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Using the RSA public key crypto system, if p=13, q=31 and d=7, then the value of e is

1. 101
2. 103
3. 105
4. 107
in Others
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Compute  φ= (p − 1)(q − 1) =12 x 30 =360
choose an int e such that 1<e<φ  and e & φ are co-prime
d.e =1 mod φ
7. e=1 mod 360 =361 mod 360 =721 mod 360 =>7e=721 =>e=103
hence ans is B

by Boss (49.3k points)
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Compute z=(p-1)*(q-1) i.e 12*30=360
Now, we know (de)mod z=1 so 7*103 mod 360 =1 i.e 721 mod 360 =1
+1

7.e mode 360=1

=>(7*e)%360=1  (when 7* e will be mode with 360 reminder will be =1)

=>so multiple of 360 == 7*e  and reminder 1(i.e)7.e  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.

+1 vote