INFA 640 Cryptology and Data Protection Correct Answers

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INFA 640 Cryptology and Data ProtectionCorrect Answers1. A 2,000-bit message is used to generate a 256-bit hash. One the average, how many othermessages could be expected to generate the same hash value? What does this tell us aboutthe length of a hash as compared to the length of the message?2. Using the English alphabet (i.e., mod 26 arithmetic) let plaintext = {p1, p2,… , pn} andcorresponding ciphertext = {c1, c2,… , cn}. Suppose the encryption function is ci = pi + 5(mod 26). If you receive the ciphertext message RNQJDHDWZX, decrypt to recover theplaintext. What is the decryption function, and the recovered plaintext? What type of cipheris this? What are some weaknesses of this cipher?3. Substantiate or refute the following statement: The cryptographic basis of the Enigmamachine is the use of a trapdoor function.4. Consider the following plaintext message: THE BOILING POINT OF WATER IS 212 DEGREESFAHRENHEIT. a. If this message is sent unencrypted and successfully received, what is itsentropy? b. If this message is encrypted with DES using a random 56-bit key, what is theencrypted message’s entropy? c. If this message is encrypted with 3DES (using an optimalset of keys) what is the encrypted message’s entropy?5. A particular cipher is implemented by combining the ASCII representation of plaintextcharacters with pseudorandom bytes (eight-bit binary strings of 1s and 0s) using the XORfunction. In the process of encrypting a message, a character in the plaintext, a capital R, isXORed with the pseudorandom byte 10010101. a. What is the ciphertext (in binary form)generated by the encryption of the character R? (Please show your work.) b. How is theplaintext for this encrypted R recovered? (Please show your work.)6. The following ciphertext is a monoalphabetic ciper: ROXBOOG TOSOXUXUVG WGPNVTMOXXUGM, UX UE W HWTCOI XLWX W GOB XLVDMLX OCOT EXTDMMIOE UGXVOAUEXOGQO. HWEVG QVVIOZ Decrypt this message, and briefly describe your cryptanalysismethodology. In particular, list features of the ciphertext that hindered or helped yourdecryption process.7. An organization has 2000 members. It is desired that each member of the organization beable to communicate securely with any other member, without any other member beingable to decrypt their messages. How many unique keys are required if: a. The organizationuses a symmetric cipher. b. The organization uses an asymmetric cipher.8. The following questions are worth 2 points each: a. Bob picked N=77 for use in a RSA-encrypted message. Since N is part of the public key, Alice was able to crack Bob’s messageby determining the values of p and q that Bob used. What are the values of pand q did shedetermined? b. Is 89,201,768 a prime number? Why or why not?

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9. Acme Inc. is developing the next generation financial tracking program, and Alice hasbeen given the task of writing the encryption component, which will encrypt each user’sdata in a file on the hard drive. Alice has decided to use RSA as her encryption algorithm. Asthe cryptographic consultant for the project, do you think this is a good choice or not? Youshould state the reasons for your answer, and suggest an alternative if you do not think shemade a good choice.10. Modular arithmetic is used in public key ciphers. What is the value of X for each of thefollowing: a. X = 1,233 mod 16 b. X = 6 mod 50 c. X = 60 mod 5 d. X = 50 mod 611. Briefly compare and contrast how asymmetric cryptography is used to provideencryption as opposed to how it can be used to provide a digital signature.12. Using RSA, let p = 19, q = 13 and e = 5. Which of these is the complete private key: a.(169, 247) b. (173, 247) c. (169, 216) d. (173, 216) e. None of the above. (For full credit, pleaseshow your reasoning.)13. Encrypt-It-Rite, a vendor of encryption software, sells a symmetric cipher that uses a 56-bit key. The company decides to conduct a “challenge” to crack an encrypted message usinga brute-force approach. The average time to crack the message is found to be 12 hrs. Howmany more bits would they need to add to the key to increase the average cracking time to3072 hrs?14. Roberta, the daughter of Bob and Alice, is a summer intern at Encrypt-It-Rite, Inc. For hersummer project, Roberta would like to implement a stream cipher using public keyencryption. Is this a viable idea? Why, or why not.15. You are Alice. You have agreed with your friend Bob that you will use the Diffie-Hellmanpublic-key algorithm to exchange secret keys. You and Bob have agreed to use the publicbase g = 19 and public modulus p = 29. You have secretly picked the value SA = 23.You beginthe session by sending Bob your calculated value of TA. Bob responds by sending you thevalue TB = 17. What is the value of your shared secret key?16. Bob is concerned about the possibility of having his 100k byte file modified without hisknowledge, so he calculates a 128 bit hash. Alice, unbeknownst to Bob, changes a singlecharacter in Bob’s file. Assuming that Bob used a strong hash function, what would the hashvalue of the modified file look like, as compared with the original hash value?17. Suppose that Alice and Bob need to communicate, and have decided to use asymmetric(public key) encryption. Using only asymmetric encryption algorithms, describe a processthat would allow Alice to send a message that can only be read by Bob, and thatBob couldbe confident was sent by Alice. You should include any steps taken by Bob to read themessage, or to determine whether Alice actually sent the message.18. Bob believes that he has come up with a nifty hash function. He assigns a numeric valueVChar to each letter in the alphabet equal to the letter’s position in the alphabet, i.e., VA = 1,

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VB = 2, …, VZ = 26. For a message, he calculates the hash value H = (VChar 1 x VChar 2 xVChar 3 …x VChar N) mod(26). Bob uses this function to send a one-word message, PLANE,to his banker Bill, along with his calculated hash value for the message. Aliceis able tointercept the message, and generates an alternative message that has a hash value thatcollides with Bob’s original hash value. Show a message that Alice may have spoofed, anddemonstrate that its hash value collides with Bob’s original hash.19. Do symmetric and asymmetric ciphers protect the integrity of the messages that theyencrypt? If not, how could that service be provided?

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