Reference no: EM132336887
NETWORK SECURITY
PROBLEMS
1. Break the following monoalphabetic substitution cipher. The plaintext, consisting of letters only, is an excerpt from a poem by Lewis Carroll.
mvyy bek mnyx n yvjjyr snijrh invq n muvjvdt je n idnvy
jurhri n fehfevir pyeir oruvdq ki ndq uri jhrnqvdt ed zb jnvy
Irr uem rntrhyb jur yeoijrhi ndq jur jkhjyri nyy nqlndpr
Jurb nhr mnvjvdt ed jur iuvdtyr mvyy bek pezr ndq wevd jur qndpr
mvyy bek, medj bek, mvyy bek, medj bek, mvyy bek wevd jur qndpr
mvyy bek, medj bek, mvyy bek, medj bek, medj bek wevd jur qndpr
2. An affine cipher is a version of a monoalphabetic substitution cipher, in which the letters of an alphabet of size m are first map to the integers in the range 0 to m-1. Subsequently, the integer representing each plaintext letter is transformed to an integer representing the corresponding cipher text letter. The encryption function for a single letter is E(x)=(ax + b) mod m, where m is the size of the alphabet and a and b are the key of the cipher, and are co-prime. Trudy finds out that Bob generated a ciphertext using an affine cipher. She gets a copy of the ciphertext, and finds out that the most frequent letter of the ciphertext is ’R’, and the second most frequent letter of the ciphertext is ’K’. Show how Trudy can break the code and retrieve the plaintext.
3. Break the following columnar transposition cipher. The plaintext is taken from a popular computer textbook, so ‘‘computer’’ is a probable word. The plaintext consists entirely of letters (no spaces). The ciphertext is broken up into blocks of five characters for readability. aauan cvlre rurnn dltme aeepb ytust iceat npmey iicgo gorch srsoc nntii imiha oofpa gsivt tpsit lbolr otoex
4. Alice used a transposition cipher to encrypt her messages to Bob. For added security, she encrypted the transposition cipher key using a substitution cipher, and kept the encrypted cipher in her computer. Trudy managed to get hold of the encrypted transposition cipher key. Can Trudy decipher Alice’s messages to Bob? Why or why not?
5. Find a 77-bit one-time pad that generates the text ‘‘Hello World’’ from the ciphertext of Fig. 8-4.
6. You are a spy, and, conveniently, have a library with an infinite number of books at your disposal. Your operator also has such a library at his disposal. You have agreed to use Lord of the Rings as a one-time pad. Explain how you could use these assets to generate an infinitely long one-time pad.
7. Quantum cryptography requires having a photon gun that can, on demand, fire a single photon carrying 1 bit. In this problem, calculate how many photons a bit carries on a 250-Gbps fiber link. Assume that the length of a photon is equal to its wavelength, which for purposes of this problem, is 1 micron. The speed of light in fiber is 20 cm/nsec.
8. If Trudy captures and regenerates photons when quantum cryptography is in use, she will get some of them wrong and cause errors to appear in Bob’s one-time pad. What fraction of Bob’s one-time pad bits will be in error, on average?
9. A fundamental cryptographic principle states that all messages must have redundancy. But we also know that redundancy helps an intruder tell if a guessed key is correct. Consider two forms of redundancy. First, the initial n bits of the plaintext contain a known pattern. Second, the final n bits of the message contain a hash over the message. From a security point of view, are these two equivalent? Discuss your answer.
10. In Fig. 8-6, the P-boxes and S-boxes alternate. Although this arrangement is esthetically pleasing, is it any more secure than first having all the P-boxes and then all the S-boxes? Discuss your answer.
11. Design an attack on DES based on the knowledge that the plaintext consists exclusively of uppercase ASCII letters, plus space, comma, period, semicolon, carriage return, and line feed. Nothing is known about the plaintext parity bits.
12. In the text, we computed that a cipher-breaking machine with a million processors that could analyze a key in 1 nanosecond would take 1016 years to break the 128-bit version of AES. Let us compute how long it will take for this time to get down to 1 year, still along time, of course. To achieve this goal, we need computers to be 1016 times faster. If Moore’s Law (computing power doubles every 18 months) continues to hold, how many years will it take before a parallel computer can get the cipherbreaking time down to a year?
13. AES supports a 256-bit key. How many keys does AES-256 have? See if you can find some number in physics, chemistry, or astronomy of about the same size. Use the Internet to help search for big numbers. Draw a conclusion from your research.
14. Suppose that a message has been encrypted using DES in counter mode. One bit of ciphertext in block Ci is accidentally transformed from a 0 to a 1 during transmission. How much plaintext will be garbled as a result?
15. Now consider ciphertext block chaining again. Instead of a single 0 bit being transformed into a 1 bit, an extra 0 bit is inserted into the ciphertext stream after block Ci. How much plaintext will be garbled as a result?
16. Compare cipher block chaining with cipher feedback mode in terms of the number of encryption operations needed to transmit a large file. Which one is more efficient and by how much?
17. Using the RSA public key cryptosystem, with a = 1, b = 2 ... y = 25, z = 26.
(a) If p = 5 and q = 13, list five legal values for d.
(b) If p = 5, q = 31, and d = 37, find e.
(c) Using p = 3, q = 11, and d = 9, find e and encrypt ‘‘hello’’.
18. Alice and Bob use RSA public key encryption in order to communicate between them. Trudy finds out that Alice and Bob shared one of the primes used to determine the number n of their public key pairs. In other words, Trudy found out that na = pa × q and nb = pb × q. How can Trudy use this information to break Alice’s code?
19. Consider the use of counter mode, as shown in Fig. 8-15, but with IV = 0. Does the use of 0 threaten the security of the cipher in general?
20. In Fig. 8-20, we see how Alice can send Bob a signed message. If Trudy replaces P, Bob can detect it. But what happens if Trudy replaces both P and the signature?
21. Digital signatures have a potential weakness due to lazy users. In e-commerce transactions, a contract might be drawn up and the user asked to sign its SHA-1 hash. If the user does not actually verify that the contract and hash correspond, the user may inadvertently sign a different contract. Suppose that the Mafia try to exploit this weakness to make some money. They set up a pay Web site (e.g., pornography, gambling, etc.) and ask new customers for a credit card number.
Then they send over a contract saying that the customer wishes to use their service and pay by credit card and ask the customer to sign it, knowing that most of them will just sign without verifying that the contract and hash agree. Show how the Mafia can buy diamonds from a legitimate Internet jeweler and charge them to unsuspecting customers.
22. A math class has 25 students. Assuming that all of the students were born in the first half of the year—between January 1st and June 30th— what is the probability that at least two students have the same birthday? Assume that nobody was born on leap day, so there are 181 possible birthdays.
23. After Ellen confessed to Marilyn about tricking her in the matter of Tom’s tenure, Marilyn resolved to avoid this problem by dictating the contents of future messages into a dictating machine and having her new secretary just type them in. Marilyn then planned to examine the messages on her terminal after they had been typed in to make sure they contained her exact words. Can the new secretary still use the birthday attack to falsify a message, and if so, how? Hint: She can.
24. Consider the failed attempt of Alice to get Bob’s public key in Fig. 8-23. Suppose that Bob and Alice already share a secret key, but Alice still wants Bob’s public key. Is there now a way to get it securely? If so, how?
25. Alice wants to communicate with Bob, using public-key cryptography. She establishes a connection to someone she hopes is Bob. She asks him for his public key and he sends it to her in plaintext along with an X.509 certificate signed by the root CA. Alice already has the public key of the root CA. What steps does Alice carry out to verify that she is talking to Bob? Assume that Bob does not care who he is talking to (e.g., Bob is some kind of public service).
26. Suppose that a system uses PKI based on a tree-structured hierarchy of CAs. Alice wants to communicate with Bob, and receives a certificate from Bob signed by a CA X after establishing a communication channel with Bob. Suppose Alice has never heard of X. What steps does Alice take to verify that she is talking to Bob?
27. Can IPsec using AH be used in transport mode if one of the machines is behind a NAT box? Explain your answer.
28. Alice wants to send a message to Bob using SHA-1 hashes. She consults with you regarding the appropriate signature algorithm to be used. What would you suggest?
29. Give one reason why a firewall might be configured to inspect incoming traffic. Give one reason why it might be configured to inspect outgoing traffic. Do you think the inspections are likely to be successful?
30. Suppose an organization uses VPN to securely connect its sites over the Internet. Jim, a user in the organization, uses the VPN to communicate with his boss, Mary. Describe one type of communication between Jim and Mary which would not require use of encryption or other security mechanism, and another type of communication which would require encryption or other security mechanisms. Explain your answer.
31. Change one message in the protocol of Fig. 8-34 in a minor way to make it resistant to the reflection attack. Explain why your change works.
32. The Diffie-Hellman key exchange is being used to establish a secret key between Alice and Bob. Alice sends Bob (227, 5, 82). Bob responds with (125). Alice’s secret number, x, is 12, and Bob’s secret number, y, is 3. Show how Alice and Bob compute the secret key.
33. Two users can establish a shared secret key using the Diffie-Hellman algorithm, even if they have never met, share no secrets, and have no certificates
(a) Explain how this algorithm is susceptible to a man-in-the-middle attack.
(b) How would this susceptibility change if n or g were secret?
34. In the protocol of Fig. 8-39, why is A sent in plaintext along with the encrypted session key?
35. In the Needham-Schroeder protocol, Alice generates two challenges, RA and RA 2. This seems like overkill. Would one not have done the job?
36. Suppose an organization uses Kerberos for authentication. In terms of security and service availability, what is the effect if AS or TGS goes down?
37. Alice is using the public-key authentication protocol of Fig. 8-43 to authenticate communication with Bob. However, when sending message 7, Alice forgot to encrypt RB. Trudy now knows the value of RB. Do Alice and Bob need to repeat the authentication procedure with new parameters in order to ensure secure communication? Explain your answer.
38. In the public-key authentication protocol of Fig. 8-43, in message 7, RB is encrypted with KS. Is this encryption necessary, or would it have been adequate to send it back in plaintext? Explain your answer.
39. Point-of-sale terminals that use magnetic-stripe cards and PIN codes have a fatal flaw: a malicious merchant can modify his card reader to log all the information on the card and the PIN code in order to post additional (fake) transactions in the future. Next generation terminals will use cards with a complete CPU, keyboard, and tiny display on the card. Devise a protocol for this system that malicious merchants cannot break.
40. Is it possible to multicast a PGP message? What restrictions would apply?
41. Assuming that everyone on the Internet used PGP, could a PGP message be sent to an arbitrary Internet address and be decoded correctly by all concerned? Discuss your answer.
42. The attack shown in Fig. 8-47 leaves out one step. The step is not needed for the spoof to work, but including it might reduce potential suspicion after the fact. What is the missing step?
43. The SSL data transport protocol involves two nonces as well as a premaster key. What value, if any, does using the nonces have?
44. Consider an image of 2048 × 512 pixels. You want to encrypt a file sized 2.5 MB. What fraction of the file can you encrypt in this image? What fraction would you be able to encrypt if you compressed the file to a quarter of its original size? Show your calculations.
45. The image of Fig. 8-54(b) contains the ASCII text of five plays by Shakespeare. Would it be possible to hide music among the zebras instead of text? If so, how would it work and how much could you hide in this picture? If not, why not?
46. You are given a text file of size 60 MB, which is to be encrypted using steganography in the low-order bits of each color in an image file. What size image would be required in order to encrypt the entire file? What size would be needed if the file were first compressed to a third of its original size? Give your answer in pixels, and show your calculations. Assume that the images have an aspect ratio of 3:2, for example,
3000 × 2000 pixels.
47. Alice was a heavy user of a type 1 anonymous remailer. She would post many messages to her favorite newsgroup, alt.fanclub.alice, and everyone would know they all came from Alice because they all bore the same pseudonym. Assuming that the remailer worked correctly, Trudy could not impersonate Alice. After type 1 remailers were all shut down, Alice switched to a cypherpunk remailer and started a new thread in her newsgroup. Devise a way for her to prevent Trudy from posting new messages to the newsgroup, impersonating Alice.
48. Search the Internet for an interesting case involving privacy and write a one-page report on it.
49. Search the Internet for some court case involving copyright versus fair use and write a 1-page report summarizing your findings.
50. Write a program that encrypts its input by XORing it with a keystream. Find or write as good a random number generator as you can to generate the keystream. The program should act as a filter, taking plaintext on standard input and producing ciphertext on standard output (and vice versa). The program should take one parameter, the key that seeds the random number generator.
51. Write a procedure that computes the SHA-1 hash of a block of data. The procedure should have two parameters: a pointer to the input buffer and a pointer to a 20-byte output buffer. To see the exact specification of SHA-1, search the Internet for FIPS 180-1, which is the full specification.
52. Write a function that accepts a stream of ASCII characters and encrypts this input using a substitution cipher with the Cipher Block Chaining mode. The block size should be 8 bytes. The program should take plaintext from the standard input and print the ciphertext on the standard output. For this problem, you are allowed to select any reasonable system to determine that the end of the input is reached, and/or when padding should be applied to complete the block. You may select any output format, as long as it is unambiguous. The program should receive two parameters:
1. A pointer to the initializing vector; and 2. A number, k, representing the substitution cipher shift, such that each ASCII character would be encrypted by the kth character ahead of it in the alphabet. For example, if x = 3, then A is encoded by D, B is encoded by E etc. Make reasonable assumptions with respect to reaching the last character in the ASCII set. Make sure to document clearly in your code any assumptions you make about the input and encryption algorithm.
53. The purpose of this problem is to give you a better understanding as to the mechanisms of RSA. Write a function that receives as its parameters primes p and q, calculates public and private RSA keys using these parameters, and outputs n, z, d and e as printouts to the standard output. The function should also accept a stream of ASCII characters and encrypt this input using the calculated RSA keys. The program should take plaintext from the standard input and print the ciphertext to the standard output.
The encryption should be carried out character-wise, that is, take each character in the input and encrypt it independently of other characters in the input. For this problem, you are allowed to select any reasonable system to determine that the end of the input is reached. You may select any output format, as long as it is unambiguous. Make sure to document clearly in your code any assumptions you make about the input and encryption algorithm.
Book- COMPUTER NETWORKS By ANDREW S. TANENBAUM and DAVID J. WETHERALL.