<Text-field style="Heading 1" layout="Heading 1">Problem 1</Text-field>

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Test 1

This portion of the exam is open notes, open book. You MAY NOT talk to any other person about this exam EXCEPT for Dr. Dan. Seriously, do not cheat.

This portion of the exam is due at noon on Wednesday, March 11.

Enjoy.

Dr Dan

Run these first. This will load the number theory package and the programs mess2num and num2mess.

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<Text-field style="Heading 1" layout="Heading 1">Problem 1</Text-field>

You chose the following p,g,and a for an ElGamal encryption. I encrypted a message using this public key, the result of which is the two values c1 and c2 below.

a) Decrypt my message. If you do it correctly, you will be able to put the number into num2mess and get something coherent.

b) Encrypt the message "I am the Walrus." Don't forget the period. Use k=1234.

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<Text-field style="Heading 1" layout="Heading 1">Problem 2</Text-field>

The following are the values of e, p, and q that you are using for an RSA code. You have sent me e and N, and I used them to encrypt a message, the result of which is the number c. Decrypt the message. Again, if you did it correctly, num2mess will give you something coherent.

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<Text-field style="Heading 1" layout="Heading 1">Problem 3</Text-field>

3) For the following N, Eve has somehow figured out that the following pairs are valid encryption/decryption pairs. Use this information to factor N.

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 1" layout="Heading 1">Problem 4</Text-field>

I calculated the following number B by working out 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. Determine if b is even or odd. Of course, I need work, not just a guess.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY7LUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSomY29sb25lcTtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjc3Nzc3OGVtRicvRk5GU0Y1LUYsNiVRKnNhZmVwcmltZUYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYjLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEiMkYnRjktRiM2Iy1GW282JFEkMTIzRidGOS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGOS1GNjYtUSI7RidGOUY7L0Y/RjFGQEZCRkRGRkZIRkpGVC1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4wZW1GJy8lJmRlcHRoR0ZfcC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJ0Y1LUYsNiVRImdGJ0YvRjJGNUZPRjUtRiw2JVEpcHJpbXJvb3RGJ0YvRjItRlk2JC1GIzYmLUZbbzYkUSc1NTU1NTVGJ0Y5LUY2Ni1RIixGJ0Y5RjtGaW9GQEZCRkRGRkZIRkovRk5RLDAuMzMzMzMzM2VtRidGNUYrRjlGZm9Gam9GNS1GLDYlUSJCRidGL0YyRk8tRltvNiRRRTc2MDQ4ODk1NTIyMjY0NjIxOTAxNzUxNjY4MzQwMDIxNTM4MkYnRjlGZm9Gam8tRltwNiZGXXBGYHBGY3AvRmZwUSVhdXRvRictRiw2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

JSFH

<Text-field style="Heading 1" layout="Heading 1">Problem 5</Text-field>

Solve 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 using Pohlig-Hellman. Oh sure, you can check your answer using mlog, but I still want to see all of the work.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=