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Unit 5: Public Key Cryptography - Practice Quiz

MTH381 — Number Theory And Cryptography 60 Questions
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1 In public-key cryptography, how many keys does each user typically have?

introduction to public-key cryptography Easy
A. Two keys: a public key and a private key
B. One shared secret key
C. Three keys for each session
D. No keys, only passwords

2 Which term is another name for public-key cryptography?

introduction to public-key cryptography Easy
A. Stream cryptography
B. Symmetric cryptography
C. Hash cryptography
D. Asymmetric cryptography

3 In a public-key system, which key is used to encrypt a message intended for a recipient?

introduction to public-key cryptography Easy
A. The sender's private key
B. A shared symmetric key
C. The recipient's private key
D. The recipient's public key

4 Public-key cryptography helps solve which major problem of symmetric cryptography?

introduction to public-key cryptography Easy
A. Lack of encryption algorithms
B. Key distribution over insecure channels
C. Excessive key length
D. Slow hashing speed

5 What is the main purpose of the Diffie-Hellman protocol?

Diffie-Hellman key exchange Easy
A. To securely establish a shared secret key
B. To hash passwords
C. To compress encrypted data
D. To digitally sign documents

6 The security of the Diffie-Hellman key exchange is based on the difficulty of which problem?

Diffie-Hellman key exchange Easy
A. Integer factorization
B. Matrix inversion
C. The discrete logarithm problem
D. Sorting large arrays

7 In Diffie-Hellman, if is the prime and is the generator, what does Alice send to Bob given her secret ?

Diffie-Hellman key exchange Easy
A.
B.
C.
D.

8 After exchanging values, both parties in Diffie-Hellman compute the same shared secret of the form:

Diffie-Hellman key exchange Easy
A.
B.
C.
D.

9 The security of RSA relies on the difficulty of which mathematical problem?

the RSA cryptosystem Easy
A. Finding shortest paths
B. Solving linear equations
C. Computing discrete logarithms
D. Factoring large composite numbers

10 In RSA, the modulus is computed as:

the RSA cryptosystem Easy
A.
B.
C.
D.

11 In RSA, Euler's totient for (with prime) equals:

the RSA cryptosystem Easy
A.
B.
C.
D.

12 Which pair of values forms the public key in RSA?

the RSA cryptosystem Easy
A.
B.
C.
D.

13 In RSA key generation, the public exponent must satisfy which condition with respect to ?

the RSA cryptosystem Easy
A.
B.
C. divides
D.

14 In RSA, a plaintext message is encrypted to ciphertext using which formula?

RSA encryption Easy
A.
B.
C.
D.

15 Which key is used by the sender to perform RSA encryption of a confidential message?

RSA encryption Easy
A. The sender's private key
B. The recipient's public key
C. The recipient's private key
D. The sender's public key

16 Using the public key , what is the ciphertext for the message ?

RSA encryption Easy
A.
B.
C.
D.

17 In RSA, ciphertext is decrypted back to plaintext using which formula?

RSA decryption Easy
A.
B.
C.
D.

18 Which key is required to perform RSA decryption?

RSA decryption Easy
A. The generator
B. A shared session key
C. The public key
D. The private key

19 The ElGamal cryptosystem's security is based on the hardness of which problem?

ElGamal cryptosystem Easy
A. The knapsack problem
B. Graph coloring
C. Integer factorization
D. The discrete logarithm problem

20 A key feature of ElGamal encryption is that it is:

ElGamal cryptosystem Easy
A. Based on factoring like RSA
B. Probabilistic, producing different ciphertexts for the same message
C. Deterministic, always giving the same ciphertext
D. Symmetric, using one shared key

21 In a public-key cryptosystem, if Alice wants to send a confidential message to Bob, which key does she use for encryption?

introduction to public-key cryptography Medium
A. Bob's public key
B. Alice's private key
C. Alice's public key
D. Bob's private key

22 What is the primary security assumption that makes RSA computationally secure?

introduction to public-key cryptography Medium
A. Difficulty of factoring large integers
B. Difficulty of computing modular addition
C. Difficulty of generating random numbers
D. Difficulty of sorting large arrays

23 In public-key cryptography, how is a digital signature typically created by a sender?

introduction to public-key cryptography Medium
A. By encrypting the message digest with the sender's private key
B. By encrypting the full message with the receiver's private key
C. By encrypting the message digest with the receiver's public key
D. By encrypting the full message with the sender's public key

24 In the Diffie-Hellman key exchange with public parameters and , Alice chooses secret . What is her public value ?

Diffie-Hellman key exchange Medium
A.
B.
C.
D.

25 Which mathematical problem must be hard for the Diffie-Hellman key exchange to remain secure?

Diffie-Hellman key exchange Medium
A. The traveling salesman problem
B. The discrete logarithm problem
C. The subset-sum problem
D. The integer factorization problem

26 Using , , Alice's public value , and Bob's secret , what shared secret does Bob compute as ?

Diffie-Hellman key exchange Medium
A.
B.
C.
D.

27 The Diffie-Hellman key exchange is vulnerable to which of the following attacks if no authentication is used?

Diffie-Hellman key exchange Medium
A. Chosen-plaintext attack
B. Man-in-the-middle attack
C. Birthday attack on the hash
D. Timing attack on factoring

28 In RSA, suppose and . What is the value of Euler's totient ?

the RSA cryptosystem Medium
A.
B.
C.
D.

29 In RSA, the public exponent must satisfy which condition relative to ?

the RSA cryptosystem Medium
A.
B. divides
C. is a prime factor of
D.

30 Given and public exponent , what is the private exponent such that ?

the RSA cryptosystem Medium
A.
B.
C.
D.

31 Why must the two primes and in RSA be kept secret?

the RSA cryptosystem Medium
A. Knowing them speeds up encryption for attackers
B. Knowing them allows computing and hence the private key
C. Knowing them reveals the plaintext directly
D. Knowing them changes the value of

32 Using RSA with and , what is the ciphertext for the plaintext message ?

RSA encryption Medium
A.
B.
C.
D.

33 In RSA encryption with public key , which formula produces the ciphertext from plaintext ?

RSA encryption Medium
A.
B.
C.
D.

34 Using RSA with and , what is the ciphertext for plaintext ?

RSA encryption Medium
A.
B.
C.
D.

35 What is a critical requirement on the plaintext before RSA encryption with modulus ?

RSA encryption Medium
A. must be a prime number
B. must be less than
C. must equal
D. must be greater than

36 Using RSA with , , and ciphertext , what is the recovered plaintext ?

RSA decryption Medium
A.
B.
C.
D.

37 In RSA decryption, which key component is used to recover the plaintext from the ciphertext?

RSA decryption Medium
A. The public exponent
B. The prime alone
C. The private exponent
D. The totient

38 Using RSA with , , and ciphertext , what plaintext is recovered? (Given , .)

RSA decryption Medium
A.
B.
C.
D.

39 In the ElGamal cryptosystem, on what hard problem is its security based?

ElGamal cryptosystem Medium
A. The discrete logarithm problem
B. The knapsack problem
C. The quadratic residue problem
D. The integer factorization problem

40 In ElGamal encryption, the ciphertext consists of which pair of components?

ElGamal cryptosystem Medium
A.
B.
C.
D.

41 In a Diffie-Hellman key exchange with prime and generator , Alice picks private key and Bob picks private key . What is the shared secret key?

Diffie-Hellman key exchange Hard
A.
B.
C.
D.

42 Which computational problem must be hard for the Diffie-Hellman key exchange to be secure against a passive eavesdropper who observes , , , and ?

Diffie-Hellman key exchange Hard
A. The integer factorization problem
B. The subset sum problem
C. The Computational Diffie-Hellman (CDH) problem
D. The quadratic residuosity problem

43 The basic Diffie-Hellman protocol is vulnerable to which attack because it provides no authentication of the communicating parties?

Diffie-Hellman key exchange Hard
A. Man-in-the-middle attack
B. Chosen-ciphertext attack
C. Timing side-channel attack
D. Birthday attack

44 For RSA with and , the public exponent is . What is the private exponent ?

the RSA cryptosystem Hard
A.
B.
C.
D.

45 Using RSA with and , the ciphertext for message is computed as . What is ?

RSA encryption Hard
A.
B.
C.
D.

46 With RSA parameters and , decrypting ciphertext gives which plaintext?

RSA decryption Hard
A.
B.
C.
D.

47 Why does RSA decryption using the Chinese Remainder Theorem (CRT) provide a significant speedup over direct modular exponentiation with modulo ?

RSA decryption Hard
A. Exponentiations are done modulo and separately, each with smaller moduli and reduced exponents
B. It removes the need to compute during decryption
C. It converts the private exponent into a public one to skip a step
D. It replaces exponentiation with a single modular inversion

48 If an attacker learns both and for an RSA modulus, how can they recover the primes and ?

the RSA cryptosystem Hard
A. By computing directly
B. By taking and
C. By factoring into its prime powers
D. By solving the quadratic

49 In ElGamal encryption over with , generator , private key (so public ), a sender encrypts using ephemeral . What is the ciphertext pair ?

ElGamal cryptosystem Hard
A.
B.
C.
D.

50 In the ElGamal cryptosystem, what is the security consequence of reusing the same ephemeral key to encrypt two different messages and ?

ElGamal cryptosystem Hard
A. An attacker who learns can recover from the ratio
B. The private key is immediately exposed to any observer
C. Both ciphertexts decrypt to the same value regardless of the messages
D. The modulus can be factored from the two ciphertext pairs

51 The ciphertext in ElGamal encryption is roughly twice the size of the plaintext. What is the fundamental reason for this message expansion?

ElGamal cryptosystem Hard
A. The plaintext is padded to twice its length before encryption
B. Both the public and private keys are appended to the ciphertext
C. Each ciphertext consists of two group elements, and
D. The message is encrypted twice using two independent ephemeral keys

52 Which property distinguishes a trapdoor one-way function, as used in public-key encryption, from an ordinary one-way function?

introduction to public-key cryptography Hard
A. It maps arbitrarily long inputs to fixed-length outputs deterministically
B. It requires the same key for both evaluation and inversion
C. It is impossible to invert even with the secret key
D. It can be efficiently inverted only with knowledge of secret trapdoor information

53 A hybrid cryptosystem combines public-key and symmetric-key cryptography. What is the primary motivation for this design?

introduction to public-key cryptography Hard
A. Symmetric encryption cannot protect messages longer than the key length
B. Public-key encryption is slow, so it is used only to exchange a fast symmetric session key
C. Public-key algorithms cannot decrypt data they themselves encrypted
D. Symmetric keys must be published while asymmetric keys remain private

54 In a common-modulus attack, two users share modulus with coprime public exponents and . If the same message is encrypted as and , how can an attacker recover ?

the RSA cryptosystem Hard
A. Factor using and then decrypt normally
B. Compute
C. Compute
D. Find with , then compute

55 Why is textbook (unpadded) RSA encryption insecure, being only deterministic and homomorphic under multiplication?

RSA encryption Hard
A. Decryption fails whenever the message exceeds half the modulus size
B. The ciphertext is always smaller than the plaintext, leaking information
C. Identical plaintexts always yield identical ciphertexts and enables malleability
D. The public exponent can be recovered directly from any ciphertext

56 In a low-exponent broadcast (Håstad) attack, the same message is sent to three recipients with and pairwise coprime moduli . How is recovered?

RSA decryption Hard
A. Use CRT to find , then take the integer cube root
B. Average the three ciphertexts and reduce modulo the smallest
C. Multiply all three ciphertexts and take the ninth root modulo
D. Compute the pairwise of the three moduli to factor them

57 To prevent small-subgroup confinement attacks in Diffie-Hellman, one uses a safe prime (with prime) and a generator of the order- subgroup. What does this ensure?

Diffie-Hellman key exchange Hard
A. Both private keys are guaranteed to be quadratic residues modulo
B. The discrete logarithm becomes solvable only by the legitimate parties
C. The modulus can no longer be factored by any known algorithm
D. Shared secrets lie in a large prime-order subgroup, so an attacker cannot force them into a small subgroup

58 The semantic security of ElGamal encryption relies on which assumption being intractable?

ElGamal cryptosystem Hard
A. The integer factorization assumption
B. The Decisional Diffie-Hellman (DDH) assumption
C. The elliptic-curve pairing assumption
D. The RSA problem

59 Fermat's factorization method efficiently breaks an RSA modulus under which condition on the primes?

the RSA cryptosystem Hard
A. When is chosen smaller than both and
B. When and differ by exactly a factor of two
C. When and are both Sophie Germain primes
D. When and are very close to each other, so is small

60 For RSA to correctly encrypt and decrypt all messages, the public exponent must satisfy which condition relative to ?

RSA encryption Hard
A. must be a prime factor of
B. and must share exactly one common prime factor
C. , so that has a multiplicative inverse modulo
D. must equal for invertibility
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