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Applied Cryptography

Which of the following correctly describes the hash functions SHA-2 and SHA-3?

  1. ASHA-3 is an improved version of SHA-2 that keeps the same internal structure and only lengthens the output
  2. BSHA-3 is based on a sponge construction different from that of SHA-2, and SHA-2 is also widely used today
  3. CSHA-256 is a member of SHA-3: in the SHA-3 family, the one with a 256-bit output is called SHA-256
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Answer: B. SHA-3 is based on a sponge construction different from that of SHA-2, and SHA-2 is also widely used today

SHA-2 is a family of hash functions including SHA-224, SHA-256, SHA-384 and SHA-512, built on the Merkle–Damgård construction, which passes blocks through a compression function one after another. SHA-3 was standardized in 2015 as FIPS 202 based on Keccak, chosen in a NIST competition, and uses a sponge construction that absorbs the input into a large internal state and squeezes out the output. SHA-3 was not created because SHA-2 was broken; it serves as an alternative with a different structure, and SHA-2 is still widely used. SHA-1, on the other hand, had a real collision published in 2017 and is no longer used for purposes such as digital signatures.

  • A. The internal structure of SHA-3 is completely different from that of SHA-2.
  • B. Correct. Two families with different structures are both used as standards.
  • C. SHA-256 is a member of SHA-2. The SHA-3 function with a 256-bit output is written SHA3-256.
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More Applied Cryptography questions

  1. Using the hash SHA-256(K ‖ m) of a secret key K concatenated with a message m as a tag for detecting tampering is considered dangerous. Which of the following is the reason?
  2. Let 1 GiB = 2³⁰ bytes and 1 EiB = 2⁶⁰ bytes. A block cipher with a 64-bit block (such as 3DES) is used in CBC mode to encrypt a large amount of data under one key. Treating the ciphertext blocks as random 64-bit values, which of the following is the approximate amount of data at which, by the birthday paradox, the probability that a pair of identical ciphertext blocks appears can no longer be ignored?
  3. In protocols such as TLS 1.3, the shared secret obtained from an ECDHE key exchange is not used directly as an encryption key; instead keys are made by passing it through a key derivation function (KDF) such as HKDF. Which of the following is an appropriate reason?
  4. The mechanism of RSA is checked with small numbers. From the primes p = 5 and q = 11, n = pq is formed, and the public exponent is e = 3. With φ(n) = (p − 1)(q − 1), which of the following is the private exponent d (0 < d < φ(n)) that satisfies e × d ≡ 1 (mod φ(n))?
  5. In RSA, let the public key be n = 55 and e = 3. Which of the following is the ciphertext c when the plaintext m = 7 is encrypted as c = m^e mod n?

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