The first step is to find two large prime numbers. Replace the number 8943759834759342875902348781 below with your very own big, odd number and let Maple find a big prime number for you. a:=-1; for i from 8943759834759342875902348781 by 2 while (a < 0) do if (isprime(i) = true) then print(i); a:=1; end if; end do;

NiM+JSJhRyEiIg== NiMiPSh5W0IhZihHTWZaJClmUCUqKQ==

I repeated the statement above twice with two different big, odd numbers. These are the two prime numbers that I got. I went ahead and tested them with isprime to make sure they are both prime. isprime(8943759834759342875902348787);

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isprime(8945937593487590387543966783477);

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Now, I set my big prime numbers equal to p and q for convenience. p:=8943759834759342875902348787;

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q:=8945937593487590387543966783477;

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Now, I need to find a number that has no divisors in common with p-1 and q-1. What I am going to do is pick the prime number 103 and check whether 103 divides evenly into p-1 or q-1. If it doesn't , then that is going to be my encoding power. If on the off chance it did divide either p-1 or q-1, I would just pick a different prime number and try again. p-1 mod 103;

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q-1 mod 103;

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OK, my encoding power is 103, and my big product of prime numbers is p*q. p*q;

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Now, I need to find a decoding power. This is done with the following isolve command. isolve(103*d - (p-1)*(q-1)*y = 1, {d,y});

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I read the above and note that the decoding power is given by d = 3107... I am going to save that in a variable now. d:=31071967896271054316676515773164315464667470400851997460247;

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Now, suppose you wanted to send the message "Darrin's the greatest!" Using the correspondence given on the handout, Darrin's the greatest! is the number 391027271823706229171462162714102914282963. All that you need to make sure is that the total message is shorter than the product of the two prime numbers. If it is longer, you have to break it up into pieces. OK, to send the message, you would compute 391027271823706229171462162714102914282963&^ 103 mod p*q;

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You would send the number LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW5HRiQ2JFFmbjIxMDU0NTc5NjE0ODMwNDUyMTkyNzU5MjQ2NzMzMzc1OTEzMDU5OTE0NTIzNzAxNTEwODEzNTEyOTAxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn in an e-mail to me. No one knows the special decoding power d that I have computed above, so no one can figure out what the original message was that you are sendng. In order for me to figure out your message, I would compute 49381975845667769440782975099387054231226915694662148156169&^ d mod p*q;

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JSFH Behold! This is the message that you sent me.