English
Menu

Applied Cryptography

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?

  1. A13
  2. B21
  3. C23
Show answer and explanation

Answer: A. 13

7³ = 343, and 343 = 6 × 55 + 13, so c = 13. The private exponent for this public key is d = 27 (with p = 5, q = 11 and φ(n) = 40, 3 × 27 ≡ 1), and computing 13^27 mod 55 gives back the original plaintext 7. Encryption needs only the public key, but decryption requires d.

  • A. Correct. 343 mod 55 = 13.
  • B. 21 is 7 × 3, the value obtained by multiplying instead of raising to a power.
  • C. 23 is the remainder of 343 divided by φ(n) = 40. The modulus for encryption is n = 55.
Practice this topic Back to topic

Books on Applied Cryptography Ad

As an Amazon Associate I earn from qualifying purchases.

More Applied Cryptography questions

  1. Which of the following correctly describes a problem with using textbook RSA (computing c = m^e mod n directly from the plaintext m) without padding in real communication?
  2. In Diffie–Hellman key exchange, a prime p and a generator g are public; A and B choose secret values a and b and send each other g^a mod p and g^b mod p. Which of the following is the reason an eavesdropper is believed unable to find the shared secret g^(ab) mod p even after seeing all these public values?
  3. Diffie–Hellman key exchange is checked with small numbers. Let p = 23 and g = 5; A chooses the secret value a = 6 and B the secret value b = 15. A sends A = g^a mod p and B sends B = g^b mod p. Which of the following is the shared secret the two obtain?
  4. Which of the following is the correct combination of a weakness of Diffie–Hellman key exchange without authentication and its countermeasure?
  5. In the table of NIST SP 800-57, which of the following is the combination of RSA key length (the number of bits of n) and elliptic-curve key length given as the guideline for security comparable to a 128-bit symmetric-key cipher (AES-128)?

Comparisons in this topic