To determine:The decoded message for the following encoded messages. E=926

Lewis Harvey

Lewis Harvey

Answered question

2021-04-25

To determine:The decoded message for the following encoded messages.
E=926

Answer & Explanation

Jozlyn

Jozlyn

Skilled2021-04-27Added 85 answers

Given information:
p=17,q=59, and s=3
Explanation:
Since, gcd (3,16)=1, there exist integers a and x such that
3a+16x=1.
We know that 3(11)16(2)=1.
Thus, a=11.
Also, 3(39)58(2)=1
Thus, b=39.
It is given that E=926.
So, Ea=(926)11=2(bmod17).
Also, Eb=(926)39=35(bmod59).
Now the problem is reduced to solvinga pair of congruences.
x2(bmod17)
x35(bmod59)
We have, 7(17)2(59)=1. Thus, x=35.7(17)2.2(59) is the solution of the above pair of congruences modulo 1003.
x=35.7(17)2.2(59)
x=4165236
x=3929
x=920(bmod1003)
Thus, M=920.
We conclude that the decoded message for E=926 is IT.

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