| "None of the above" |
| ], |
| "answer": [ |
| 3 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 3, |
| "question": "Which of the following is a valid property for congruence?", |
| "choice": [ |
| "$a \\equiv b \\ (\\mathrm{mod}\\ n)$ if $n\\mid(a-b)$", |
| "$a \\equiv b \\ (\\mathrm{mod}\\ n)$ implies $b \\equiv a \\ (\\mathrm{mod}\\ n)$", |
| "$a \\equiv b \\ (\\mathrm{mod}\\ n)$ and $b \\equiv c \\ (\\mathrm{mod}\\ n)$ implies $a \\equiv c \\ (\\mathrm{mod}\\ n)$", |
| "All of the mentioned", |
| "None of the above" |
| ], |
| "answer": [ |
| 3 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 4, |
| "question": "Assuming the plaintext is guaranteed to be unique and at most one block long, which DES mode minimizes overhead?", |
| "choice": [ |
| "Cipher Block Chaining (CBC)", |
| "Output Feedback Modes (OFB)", |
| "Electronic Code Book (ECB)", |
| "Cipher Feedback Mode (CFB)", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 5, |
| "question": "Using the Linear Congruential Method (LCM) with parameters $a = 7$, $c = 0$, and $m = 32$ ($X_{n+1} \\equiv (aX_n + c) \\mod m$), determine the period of the generated sequence.", |
| "choice": [ |
| "11", |
| "4", |
| "13", |
| "7", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 6, |
| "question": "In the Linear Congruential Method (LCM), what is the most suitable choice for the modulus $m$ to maximize the period?", |
| "choice": [ |
| "$2^{31} - 1$", |
| "$2^{32}$", |
| "$2^{31}$", |
| "$2^{32} - 1$", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 7, |
| "question": "Find the solution of $x^2 \\equiv 3 \\mod 11$.", |
| "choice": [ |
| "$x \\equiv -9 \\mod 11$ and $x \\equiv 9 \\mod 11$", |
| "$x \\equiv 9 \\mod 11$", |
| "$x \\equiv 5 \\mod 11$ and $x \\equiv 6 \\mod 11$", |
| "No Solution", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 8, |
| "question": "Let $(E, D)$ be a (one-time) semantically secure cipher with key space $K = \\{0,1\\}^\\ell$. A bank wishes to split a decryption key $k \\in \\{0,1\\}^\\ell$ into three pieces $p_1, p_2, p_3$ so that any two of the pieces enable decryption using $k$, but no single piece can decrypt. The bank generates two random pairs $(k_1, k_1')$ and $(k_2, k_2')$ such that $k_1 \\oplus k_1' = k_2 \\oplus k_2' = k$. How should the bank assign pieces so that any two pieces enable decryption using $k$, but no single piece can decrypt?", |
| "choice": [ |
| "$p_1 = (k_1, k_2)$, $p_2 = (k_1', k_2')$, $p_3 = (k_2')$", |
| "$p_1 = (k_1, k_2)$, $p_2 = (k_2, k_2')$, $p_3 = (k_2')$", |
| "$p_1 = (k_1, k_2)$, $p_2 = (k_1', k_2)$, $p_3 = (k_2')$", |
| "$p_1 = (k_1, k_2)$, $p_2 = (k_1')$, $p_3 = (k_2')$", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 9, |
| "question": "Suppose Alice is broadcasting packets to 6 recipients $B_1, \\ldots, B_6$. Privacy is not important, but integrity is. Each recipient should be assured that the packets are from Alice. Alice sets up 4 secret keys $S = \\{k_1, k_2, k_3, k_4\\}$. She gives each user $B_i$ a subset $S_i \\subseteq S$ of the keys. When Alice transmits a packet, she appends 4 tags computed with each of her 4 keys. User $B_i$ accepts a packet as valid only if all tags corresponding to his keys in $S_i$ are valid. \nHow should Alice assign keys to the 6 users so that no single user can forge packets on behalf of Alice and fool some other user?", |
| "choice": [ |
| "$S_1 = \\{k_1, k_2\\}$, $S_2 = \\{k_1, k_3, k_4\\}$, $S_3 = \\{k_1, k_4\\}$, \\\\\n$S_4 = \\{k_2, k_3\\}$, $S_5 = \\{k_2, k_3, k_4\\}$, $S_6 = \\{k_3, k_4\\}$", |
| "$S_1 = \\{k_2, k_4\\}$, $S_2 = \\{k_2, k_3\\}$, $S_3 = \\{k_3, k_4\\}$, \\\\\n$S_4 = \\{k_1, k_3\\}$, $S_5 = \\{k_1, k_2\\}$, $S_6 = \\{k_1, k_4\\}$", |
| "$S_1 = \\{k_1, k_2\\}$, $S_2 = \\{k_1, k_3\\}$, $S_3 = \\{k_1, k_4\\}$, \\\\\n$S_4 = \\{k_2, k_3, k_4\\}$, $S_5 = \\{k_2, k_3\\}$, $S_6 = \\{k_3, k_4\\}$", |
| "$S_1 = \\{k_1, k_2\\}$, $S_2 = \\{k_1\\}$, $S_3 = \\{k_1, k_4\\}$, \\\\\n$S_4 = \\{k_2, k_3\\}$, $S_5 = \\{k_2, k_4\\}$, $S_6 = \\{k_3, k_4\\}$", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 10, |
| "question": "Suppose $H_1$ and $H_2$ are collision resistant hash functions mapping inputs in a set $M$ to $\\{0,1\\}^{256}$. Our goal is to show that the function $H_2(H_1(m))$ is also collision resistant. We prove the contrapositive: suppose $H_2(H_1(\\cdot))$ is not collision resistant, that is, we are given $x \\neq y$ such that $H_2(H_1(x)) = H_2(H_1(y))$. We build a collision for either $H_1$ or for $H_2$. This will prove that if $H_1$ and $H_2$ are collision resistant then so is $H_2(H_1(\\cdot))$. Which of the following must be true", |
| "choice": [ |
| "Either $H_2(x), H_2(y)$ are a collision for $H_1$ or $x, y$ are a collision for $H_2$.", |
| "Either $x, H_1(y)$ are a collision for $H_2$ or $H_2(x), y$ are a collision for $H_1$.", |
| "Either $x, y$ are a collision for $H_1$ or $H_1(x), H_1(y)$ are a collision for $H_2$.", |
| "Either $x, y$ are a collision for $H_2$ or $H_1(x), H_1(y)$ are a collision for $H_1$.", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 11, |
| "question": "Let $(E,D)$ be a secure tweakable block cipher. Define the following MAC $(S,V)$$$S(k,m) := E(k,m,0) \\quad \\text{and} \\quad V(k,m,\\text{tag}) := \\begin{cases} 1 & \\text{if } E(k,m,0) = \\text{tag} \\\\ 0 & \\text{otherwise} \\end{cases}$$ \nIn other words, the message $m$ is used as the tweak, and the plaintext given to $E$ is always set to $0$. Is this MAC secure?", |
| "choice": [ |
| "It depends on the specific tweakable block cipher.", |
| "Yes", |
| "No", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 12, |
| "question": "Consider a key exchange protocol using an online Trusted Third Party (TTP). Suppose Alice, Bob, and Carol are three users of this system, each sharing a secret key with the TTP denoted $k_a, k_b, k_c$ respectively. They wish to generate a group session key $k_{ABC}$ that will be known to Alice, Bob, and Carol, but unknown to an eavesdropper. How would you modify a typical TTP-based protocol to accommodate this group key exchange? (Note: assume all these protocols are insecure against active attacks).", |
| "choice": [ |
| "\\begin{minipage}[t]{\\linewidth}\nAlice contacts the TTP. The TTP generates a random $k_{AB}$ and a random $k_{AC}$. The TTP sends to Alice: \\\\\n$E(k_a, k_{AB})$, $ticket_1 \\leftarrow E(k_b, k_{AB})$, $ticket_2 \\leftarrow E(k_c, k_{AC})$. \\\\\nAlice sends $ticket_1$ to Bob and $ticket_2$ to Carol.\n\\end{minipage}", |
| "\\begin{minipage}[t]{\\linewidth}\nAlice contacts the TTP. The TTP generates a random $k_{ABC}$ and sends to Alice: \\\\\n$E(k_a, k_{ABC})$, $ticket_1 \\leftarrow E(k_b, k_{ABC})$, $ticket_2 \\leftarrow E(k_c, k_{ABC})$. \\\\\nAlice sends $ticket_1$ to Bob and $ticket_2$ to Carol.\n\\end{minipage}", |
| "\\begin{minipage}[t]{\\linewidth}\nBob contacts the TTP. The TTP generates a random $k_{AB}$ and a random $k_{BC}$. The TTP sends to Bob: \\\\\n$E(k_a, k_{AB})$, $ticket_1 \\leftarrow E(k_a, k_{AB})$, $ticket_2 \\leftarrow E(k_c, k_{BC})$. \\\\\nBob sends $ticket_1$ to Alice and $ticket_2$ to Carol.\n\\end{minipage}", |
| "\\begin{minipage}[t]{\\linewidth}\nAlice contacts the TTP. The TTP generates a random $k_{ABC}$ and sends to Alice: \\\\\n$E(k_a, k_{ABC})$, $ticket_1 \\leftarrow k_{ABC}$, $ticket_2 \\leftarrow k_{ABC}$. \\\\\nAlice sends $ticket_1$ to Bob and $ticket_2$ to Carol.\n\\end{minipage}", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 13, |
| "question": "Suppose we modify the Diffie-Hellman protocol. Alice chooses a random $a \\in \\{1, \\ldots, p-1\\}$ and sends $A = g^a \\pmod{p}$ to Bob. Bob, however, chooses a random $b \\in \\{1, \\ldots, p-1\\}$ and sends $B = g^{1/b} \\pmod{p}$ to Alice (where $1/b$ denotes $b^{-1} \\pmod{p-1}$, the modular multiplicative inverse of $b$ modulo $p-1$). What shared secret can they generate, and how would they do it?", |
| "choice": [ |
| "Shared secret is $g^{ab}$. Alice computes $B^{1/a} \\pmod{p}$ and Bob computes $A^b \\pmod{p}$.", |
| "Shared secret is $g^{a/b}$. Alice computes $B^a \\pmod{p}$ and Bob computes $A^{1/b} \\pmod{p}$.", |
| "Shared secret is $g^{b/a}$. Alice computes $B^a \\pmod{p}$ and Bob computes $A^{1/b} \\pmod{p}$.", |
| "Shared secret is $g^{a/b}$. Alice computes $B^{1/a} \\pmod{p}$ and Bob computes $A^b \\pmod{p}$.", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 14, |
| "question": "Consider a toy key exchange protocol using public key encryption. Suppose that when sending his reply $c \\leftarrow E(pk, x)$ to Alice, Bob appends a MAC $t:= S(x, c)$ to the ciphertext, so that what is sent to Alice is the pair $(c,t)$. Alice verifies the tag $t$ and rejects the message from Bob if the tag does not verify. Will this additional step prevent the man-in-the-middle attack described in lectures?", |
| "choice": [ |
| "Yes", |
| "It depends on what public key encryption system is used.", |
| "No", |
| "It depends on what MAC system is used.", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 15, |
| "question": "Suppose $n+1$ parties, denoted $B, A_1, \\ldots, A_n$, wish to establish a shared group key. They require a protocol such that upon completion, all parties possess a common secret key $k$. An eavesdropper observing the entire communication must not be able to determine $k$. The parties agree on the following protocol, which operates in a group $G$ of prime order $q$ with a generator $g$ \\begin{enumerate} \n\\item For $i=1, \\ldots, n$, party $A_i$ chooses a random secret integer $a_i \\in \\{1, \\ldots, q-1\\}$ (i.e., $a_i \\in \\mathbb{Z}_q^*$) and sends $X_i = g^{a_i}$ to Party $B$. \n\\item Party $B$ generates a random secret integer $b \\in \\{1, \\ldots, q-1\\}$ (i.e., $b \\in \\mathbb{Z}_q^*$). For each $i=1, \\ldots, n$, Party $B$ computes $Y_i = X_i^b = (g^{a_i})^b = g^{a_i b}$ and sends $Y_i$ to Party $A_i$. \n\\end{enumerate} \nThe intended shared group key is $k = g^b$. Party $B$ can compute this key directly since $B$ knows $b$. How can each Party $A_i$ (who knows $a_i$ and receives $Y_i$) compute this group key $k=g^b$?", |
| "choice": [ |
| "Party $A_i$ computes $g^b$ as $Y_i^{a_i}$.", |
| "Party $A_i$ computes $g^b$ as $Y_i^{1/a_i}$.", |
| "Party $A_i$ computes $g^b$ as $Y_i - a_i$.", |
| "Party $A_i$ computes $g^b$ as $(Y_i^{-1})^{1/a_i}$.", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 16, |
| "question": "Recall that the standard RSA trapdoor permutation operates in the group $\\mathbb{Z}_N^*$, where $N$ is the product of two large distinct primes. The public key is $(N,e)$ and the private key is $(N,d)$, where $d$ is the modular multiplicative inverse of $e$ modulo $\\phi(N)$ (i.e., $e \\cdot d \\equiv 1 \\pmod{\\phi(N)}$). \n \nSuppose, hypothetically, that RSA was defined modulo a prime $p$ instead of a composite $N$. In this modified scenario, the \"public key\" would be $(p,e)$. How would one compute the corresponding \"private key\" exponent $d$ given $(p,e)$?", |
| "choice": [ |
| "$d \\leftarrow e^{-1} \\pmod{p^2}$", |
| "$d \\leftarrow e^2 \\pmod{p}$", |
| "$d \\leftarrow e^{-1} \\pmod{p-1}$", |
| "$d \\leftarrow -e \\pmod{p}$", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 17, |
| "question": "Let $(E, D)$ be a CPA-secure cipher defined over $(K, M, C)$ and let $H_1: M \\to T$ and $H_2: C \\to T$ be collision-resistant hash functions. Consider the following modified encryption schemes\\medskip \n \n\\textbf{Scheme A):} \n\\begin{itemize} \n\\item Encryption: $E_1(k, m) := E(k, m) \\| E(k, m)$ (concatenation of two ciphertexts) \n\\item Decryption: $D_1(k, c_1 \\| c_2) := \\begin{cases} D(k, c_1) & \\text{if } D(k, c_1) = D(k, c_2) \\\\ \\text{reject} & \\text{otherwise} \\end{cases}$ \n\\end{itemize} \n\\medskip \n \n\\textbf{Scheme B):} \n\\begin{itemize} \n\\item Encryption: $E_2(k, m) := \\text{let } c \\leftarrow E(k, m); \\text{ output } (c, c)$ \n\\item Decryption: $D_2(k, (c_1, c_2)) := \\begin{cases} D(k, c_1) & \\text{if } c_1 = c_2 \\\\ \\text{reject} & \\text{otherwise} \\end{cases}$ \n\\end{itemize} \n\\medskip \n \n\\textbf{Scheme C):} \n\\begin{itemize} \n\\item Encryption: $E_3(k, m) := \\text{let } c \\leftarrow E(k, m); \\text{ output } (c, H_1(m))$ \n\\item Decryption: $D_3(k, (c, h)) := \\begin{cases} D(k, c) & \\text{if } H_1(D(k, c)) = h \\\\ \\text{reject} & \\text{otherwise} \\end{cases}$ \n\\end{itemize} \n\\medskip \n \n\\textbf{Scheme D):} \n\\begin{itemize} \n\\item Encryption: $E_4(k, m) := \\text{let } c \\leftarrow E(k, m); \\text{ output } (c, H_2(c))$ \n\\item Decryption: $D_4(k, (c, h)) := \\begin{cases} D(k, c) & \\text{if } H_2(c) = h \\\\ \\text{reject} & \\text{otherwise} \\end{cases}$ \n\\end{itemize} \n\\medskip \n \nWhich of the above schemes guarantees authenticated encryption (AE) security (Authenticated-encryption (AE) = CPA privacy + ciphertext-integrity (INT-CTXT))?", |
| "choice": [ |
| "Scheme A", |
| "Scheme B", |
| "Scheme C", |
| "Scheme D", |
| "None of the above" |
| ], |
| "answer": [ |
| 4 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 18, |
| "question": "Which of the following AES modes of operation fails to provide semantic security under standard assumptions, meaning it may leak patterns from plaintext to ciphertext?", |
| "choice": [ |
| "AES in CBC mode with a random IV", |
| "AES in CTR mode", |
| "AES in ECB mode", |
| "AES in GCM mode", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 19, |
| "question": "In the idealized Random Oracle Model, which cryptographic primitive is most often analyzed as if it were a truly random function to support security proofs?", |
| "choice": [ |
| "Block ciphers", |
| "Public-key encryption systems", |
| "Cryptographic hash functions", |
| "Message authentication codes", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 20, |
| "question": "Which of the following values among 17, 20, 38, and 50 does \\textbf{NOT} admit primitive roots in the multiplicative group $\\mathbb{Z}_n^*$?", |
| "choice": [ |
| "17", |
| "50", |
| "38", |
| "20", |
| "None of the above" |
| ], |
| "answer": [ |
| 3 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 21, |
| "question": "Evaluate Euler's totient function: $\\phi(25) = $", |
| "choice": [ |
| "22", |
| "24", |
| "20", |
| "25", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 22, |
| "question": "Find an integer $x$ such that $0 \\le x \\le 28$ and $x^{85} \\equiv 6 \\pmod{35}$. Which value of $x$ satisfies the congruence?", |
| "choice": [ |
| "6", |
| "28", |
| "8", |
| "32", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 23, |
| "question": "Which of the following is the smallest positive integer $x$ that satisfies the following system of congruences:\n\\begin{align*}\n x &\\equiv 2 \\pmod{3},\\ \n x &\\equiv 5 \\pmod{7},\\\n x &\\equiv 11 \\pmod{13}.\\end{align*}", |
| "choice": [ |
| "16", |
| "54", |
| "89", |
| "121", |
| "None of the above" |
| ], |
| "answer": [ |
| 3 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 24, |
| "question": "Using Rabin cryptosystem with parameters $p=23$ and $q=7$, compute the ciphertext for plaintext $28$. The ciphertext is", |
| "choice": [ |
| "42", |
| "93", |
| "140", |
| "127", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 25, |
| "question": "Within the ElGamal cryptosystem, suppose the prime $p = 31$. If $g$ is chosen as the smallest primitive root modulo $p$ and the private key $d = 10$, compute the value of $y$ such that $y \\equiv g^d \\bmod p$.", |
| "choice": [ |
| "24", |
| "36", |
| "25", |
| "62", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 26, |
| "question": "Let $E(k,x)$ be a secure block cipher. Consider the following tweakable block cipher construction$$E'((k_1,k_2), t, x) = E(k_1, x) \\oplus E(k_2, t)$$ \nwhere $(k_1, k_2)$ is the key, $t$ is the tweak, and $x$ is the plaintext block. Is this tweakable block cipher secure?", |
| "choice": [ |
| "Yes, it is secure assuming $E$ is a secure block cipher.", |
| "\\begin{minipage}[t]{\\linewidth}\nNo because for $x \\neq x'$ we have \\\\\n$E'((k_1,k_2), 0, x) \\oplus E'((k_1,k_2), 0, x) = E'((k_1,k_2), 0, x') \\oplus E'((k_1,k_2), 0, x')$\n\\end{minipage}", |
| "\\begin{minipage}[t]{\\linewidth}\nNo because for $t \\neq t'$ we have \\\\\n$E'((k_1,k_2), t, 0) \\oplus E'((k_1,k_2), t, 1) = E'((k_1,k_2), t', 0) \\oplus E'((k_1,k_2), t', 1)$\n\\end{minipage}", |
| "\\begin{minipage}[t]{\\linewidth}\nNo because for $t \\neq t'$ we have \\\\\n$E'((k_1,k_2), t, 0) \\oplus E'((k_1,k_2), t', 1) = E'((k_1,k_2), t', 1) \\oplus E'((k_1,k_2), t', 0)$\n\\end{minipage}", |
| "\\begin{minipage}[t]{\\linewidth}\nNo because for $x \\neq x'$ and $t \\neq t'$ we have \\\\\n$E'((k_1,k_2), t, x) \\oplus E'((k_1,k_2), t', x) = E'((k_1,k_2), t, x') \\oplus E'((k_1,k_2), t', x)$\n\\end{minipage}", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 27, |
| "question": "Given a superincreasing sequence $l=\\{38, 20, 9, 4, 2, 1\\}$ (The sequence is from right to left, corresponding to the bits from low to high.) that sums to 23, determine the binary vector $n$ which yields this total.", |
| "choice": [ |
| "011111", |
| "010011", |
| "010111", |
| "010010", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 28, |
| "question": "For RSA with $p = 11$, $q = 17$, and public exponent $e = 7$, decrypt the ciphertext 44 to recover the plaintext.", |
| "choice": [ |
| "88", |
| "22", |
| "13", |
| "41", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 29, |
| "question": "Consider a knapsack cryptosystem where letters A-Z are mapped to integers 0 through 25. You receive ciphertext values 14, 25, and 89. If the public key is \\{57, 14, 3, 24, 8\\} (The sequence is from right to left, corresponding to the bits from low to high.), what plaintext corresponds to this message?", |
| "choice": [ |
| "INK", |
| "TIN", |
| "KIN", |
| "INT", |
| "None of the above" |
| ], |
| "answer": [ |
| 3 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 30, |
| "question": "How many real versus imaginary roots (when $y=0$) exist for the elliptic curve equation $y^2 = x^3 - 4x$?", |
| "choice": [ |
| "All solutions are imaginary", |
| "All roots are real", |
| "Two real, one imaginary root", |
| "One real, two imaginary roots", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 31, |
| "question": "Let $P = (4, 3.464)$ be a point on the elliptic curve $y^2 = x^3 - 17x + 16$ over the real numbers. What is the result of computing $2P$ on this curve?", |
| "choice": [ |
| "(11.694, -43.723)", |
| "(12.022, -39.362)", |
| "(43.022, 39.362)", |
| "(32.022, 42.249)", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 32, |
| "question": "Bob chooses the elliptic curve $E_{67}(2, 3)$ defined over $GF(67)$, along with the base point $e_1 = (2, 22)$ and a private scalar $d = 4$. He computes $e_2 = d \\cdot e_1$ and publishes $(E, e_1, e_2)$. If Alice wishes to send $P = (24, 26)$ and randomly selects $r = 2$, what are the resulting ciphertext points $C_1$ and $C_2$? ($E_p(a, b) : y^2 = x^3 + ax+b \\mod p$)", |
| "choice": [ |
| "C1=(35,1) ; C2 =(21,44)", |
| "C1=(44,21) ; C2 =(1,35)", |
| "C1=(44,21) ; C2 =(44,21)", |
| "C1=(21,44); C2 =(35,1)", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 33, |
| "question": "Which of the following best characterizes the mathematical relationship between inputs and outputs in a standard MAC algorithm, considering multiple inputs can lead to the same authentication tag?", |
| "choice": [ |
| "injective (one-to-one) mapping", |
| "many-to-one transformation", |
| "surjective (onto) mapping", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 34, |
| "question": "Given a MAC algorithm with a key of size $k$ bits and an authentication tag of $n$ bits, what is the expected computational effort required for a brute-force attack that attempts to guess either the key or a valid tag?", |
| "choice": [ |
| "$2^k$", |
| "$2^n$", |
| "$\\min(2^k,\\ 2^n)$", |
| "$\\frac{2^k}{2^n}$", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 35, |
| "question": "What is the estimated number of operations required to generate a collision for a hashing algorithm $\\mathbf{H}: \\{0, 1\\}^* \\rightarrow \\{0, 1\\}^n$ ?", |
| "choice": [ |
| "$\\mathcal{O}(2^{n/2})$", |
| "$\\mathcal{O}(2^n)$", |
| "$\\mathcal{O}(2^{2n})$", |
| "$\\mathcal{O}(2^{n-1})$", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 36, |
| "question": "In the elliptic curve group defined by $y^2 = x^3 - 17x + 16$ over real numbers, what is $P + Q$ if $P = (0, -4)$ and $Q = (1, 0)$?", |
| "choice": [ |
| "(15, -56)", |
| "(-23, -43)", |
| "(69, 26)", |
| "(12, -86)", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 37, |
| "question": "The security of the RSA encryption scheme primarily corresponds to which of the following computationally hard problems?", |
| "choice": [ |
| "The discrete logarithm problem", |
| "The problem of factoring large composite integers", |
| "Elliptic curve point addition and multiplication", |
| "A hybrid of factoring and discrete logarithm problems" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 38, |
| "question": "In the context of cryptographic algorithms, what best describes the avalanche effect?", |
| "choice": [ |
| "A minor change in the plaintext causes a significant change in the ciphertext", |
| "Changing both the key and the plaintext simultaneously leads to encryption failure", |
| "Changing the key slightly will force a completely different plaintext", |
| "A slight change in the ciphertext affects the decryption key", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 39, |
| "question": "Which of the following is a correct difference between CBC (Cipher Block Chaining) mode and Counter (CTR) mode encryption?", |
| "choice": [ |
| "CBC mode requires padding for partial blocks, whereas CTR mode does not.", |
| "CTR mode is inherently sequential and cannot be parallelized, whereas CBC can.", |
| "CBC mode allows random access decryption, whereas CTR mode does not.", |
| "In CBC mode, encryption can be parallelized, whereas decryption cannot in CTR mode.", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 40, |
| "question": "Why is it important to use a random Initialization Vector (IV) in CBC mode encryption?", |
| "choice": [ |
| "A random IV prevents leakage of message patterns across different encryptions.", |
| "A random IV ensures resistance against chosen plaintext attacks in block cipher ECB mode.", |
| "A random IV allows decryption without knowing the key.", |
| "A random IV ensures integrity protection of the ciphertext.", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 41, |
| "question": "When implementing CBC-MAC, which type of IV should be used and why?", |
| "choice": [ |
| "A fixed IV, to guarantee deterministic and repeatable MAC outputs.", |
| "No IV is required for CBC-MAC.", |
| "A random IV, to ensure non-determinism in message authentication.", |
| "A unique IV per message, to prevent replay attacks.", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 42, |
| "question": "Given an RSA public key $(N,e)$ and the factorization $N = pq$, how can the secret key $d$ be computed?", |
| "choice": [ |
| "$d = e^{-1} \\mod \\varphi(N)$, where $\\varphi(N) = (p - 1)(q - 1)$", |
| "$d = e^{-1} \\mod (N - 1)$", |
| "$d = ep \\mod (q - 1)$", |
| "$d = p^{-1} \\mod q$", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 43, |
| "question": "Which of the following best defines a collision-resistant hash function?", |
| "choice": [ |
| "It is hard to find any two distinct inputs $x \\neq x'$ such that $H(x) = H(x')$", |
| "Given $x$, it is hard to find $y$ such that $H(x) = H(y)$.", |
| "No collisions exist for any practical input set.", |
| "It is hard to invert the hash output.", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 44, |
| "question": "If a hash function $H$ is one-way, must it also be collision-resistant?", |
| "choice": [ |
| "No, a function can be one-way yet still allow finding collisions efficiently.", |
| "Yes, one-wayness always implies collision resistance.", |
| "Yes, since inverting implies finding collisions.", |
| "It depends on whether the output length $n$ is large enough.", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 45, |
| "question": "Let p be a prime such that $p \\equiv 2 \\pmod{3}$, and let $\\alpha \\in \\mathbb{Z}_p^*$. Which of the following efficiently computes the cube root of $\\alpha\\pmod{p}$?", |
| "choice": [ |
| "Compute $\\alpha^{\\frac{2p-1}{3}} \\pmod{p}$.", |
| "Compute $\\alpha^{\\frac{p+1}{3}} \\pmod{p}$.", |
| "Compute $\\alpha^{\\frac{p-1}{2}} \\pmod{p}$.", |
| "Cube roots modulo such primes cannot be efficiently computed.", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 46, |
| "question": "What is the performance advantage of using a modulus $N' = p'q'r'$ (product of three equal-sized primes) over $N = pq$ in RSA ($\\lfloor\\log_2(N)\\rceil = \\lfloor\\log_2(N')\\rceil$), when employing the Chinese Remainder Theorem (CRT) for decryption?", |
| "choice": [ |
| "CRT does not apply to $N'$.", |
| "Decryption is faster due to smaller moduli and exponents.", |
| "Decryption is slower due to more primes involved.", |
| "Encryption becomes faster, but decryption remains the same.", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 47, |
| "question": "Sender $S$ digitally signs a message $m$ using its private key and sends it to receiver $R$. Considering possible cryptographic attacks, who among the following can potentially launch a birthday attack to alter $m$ while maintaining the same hash value?", |
| "choice": [ |
| "Only S", |
| "Only a third-party attacker", |
| "S and a third-party attacker", |
| "Receiver R and a third-party attacker", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 48, |
| "question": "Using a columnar transposition cipher, the plaintext 'the tomato is a plant in the nightshade family' is encrypted using the keyword 'TOMATO'. What is the resulting ciphertext, grouped by columns?", |
| "choice": [ |
| "\"TINESAX / EOAHTFX / HTLTHEY / MAILAIX / TAPNGDL / OSTNHMX\"", |
| "\"TINESAX / EOAHTEX / MAILAIX / HTLTHEY / TAPNGDL / OSTNHMX\"", |
| "\"TINESAX / EOAHTFX / HTLTHEY / MAILAIX / OSTNHMX / TAPNGDL\"", |
| "\"EOAHTFX / TINESAX / HTLTHEY / MAILAIX / TAPNGDL / OSTNHMX\"", |
| "\"TINESAX / EOAHTFX / HTLTHEY / MAIIAIX / TAPNGDL / OSTNHMX\"" |
| ], |
| "answer": [ |
| 4 |
| ], |
| "label": "classic" |
| }, |
| { |
| "id": 49, |
| "question": "Which of the following security properties is not inherently guaranteed by a digital signature mechanism?", |
| "choice": [ |
| "Authentication", |
| "Non-repudiation", |
| "Confidentiality", |
| "Integrity", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 50, |
| "question": "In a public-key cryptographic scheme, if user A wants to send a secure message to user B, which key should A use to encrypt the message?", |
| "choice": [ |
| "A's private key", |
| "B's private key", |
| "B's public key", |
| "A's public key", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 51, |
| "question": "When comparing AES with DES, which operation in DES lacks a corresponding component in AES?", |
| "choice": [ |
| "Function f", |
| "Permutation P", |
| "Swapping of left and right halves", |
| "XOR between subkey and function output", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 52, |
| "question": "In elliptic curve cryptography (ECC), the problem of \"given P, a point on the curve, and the scalar multiplication Q = kP (where k is an integer), find k\" primarily corresponds to which mathematical problem", |
| "choice": [ |
| "Integer factorization problem", |
| "Discrete logarithm problem", |
| "Elliptic curve discrete logarithm problem", |
| "Subset sum problem" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 53, |
| "question": "Imagine you are designing a secure voting system where votes need to be encrypted to ensure privacy. Which encryption scheme is most suitable for tallying votes without decrypting them all (assuming only two candidates: A and B, with encrypted votes represented as 0 or 1)?", |
| "choice": [ |
| "AES-GCM", |
| "RSA", |
| "Fully Homomorphic Encryption", |
| "ElGamal", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 54, |
| "question": "Suppose you have encrypted a message using RSA, where the public key is $(n, e)$ and the private key is $d$. If an attacker successfully factors the modulus n into two distinct prime numbers $p$ and $q$, what can the attacker now do?", |
| "choice": [ |
| "Decrypt any message encrypted with the public key without calculating $d$.", |
| "Compute the private key $d$, and thus decrypt any message encrypted with the public key.", |
| "Forge messages signed with the private key but cannot decrypt ciphertext.", |
| "Perform no meaningful attack since the encryption process remains secure.", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 55, |
| "question": "What is a primary vulnerability of the Electronic Code Book (ECB) mode of encryption?", |
| "choice": [ |
| "It needs a larger block size to be secure", |
| "It uses excessive padding for all input sizes", |
| "It is susceptible to cryptanalysis due to the one-to-one mapping between plaintext and ciphertext blocks", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 56, |
| "question": "In a digital signature system, which key should the sender (e.g., Alice) use to sign a message so that the recipient (e.g., Bob) can verify the origin and authenticity of the message?", |
| "choice": [ |
| "Bob's private key", |
| "Alice's private key", |
| "Bob's public key", |
| "Alice's username and password", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 57, |
| "question": "Based on the information available to an attacker, cryptanalysis attacks can generally be classified into four types: ciphertext-only attacks, known-plaintext attacks, chosen-plaintext attacks, and chosen-ciphertext attacks. Which type of attack is considered the most difficult for the attacker to attack successfully?", |
| "choice": [ |
| "Ciphertext-only attack", |
| "Known-plaintext attack", |
| "Chosen-plaintext attack", |
| "Chosen-ciphertext attack", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 58, |
| "question": "In the RSA blind signature scheme, how does the requester blind the original message before sending it to the signer?", |
| "choice": [ |
| "Encrypting the message with a private key", |
| "Encrypting a random blinding factor with the public key of RSA, and multiplying it with the message", |
| "Encrypting the message with a public key", |
| "Reordering blocks of the message", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 59, |
| "question": "Which transformation step in the AES encryption algorithm is primarily responsible for achieving diffusion?", |
| "choice": [ |
| "ShiftRows", |
| "SubBytes", |
| "AddRoundKey", |
| "MixColumns", |
| "None of the above" |
| ], |
| "answer": [ |
| 3 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 60, |
| "question": "Which of the following statements about confusion in cryptography is incorrect?", |
| "choice": [ |
| "Confusion aims to make the ciphertext-key relationship more complex", |
| "S-boxes play a key role in achieving confusion", |
| "Confusion can be effectively achieved using a basic XOR operation", |
| "The purpose of confusion is to prevent attackers from deducing the key", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 61, |
| "question": "If a cryptographic algorithm employs confusion but lacks diffusion, which type of attack is it most vulnerable to?", |
| "choice": [ |
| "Differential cryptanalysis", |
| "Linear cryptanalysis", |
| "Brute force attack", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 62, |
| "question": "What is the main objective of diffusion in the design of a secure encryption system?", |
| "choice": [ |
| "Making small changes in the plaintext significantly affect the ciphertext", |
| "Reducing the number of encryption rounds", |
| "Enhancing the non-linearity between ciphertext and key", |
| "Improving encryption speed", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 63, |
| "question": "Let $(Gen, E, D)$ be a chosen ciphertext secure public-key encryption system with message space $\\{0,1\\}^{128}$. Which of the following is also chosen ciphertext secure?", |
| "choice": [ |
| "$(Gen, E', D')$ where $E'(pk, m) = (E(pk, m), E(pk, 0^{128}))$ and $D'(sk, (c_1, c_2)) = D(sk, c_1)$.", |
| "$(Gen, E', D')$ where $E'(pk, m) = (E(pk, m), E(pk, m))$ and \\\\\n$D'(sk, (c_1, c_2)) = \\begin{cases} D(sk, c_1) & \\text{if } D(sk, c_1) = D(sk, c_2) \\\\ \\perp & \\text{otherwise} \\end{cases}$.", |
| "$(Gen, E', D')$ where $E'(pk, m) = E(pk, m \\oplus 1^{128})$ and $D'(sk, c) = D(sk, c) \\oplus 1^{128}$.", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 64, |
| "question": "The letter frequency analysis method is most effective against which type of classical cipher algorithm?", |
| "choice": [ |
| "Transposition cipher", |
| "Monoalphabetic substitution cipher", |
| "Polyalphabetic substitution cipher", |
| "Stream cipher", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "classic" |
| }, |
| { |
| "id": 65, |
| "question": "Which of the following cipher algorithms offers the strongest resistance to frequency analysis but the weakest resistance to known-plaintext attacks?", |
| "choice": [ |
| "Affine cipher", |
| "Vigen\u00e8re cipher", |
| "Rotational cipher", |
| "Hill cipher", |
| "None of the above" |
| ], |
| "answer": [ |
| 3 |
| ], |
| "label": "classic" |
| }, |
| { |
| "id": 66, |
| "question": "The index of coincidence method is particularly effective for breaking which type of cipher?", |
| "choice": [ |
| "Transposition cipher", |
| "Polyalphabetic substitution cipher", |
| "Stream cipher", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "classic" |
| }, |
| { |
| "id": 67, |
| "question": "The Vigen\u00e8re cipher, a representative example of classical cipher systems, employs which type of encryption approach?", |
| "choice": [ |
| "Transposition cipher", |
| "Monoalphabetic substitution cipher", |
| "Polyalphabetic substitution cipher", |
| "Stream cipher", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "classic" |
| }, |
| { |
| "id": 68, |
| "question": "In the DES algorithm, if all the subkeys generated from a given initial key k are identical, such a key is called a weak key. How many weak keys exist in DES?", |
| "choice": [ |
| "2", |
| "4", |
| "8", |
| "16", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 69, |
| "question": "The Index Calculus method is used to analyze which type of cryptographic algorithm?", |
| "choice": [ |
| "Knapsack cryptosystem", |
| "RSA", |
| "ElGamal", |
| "ECC", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 70, |
| "question": "Suppose an affine cipher uses the encryption rule \\( c \\equiv 17m + 2 \\pmod{26} \\). Which of the following represents the correct decryption function?", |
| "choice": [ |
| "\\( m \\equiv 3c + 6 \\pmod{26} \\)", |
| "\\( m \\equiv 3c - 2 \\pmod{26} \\)", |
| "\\( m \\equiv 23c + 6 \\pmod{26} \\)", |
| "\\( m \\equiv 23c - 2 \\pmod{26} \\)", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 71, |
| "question": "Consider a maximum-length sequence (m-sequence) generated by an n-stage linear feedback shift register (LFSR). In one full period of this sequence, how many runs of consecutive 1s with length exactly n-1 occur?", |
| "choice": [ |
| "0", |
| "1", |
| "2", |
| "n", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 72, |
| "question": "The (t, n)-threshold scheme proposed by Shamir is based on which of the following?", |
| "choice": [ |
| "Lagrange interpolation polynomial", |
| "Discrete logarithm problem", |
| "Knapsack problem", |
| "Large integer factorization problem", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 73, |
| "question": "Which of the following statements about digital signatures is correct?", |
| "choice": [ |
| "A digital signature appends a piece of irrelevant digital information to the transmitted data", |
| "A digital signature solves the problem of secure data transmission by encryption", |
| "A digital signature typically uses symmetric encryption mechanisms", |
| "A digital signature can solve security issues such as tampering and forgery", |
| "None of the above" |
| ], |
| "answer": [ |
| 3 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 74, |
| "question": "What additional property transforms a commutative ring into a mathematical field?", |
| "choice": [ |
| "Existence of reciprocals for all non-null elements", |
| "Presence of opposites for all elements", |
| "Availability of reciprocals for all elements", |
| "Partial availability of reciprocals", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 75, |
| "question": "In the AES algorithm, which component introduces non-linearity?", |
| "choice": [ |
| "Byte substitution", |
| "Row shifting", |
| "Column mixing", |
| "Round key addition", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 76, |
| "question": "For the affine cipher $y \\equiv (a\\cdot x + b) \\mod 26$, what constraint applies to the coefficient 'a'?", |
| "choice": [ |
| "Any integer value is acceptable", |
| "Must be divisible by 2", |
| "Must be relatively prime to 26", |
| "Must be divisible by 13", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 77, |
| "question": "What correctly describes key management in public-key systems?", |
| "choice": [ |
| "All cryptographic keys are public", |
| "Encryption keys are public while decryption keys are private", |
| "Private keys are exchanged between parties", |
| "Both encryption and decryption keys remain secret", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 78, |
| "question": "Given two distinct primes \\( p \\) and \\( q \\), let \\( n = p \\cdot q \\). What is the value of Euler's totient function \\( \\varphi(n) \\)?", |
| "choice": [ |
| "\\( p + q - 1 \\)", |
| "\\( p \\cdot q \\)", |
| "\\( (p - 1)(q - 1) \\)", |
| "\\( (p + 1)(q + 1) \\)", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 79, |
| "question": "What algebraic structure do residue classes modulo a prime p form?", |
| "choice": [ |
| "A non-field ring", |
| "An additive group only", |
| "A finite field", |
| "An infinite field", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 80, |
| "question": "In public key cryptography, what is the correct sequence for signing-then-encrypting a message?", |
| "choice": [ |
| "Sign with X's private key \u2192 Encrypt with Y's public key", |
| "Sign with Y's public key \u2192 Encrypt with X's private key", |
| "Encrypt with X's public key \u2192 Sign with Y's private key", |
| "Encrypt with Y's private key \u2192 Sign with X's public key", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 81, |
| "question": "The Euclidean Algorithm produces a sequence $X_1 > X_2 > \\ldots > X_k = 0$ of positive integers where each $X_t$ for $2 < t \\leq k$ is the remainder obtained by dividing $X_{t-2}$ by $X_{t-1}$. If $X_{k-1} = 45$, then the set of all positive common divisors of $X_1$ and $X_2$ is", |
| "choice": [ |
| "{1, 3, 5, 9, 15, 45}", |
| "{1, 3, 5, 15}", |
| "{1, 3, 5}", |
| "{1, 9, 15, 45}", |
| "{1, 3, 5, 9, 15}", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 82, |
| "question": "Let $L$ be the least common multiple of 175 and 105. Among all common divisors $x > 1$ of 175 and 105, let $D$ be the smallest. Which of the following is correct?", |
| "choice": [ |
| "$D = 5$ and $L = 1050$", |
| "$D = 7$ and $L = 1050$", |
| "$D = 5$ and $L = 525$", |
| "$D = 7$ and $L = 525$", |
| "$D = 5$ and $L = 35$", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 83, |
| "question": "The Euclidean Algorithm is used to produce a sequence \\( X_1 > X_2 > X_3 > X_4 > X_5 = 0 \\) of positive integers where \\( X_t = q_{t+1}X_{t+1} + X_{t+2} \\), for \\( t = 1, 2, 3 \\). The quotients are \\( q_2 = 3 \\), \\( q_3 = 2 \\), and \\( q_4 = 2 \\). Which of the following is correct?", |
| "choice": [ |
| "gcd(\\( X_1, X_2 \\)) = \\( -2X_1 + 6X_2 \\)", |
| "gcd(\\( X_1, X_2 \\)) = \\( -2X_1 - 6X_2 \\)", |
| "gcd(\\( X_1, X_2 \\)) = \\( -2X_1 - 7X_2 \\)", |
| "gcd(\\( X_1, X_2 \\)) = \\( 2X_1 + 7X_2 \\)", |
| "gcd(\\( X_1, X_2 \\)) = \\( -2X_1 + 7X_2 \\)", |
| "None of the above" |
| ], |
| "answer": [ |
| 4 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 84, |
| "question": "Which cipher mode should always be used when available to ensure both confidentiality and integrity?", |
| "choice": [ |
| "ECB", |
| "CBC", |
| "GCM or CCM", |
| "CTR", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 85, |
| "question": "In RSA encryption, what must be enabled to protect against Known Plaintext Attacks?", |
| "choice": [ |
| "Random Padding (OAEP)", |
| "Initialization Vector (IV)", |
| "Key Derivation Function (KDF)", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 86, |
| "question": "How many distinct solutions exist for the congruence equation \\( x^2 \\equiv 1 \\mod 30 \\)?", |
| "choice": [ |
| "1", |
| "2", |
| "4", |
| "8", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 87, |
| "question": "Which of the following quotient rings does NOT define a field isomorphic to \\( \\text{GF}(2^5) \\)?", |
| "choice": [ |
| "$GF(2)[x] / \\langle x^5 + x^4 + x^3 + x + 1 \\rangle$", |
| "$ GF(2)[x] / \\langle x^5 + x^3 + 1 \\rangle$", |
| "$GF(2)[x] / \\langle x^5 + x^4 + x^3 + x^2 + 1 \\rangle$", |
| "$GF(2)[x] / \\langle x^5 + x^4 + 1 \\rangle$", |
| "None of the above" |
| ], |
| "answer": [ |
| 3 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 88, |
| "question": "Which of the following irreducible polynomials over \\( \\text{GF}(3) \\) is also primitive?", |
| "choice": [ |
| "\\( x^3 + 2x + 1 \\)", |
| "\\( x^3 + 2x + 2 \\)", |
| "\\( x^3 + x^2 + 2 \\)", |
| "\\( x^3 + x^2 + x + 2 \\)", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 89, |
| "question": "In a Feistel network cipher, each round consists of \\( L_i = R_{i-1} \\), and which of the following describes \\( R_i \\)?", |
| "choice": [ |
| "\\( R_i = L_{i-1} \\oplus f(L_{i-1}, k_i) \\)", |
| "\\( R_i = L_{i-1} \\oplus f(R_{i-1}, k_i) \\)", |
| "\\( R_i = R_{i-1} \\oplus f(R_{i-1}, k_i) \\)", |
| "\\( R_i = R_{i-1} \\oplus f(L_{i-1}, k_i) \\)", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 90, |
| "question": "The block cipher IDEA uses a combination of algebraic operations from three distinct groups. Which of the following is \\textbf{NOT} one of them?", |
| "choice": [ |
| "\\( (\\{0,1\\}^{16}, \\oplus) \\)", |
| "\\( \\mathbb{Z}_{65536}, + \\mod 65536 \\)", |
| "\\( S_{16}, \\circ \\text{ (composition)} \\)", |
| "\\( \\mathbb{Z}_{65537}^*, \\times \\mod 65537 \\)", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 91, |
| "question": "Let \\( m_i \\) and \\( c_i \\) denote plaintext and ciphertext blocks in CBC mode. For \\( i > 1 \\), what is the correct decryption operation?", |
| "choice": [ |
| "\\( m_i = d_k(c_i) \\oplus m_{i-1} \\)", |
| "\\( m_i = d_k(c_i \\oplus m_{i-1}) \\)", |
| "\\( m_i = d_k(c_i) \\oplus c_{i-1} \\)", |
| "\\( m_i = d_k(c_i \\oplus c_{i-1}) \\)", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 92, |
| "question": "The block cipher SAFER uses an 8-bit substitution defined as \\( S(x) = 45^x \\mod 257 \\), with 256 represented by 0. Which function below is NOT a bijective mapping on 8-bit values?", |
| "choice": [ |
| "\\( S(x) = 45^{5x} \\mod 257 \\)", |
| "\\( S(x) = 45^{6x} \\mod 257 \\)", |
| "\\( S(x) = 45^{9x} \\mod 257 \\)", |
| "\\( S(x) = 45^{15x} \\mod 257 \\)", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 93, |
| "question": "In a hybrid cryptosystem, what is the role of the symmetric key?", |
| "choice": [ |
| "It is used to encrypt the public key", |
| "It is used to encrypt the session data after it is established", |
| "It is used to encrypt the private key", |
| "It is used for the authentication of the message sender", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 94, |
| "question": "For which prime numbers $p$ and $q$ can a cyclic multiplicative subgroup of order $q$ be constructed within $(\\mathbb{Z}_p^*, \\times)$? Cryptographic schemes based on the discrete logarithm problem typically operate on such groups.", |
| "choice": [ |
| "$p = 859$, $q = 103$", |
| "$p = 853$, $q = 101$", |
| "$p = 857$, $q = 107$", |
| "$p = 863$, $q = 109$", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 95, |
| "question": "Consider a key management scheme devised by an administrator. The administrator generates an RSA modulus $N$ and a master secret $s \\in \\mathbb{Z}_N^*$. For each user $i$, a secret key $s_i = s^{r_i} \\pmod{N}$ is assigned, where $r_i$ is the $i$-th prime number (e.g., $r_1=2, r_2=3, \\ldots$). \n \nTo encrypt a file intended for a group of users, say users $i, j,$ and $t$, the administrator uses the key $k = s^{r_i r_j r_t} \\pmod{N}$. Each authorized user can compute $k$. For instance, user $i$ computes $k = (s_i)^{r_j r_t} = (s^{r_i})^{r_j r_t} = s^{r_i r_j r_t} \\pmod{N}$. The scheme aims to ensure that only the designated users can compute $k$ and access the file. \n \nHowever, this system is insecure. Any two colluding users can combine their secret keys to recover the master secret $s$. Consider users 1 and 2, with secret keys $s_1 = s^{r_1} \\pmod{N}$ and $s_2 = s^{r_2} \\pmod{N}$ respectively. Since $r_1$ and $r_2$ are distinct primes, by the Extended Euclidean Algorithm (Bezout's identity), there exist integers $a$ and $b$ such that $a \\cdot r_1 + b \\cdot r_2 = 1$. \n \nHow can users 1 and 2 compute the master secret $s$ using their keys $s_1, s_2$ and the integers $a, b$? {}", |
| "choice": [ |
| "$s = s_1^b \\cdot s_2^a \\pmod{N}$", |
| "$s = s_1^a + s_2^b \\pmod{N}$", |
| "$s = s_1^b + s_2^a \\pmod{N}$", |
| "$s = s_1^a \\cdot s_2^b \\pmod{N}$", |
| "None of the above" |
| ], |
| "answer": [ |
| 3 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 96, |
| "question": "Which of the following is \\textbf{not} a property provided by Message Authentication Codes (MACs)?", |
| "choice": [ |
| "Integrity \u2014 detecting any modification of a message during transmission", |
| "Authentication \u2014 verifying the message origin for the receiver", |
| "Non-repudiation \u2014 preventing the sender from denying message origin", |
| "Fixed output length \u2014 generating authentication tags of a consistent size", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 97, |
| "question": "Which of the following statements about the Digital Signature Algorithm (DSA) is \\textbf{false}?", |
| "choice": [ |
| "Proposed by NIST as a US federal digital signature standard", |
| "Signature verification is faster than RSA at equivalent security levels", |
| "Based on the ElGamal signature scheme", |
| "Vulnerable if the same ephemeral key is reused across signatures", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 98, |
| "question": "Which of the following statements about key establishment using a Key Distribution Center (KDC) is \\textbf{false}?", |
| "choice": [ |
| "Each user shares a Key Encryption Key (KEK) with both the KDC and every other user", |
| "Only $n$ long-term keys are needed in a network with $n$ users", |
| "When a new user joins, only one secure key is required between the user and the KDC", |
| "The KDC distributes session keys encrypted under users' KEKs", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 99, |
| "question": "Which of the following quotient rings is isomorphic to the finite field $\\mathbb{GF}(81)$?", |
| "choice": [ |
| "$\\mathbb{GF}_3[x] / \\langle x^4 + x + 2 \\rangle$", |
| "$\\mathbb{GF}_3[x] / \\langle x^4 + 2x + 1 \\rangle$", |
| "$\\mathbb{GF}_3[x] / \\langle x^4 + 1 \\rangle$", |
| "$\\mathbb{GF}_3[x] / \\langle x^4 + 2 \\rangle$", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 100, |
| "question": "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?", |
| "choice": [ |
| "$\\phi(x) = x^8+1$", |
| "$\\phi(x) = x^8+2$", |
| "$\\phi(x) = x^8+3$", |
| "$\\phi(x) = x^8+4$" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 101, |
| "question": "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 $d$?", |
| "choice": [ |
| "$\\mathrm{lcm}(p - 1, q - 1)$", |
| "$\\gcd(p - 1, q - 1)$", |
| "$\\mathrm{lcm}(p + 1, q + 1)$", |
| "$\\gcd(p + 1, q + 1)$", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 102, |
| "question": "Which of the following statements about the Key Encryption Key (KEK) is \\textbf{FALSE}?", |
| "choice": [ |
| "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" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 103, |
| "question": "For arbitrary inputs $A$ and $B$, which relation does the diffusion operation $D$ in the AES diffusion layer always satisfy?", |
| "choice": [ |
| "$D(A \\oplus B) \\neq A \\oplus B$", |
| "$D(A \\oplus B) = A \\oplus B$", |
| "$D(A \\oplus B) = D(A) \\oplus D(B)$", |
| "$D(A \\oplus B) \\neq D(A) \\oplus D(B)$", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 104, |
| "question": "Which attack reduces the effective key length of 3-key Triple DES from 168 bits to approximately 112 bits?", |
| "choice": [ |
| "Meet-in-the-Middle attack", |
| "Man-in-the-Middle attack", |
| "Differential attack", |
| "Linear attack", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 105, |
| "question": "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 $n$?", |
| "choice": [ |
| "$m = 4n$", |
| "$m = 2n$", |
| "$2m = n$", |
| "$4m = n$", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 106, |
| "question": "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 $\\log(p)^2$.)", |
| "choice": [ |
| "$s = 4t$", |
| "$s = 2t$", |
| "$2s = t$", |
| "$4s = t$", |
| "None of the above" |
| ], |
| "answer": [ |
| 3 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 107, |
| "question": "Which of the following systems of congruences does \\textbf{NOT} have a solution?", |
| "choice": [ |
| "$x \\equiv 1 \\pmod{7}, \\quad x \\equiv 3 \\pmod{9}, \\quad x \\equiv 5 \\pmod{11}$", |
| "$x \\equiv 1 \\pmod{8}, \\quad x \\equiv 3 \\pmod{9}, \\quad x \\equiv 5 \\pmod{11}$", |
| "$x \\equiv 1 \\pmod{7}, \\quad x \\equiv 3 \\pmod{9}, \\quad x \\equiv 5 \\pmod{12}$", |
| "$x \\equiv 1 \\pmod{7}, \\quad x \\equiv 3 \\pmod{10}, \\quad x \\equiv 5 \\pmod{12}$", |
| "None of the above" |
| ], |
| "answer": [ |
| 2 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 108, |
| "question": "Which of the following statements about the Man-in-the-Middle (MITM) attack is \\textbf{FALSE}?", |
| "choice": [ |
| "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" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 109, |
| "question": "How many generators exist in the cyclic multiplicative group \\( \\mathbb{Z}_{243}^* \\)?", |
| "choice": [ |
| "81", |
| "110", |
| "121", |
| "162", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 110, |
| "question": "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} \n\\item They fix a public cyclic group $G$ of prime order $p$ with a generator $g \\in G$. \n\\item Alice chooses random exponents $x, y \\in \\mathbb{Z}_p$. She computes and sends to Bob the triplet$$ (A_0, A_1, A_2) = (g^x, g^y, g^{xy+a}) $$ \n(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 $A_2 = g^a \\cdot (g^x)^y$.) \n\\item Bob chooses random exponents $r, s \\in \\mathbb{Z}_p$. He computes and sends back to Alice the pair$$ (B_1, B_2) = (A_1^r \\cdot g^s, (A_2 \\cdot g^{-b})^r \\cdot A_0^s) $$ \n\\end{enumerate} \nAfter receiving $(B_1, B_2)$ from Bob, what check should Alice perform to test if $a=b$?", |
| "choice": [ |
| "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" |
| ], |
| "answer": [ |
| 3 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 111, |
| "question": "Which of the following represents the encryption process of the standard 3DES (Triple-DES) scheme with a 112-bit key?", |
| "choice": [ |
| "$\\mathrm{DES}_{k_3}(\\mathrm{DES}_{k_2}(\\mathrm{DES}_{k_1}(\\cdot)))$, 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" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 112, |
| "question": "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)?", |
| "choice": [ |
| "No, only the One Time Pad has perfect secrecy.", |
| "Yes", |
| "No, there is a simple attack on this cipher.", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 113, |
| "question": "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$$h(M) = (m_1 \\cdot m_2)^e \\pmod N$$ \nIs this hash function $h$ collision-resistant?", |
| "choice": [ |
| "Yes, it is collision resistant.", |
| "No, it is not collision resistant.", |
| "Collision resistance cannot be determined from the information given.", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 114, |
| "question": "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.", |
| "choice": [ |
| "stalxlings", |
| "stallings", |
| "secrettext", |
| "stollings", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "classic" |
| }, |
| { |
| "id": 115, |
| "question": "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?", |
| "choice": [ |
| "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." |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 116, |
| "question": "For a $n\\times n$ Hill cipher over the English alphabet, which is the correct size of its key space?", |
| "choice": [ |
| "$\\prod_{i=0}^{n-1}\\left((2^n-2^i)\\cdot(13^n-13^i)\\right)$", |
| "$\\prod_{i=0}^{n-1}(2^n-2^i) \\cdot \\prod_{i=0}^{n-1}(13^{n-1}-13^i)$", |
| "$\\prod_{i=0}^{n-1}(26^n-26^i)$", |
| "$\\prod_{i=0}^{n-1}26^i$", |
| "None of the above" |
| ], |
| "answer": [ |
| 0 |
| ], |
| "label": "classic" |
| }, |
| { |
| "id": 117, |
| "question": "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 $\\sigma$.", |
| "choice": [ |
| "$s \\leftarrow \\mathcal{D}_{0.5}, e \\leftarrow \\mathcal{U}(\\{0, 1\\}^{n})$", |
| "$s \\leftarrow \\mathcal{U}(\\{0, 1\\}^{n}), e \\leftarrow \\mathcal{U}(\\{0, 1\\}^{n})$", |
| "$s \\leftarrow \\mathcal{U}(\\{0, 1\\}^{n}), e \\leftarrow \\mathcal{D}_{0.5}$", |
| "$s \\leftarrow \\mathcal{D}_{0.5}, e \\leftarrow \\mathcal{D}_{0.5}$", |
| "None of the above" |
| ], |
| "answer": [ |
| 1 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 118, |
| "question": "The high strength of a synchronous stream cipher mainly depends on which of the following?", |
| "choice": [ |
| "The design of the keystream generator", |
| "The key length", |
| "The plaintext length", |
| "The complexity of the key", |
| "None of the above" |
| ], |
| "answer": [ |
| 0, |
| 1 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 119, |
| "question": "Which of the following cryptosystems are vulnerable to quantum attacks up to date?", |
| "choice": [ |
| "RSA", |
| "Rabin", |
| "AES-256", |
| "NTRU" |
| ], |
| "answer": [ |
| 0, |
| 1 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 120, |
| "question": "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?", |
| "choice": [ |
| "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 $e'\\neq e, e'd'\\equiv 1 \\mod \\phi(N)$" |
| ], |
| "answer": [ |
| 0, |
| 1, |
| 3 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 121, |
| "question": "Which encryption schemes utilize different keys for encryption and decryption?", |
| "choice": [ |
| "Shift cipher", |
| "RSA", |
| "Advanced Encryption Standard", |
| "Data Encryption Standard", |
| "ElGamal scheme", |
| "Secure Hash Algorithm" |
| ], |
| "answer": [ |
| 1, |
| 4 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 122, |
| "question": "Factor the polynomial $x^4 + 1$ in GF(2)", |
| "choice": [ |
| "Cannot be factored in GF(2)", |
| "Factors as $(x^2 + 1)^2$", |
| "Factors as $(x + 1)^4$", |
| "Already in simplest form" |
| ], |
| "answer": [ |
| 1, |
| 2 |
| ], |
| "label": "math" |
| }, |
| { |
| "id": 123, |
| "question": "Which statements about block cipher modes are correct?", |
| "choice": [ |
| "CBC XORs plaintext with previous ciphertext", |
| "CTR doesn't need IV", |
| "CBC's last block uses IV", |
| "CBC hides plaintext patterns" |
| ], |
| "answer": [ |
| 0, |
| 3 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 124, |
| "question": "What is true about public key message encryption?", |
| "choice": [ |
| "Encrypt with recipient's public key", |
| "Encrypt with sender's public key", |
| "Decrypt with sender's public key", |
| "Decrypt with recipient's private key" |
| ], |
| "answer": [ |
| 0, |
| 3 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 125, |
| "question": "Which of the following are essential characteristics of a secure cryptographic hash function?", |
| "choice": [ |
| "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" |
| ], |
| "answer": [ |
| 1, |
| 2, |
| 4 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 126, |
| "question": "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?", |
| "choice": [ |
| "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)) \\)" |
| ], |
| "answer": [ |
| 1, |
| 4 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 127, |
| "question": "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?", |
| "choice": [ |
| "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)) \\), $E_{k_1}(M || \\text{MAC}_{k_2}(M))$" |
| ], |
| "answer": [ |
| 2, |
| 4 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 128, |
| "question": "In the RSA encryption scheme, after selecting two large numbers $p$ and $q$, which of the following must be true about their properties?", |
| "choice": [ |
| "$p$ 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" |
| ], |
| "answer": [ |
| 0, |
| 3 |
| ], |
| "label": "asymmetric" |
| }, |
| { |
| "id": 129, |
| "question": "Differential cryptanalysis is a method of analyzing which type of cipher algorithm?", |
| "choice": [ |
| "DES", |
| "AES", |
| "RSA", |
| "Rabin" |
| ], |
| "answer": [ |
| 0, |
| 1 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 130, |
| "question": "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)", |
| "choice": [ |
| "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: $E'(k,m) = \\text{reverse}(E(k,m))$" |
| ], |
| "answer": [ |
| 1, |
| 3, |
| 5 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 131, |
| "question": "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)", |
| "choice": [ |
| "$F'(k, x) = \\begin{cases} F(k,x) & \\text{when } x \\neq 0^n \\\\ 0^n & \\text{otherwise} \\end{cases}$", |
| "$F'(k,x) = F(k,x)[0,\\ldots,n-2]$ (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 $k\\neq k'$)", |
| "$F'(k, x) = k \\oplus x$", |
| "$F'(k,x) = F(k, x) \\oplus F(k, x \\oplus 1^n)$", |
| "$F'(k,x) = F(k, x \\oplus 1^n)$" |
| ], |
| "answer": [ |
| 1, |
| 2, |
| 5 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 132, |
| "question": "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. $k\\in K, m\\in M, \\, t \\in T$)", |
| "choice": [ |
| "$S'(k,m) = S(k, m \\oplus m)$ 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 $V'(k,m,t) = V(k, m \\oplus 1^n, t)$" |
| ], |
| "answer": [ |
| 3, |
| 5 |
| ], |
| "label": "misc" |
| }, |
| { |
| "id": 133, |
| "question": "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?", |
| "choice": [ |
| "$H'(m) = H(|m|)$ (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 $m$)" |
| ], |
| "answer": [ |
| 2, |
| 4, |
| 5 |
| ], |
| "label": "symmetric" |
| }, |
| { |
| "id": 134, |
| "question": "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?", |
| "choice": [ |
| "$E'(k,m) = (E(k,m), H(m))$ 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 $D'(k,c) = \\begin{cases} D(k,c) \\oplus 1^n & \\text{if } D(k,c) \\neq \\perp \\\\ \\perp & \\text{otherwise} \\end{cases}$" |
| ], |
| "answer": [ |
| 1, |
| 3 |
| ], |
| "label": "misc" |
| } |
| ] |
