An RSA crypto system selects two primes p=11 and q=13. If the private key is…
2025
An RSA crypto system selects two primes p=11 and q=13. If the private key is d=7, which of the following can be the value of the public key 'e'?
Answer: A. 103 — First, calculate the RSA modulus n = p × q = 11 × 13 = 143. Next, compute Euler's totient function φ(n) = (p - 1)(q - 1) = 10 × 12 = 120. The public key e…
- A.
103
- B.
143
- C.
21
- D.
19
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Correct answer: A
First, calculate the RSA modulus n = p × q = 11 × 13 = 143. Next, compute Euler's totient function φ(n) = (p - 1)(q - 1) = 10 × 12 = 120. The public key e must satisfy the congruence relation e × d ≡ 1 (mod φ(n)). Substituting d = 7, we solve 7e ≡ 1 (mod 120). The modular multiplicative inverse of 7 modulo 120 is e = 103, since 7 × 103 = 721 and 721 mod 120 = 1.
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