Using the RSA public key crypto system, if p=13, q=31 and d=7, then the value of e is (A) 101 (B) 105 (C) 103 (D) 107

Using the RSA public key crypto system, if p=13, q=31 and d=7, then the value of e is (A) 101 (B) 105 (C) 103 (D) 107
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1 Answer

Answer :

(C) 103

Explanation:

Basic RSA Algorithm:

1. Choose two primes, p & q.

2. Compute n=p*q and z=(p-1)*(q-1).

3. Choose a number relatively prime to z and call it d.

4. Find e such that e*d=1modz.

Given p=13, q=31 & d=7, e=?

n=p*q=403

z=(p-1)(q-1)=360

e*d=1modz

7e=1mod360, then 7e must be 361, 721, 1081, 1441, etc. Dividing each of these in turn by 7 to see which is divisible by 7, we find that 721/7 = 103, hence e = 103. 
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