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Instructions
Required Reading
Questions
Grading
Record your answers to the questions below in a plain text file. Your plain text file must be named "<username>.txt", where <username> is the user name of your Computer Science Department account. I will not accept anything other than a plain text file.
Important: Unless otherwise specified, to receive full credit, the complete answer to every question must appear in your plain text file.
Show your work. If your answer is incorrect and you did not show your work, the question will get 0 points. If your answer is incorrect but you showed your work, the question might receive partial credit.
Send your plain text file to me by email at ark@cs.rit.edu. Include your full name in the email message, and include the plain text file as an attachment.
When I receive your email message, I will:
The submission deadline is Tuesday, May 7, 2013, at 11:59pm. The date/time when your email message arrives in my inbox (not when you sent the message) will determine whether your project meets the deadline.
You may submit your quiz multiple times before the deadline. I will keep and grade only your most recent submission that arrived before the deadline. There is no penalty for multiple submissions.
If you submit your quiz before the deadline, but I do not accept it, and you cannot or do not submit it again before the deadline, the quiz will be late (see below). I strongly advise you to submit the quiz several days before the deadline, so there will be time to deal with any problems that might arise in the submission process.
Late quizzes: I will not accept a late quiz unless you arrange with me for an extension. See the Course Policies for my policy on extensions. Late quizzes will receive a grade of zero.
Plagiarism: The quiz must be entirely your own work. See the Course Policies for my policy on plagiarism.
Question 1 (4 points). According to the Fermat Test, is 1820383 prime? Prove your answer.
Question 2 (4 points). Alice wishes to pick an RSA public and private key with public exponent e = 7 and secret primes p and q in the range 100 to 1000. State an RSA key pair that meets Alice's criteria and explain how you chose that key pair.
Question 3 (4 points). Bob's RSA public encryption key is (e, n) = (3, 1340839). Alice encrypts a message and sends the ciphertext 167898 to Bob. What was the plaintext?
Questions 4-5. Bob's RSA public encryption key is (e, n) = (5, 13631039). Alice wants to send messages to Bob that are composed solely of uppercase letters A through Z. Alice realizes that she can group a message into blocks of five letters and treat each block as a five-digit base-26 number, with A being the digit 0, B being 1, . . . Z being 25. The smallest possible five-digit base-26 number is AAAAA, which is 0 in base 10. The largest possible five-digit base-26 number is ZZZZZ, which is 11881375 in base 10. Alice therefore converts each five-letter block to a number, encrypts each block separately with Bob's public key, and sends the ciphertext blocks to Bob. Harry observes the ciphertext messages, and Harry is aware of the scheme Alice and Bob are using. However, Harry does not compute Bob's private key, and Harry does not decrypt the ciphertext blocks.
Question 4 (4 points). Is it possible for Harry to deduce the plaintext messages? Explain why or why not.
Question 5 (4 points). In addition to the above, Alice uses the OAEP padding on each block before encrypting it. Is it now possible for Harry to deduce the plaintext messages? Explain why or why not.
Questions 6–7. Bob and Carol and Ted and Alice are doing public key cryptography in the group Zp*, where the prime p is 988651 and the generator is 142018.
Question 6 (4 points). Alice and Bob are doing a Diffie-Hellman key exchange. Alice sends the number 623668 to Bob. Bob sends the number 7227 to Alice. What shared secret number do Alice and Bob compute? Explain how you found the answer.
Question 7 (2 points). Carol and Ted are doing El Gamal encryption. They do not use a hash function or a padding function on the messages. Ted's public key is 633541. Carol wants to send the plaintext message 444444 to Ted. Carol chooses secret random number 738661. After encrypting the message, what does Carol send to Ted?
Question 8 (2 points). Is y2 = x3 + 13x + 79 (mod 601) a valid basis for an elliptic curve group? Prove your answer.
Questions 9–11. Consider the elliptic curve group y2 = x3 + 7x + 2 (mod 17).
Question 9 (4 points). Give the set of group elements.
Question 10 (2 points). What is the order of the group?
Question 11 (4 points). Alice and Bob are doing an elliptic curve Diffie-Hellman key exchange using the generator (3, 4). Alice chooses secret random number 3. Bob chooses secret random number 4. What does Alice send to Bob, what does Bob send to Alice, and what shared secret group element do Alice and Bob compute?
Questions 12–14. Alice and Bob are using RSA to digitally sign messages. They do not use a hash function or a padding function on the messages. Alice's public key is (e, n) = (5, 6551101). Bob's public key is (e, n) = (5, 13556087).
Question 12 (4 points). Someone, supposedly Alice, sends to Bob a message 314159 with a signature 202652. Did the message come from Alice? Prove your answer.
Question 13 (4 points). Someone, supposedly Bob, sends to Alice a message 857142 with a signature 3916995. Did the message come from Bob? Prove your answer.
Question 14 (4 points). You, Harry, want to create a message with a forged signature and convince Alice the message came from Bob. Without finding Bob's private key, give an example of such a message and signature, and explain how you derived them.
The quiz is worth a total of 50 points as listed above for each question.
Important: Unless otherwise specified, to receive full credit, the complete answer to every question must appear in your plain text file. When grading your quiz, I will look only at your plain text file unless otherwise specified.
Show your work. If your answer is incorrect and you did not show your work, the question will get 0 points. If your answer is incorrect but you showed your work, the question might receive partial credit.
After grading your quiz I will put your grade and any comments I have in your encrypted grade file. For further information, see the Course Grading and Policies and the Encrypted Grades.
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