Discussion
Using the RSA public key crypto system, if \(p = 13\), \(q = 31\) and \(d = 7\), then the value of \(e\) is
Answer: B
The public exponent is e = 103. In RSA the modulus is n = p x q = 13 x 31 = 403 and phi(n) = (13 - 1)(31 - 1) = 360. The exponents must satisfy e x d = 1 (mod 360).
\[ 7 \times 103 = 721 = 2 \times 360 + 1 \]So 103 is the inverse of 7 modulo 360. Check the others: 7 x 101 = 707 leaves remainder 347, 7 x 105 = 735 leaves 15, and 7 x 107 = 749 leaves 29, so none of them gives 1.
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