Using the RSA public key crypto system, if p = 13, q = 31 and d = 7, then the…
2013
Using the RSA public key crypto system, if p = 13, q = 31 and d = 7, then the value of e is
- A.
101
- B.
103
- C.
105
- D.
107
Attempted by 58 students.
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Correct answer: B
Solution: Find e given p = 13, q = 31, and d = 7.
Compute phi(n) = (p - 1)(q - 1) = 12 * 30 = 360.
We are given d = 7. The public exponent e must satisfy e * d ≡ 1 (mod 360). So e is the modular inverse of 7 modulo 360.
Check candidate 103: 7 * 103 = 721, and 721 = 2 * 360 + 1, so 7 * 103 ≡ 1 (mod 360). Therefore e = 103.
You can also use the extended Euclidean algorithm to compute the inverse of 7 modulo 360; it yields 103 as the inverse.
Answer: 103
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