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Encoding and Encryption  

 

Information Integrity, Hashing, and Authentication

 

 

These problems will give you experience different types of hash algorithms and authentication.

You are required to show your work (particularly on the SHA-2 and SHA-3 problems)

 

  1. This will be a partial walkthrough of a single round of SHA-2 – specifically, parts of the two mixers.

Recall that SHA-2 represents a state as 8 64-bit binary numbers, called A, B, C, D, E, F, G, and H. You are to use the last 6 digits of your Banner ID to create these. Specifically:

  • The last 8 bits of block A will be the binary representation of the last two digits of your Banner ID. The other bits will all be 0.
  • The last 8 bits of block B will be the binary representation of the middle two digits of your Banner ID. The other bits will all be 0.
  • The last 8 bits of block C will be the binary representation of the first two digits of your Banner ID. The other bits will all be 0.
  • The last 8 bits of block E will be the binary representation of the last two digits of your Banner ID. The other bits will all be 0.
  • The last 8 bits of block F will be the binary representation of the middle two digits of your Banner ID. The other bits will all be 0.
  • The last 8 bits of block G will be the binary representation of the first two digits of your Banner ID. The other bits will all be 0.
  • The last 8 bits of block H will be the binary representation of the last two digits of your Banner ID. The other bits will all be 0.

For example, if your ID were 00123456, these blocks would be:
A: 0000000000000000000000000000000000000000000000000000000001010110
B: 0000000000000000000000000000000000000000000000000000000000110100
C: 0000000000000000000000000000000000000000000000000000000000010010
E: 0000000000000000000000000000000000000000000000000000000001010110
F: 0000000000000000000000000000000000000000000000000000000000110100
G: 0000000000000000000000000000000000000000000000000000000000010010
H: 0000000000000000000000000000000000000000000000000000000001010110

You may also assume that D, Wi and Ki are all 0’s (that is, they will have no effect on the below questions).

 

  1. Compute Majority(A, B, C) 
  2. Compute Rot(E). Note that this will involve all 64 bits in the block.
  3. Compute Conditional(E, F, G)
  1. This problem is a simple walkthrough of the HMAC
    In this case:

    • The key will be the binary equivalent of the last two digits of your Banner ID.
      For example, if your Banner ID ends in 93, this would be 10010011.
    • The message will be the 8 bit string 01001000.
    • The “hash” function will be the OR of the message blocks. That is, if either corresponding bit is 1, then the resulting bit is 1.
Key
IPAD
00110110
Å
01010101
  • For example, suppose the key were 01010101. HMAC would work like this:

 

01100011
01001000
Message
OR
01101011
Intermediate HMAC
11001101
Key
01011100
Å
OPAD
10010001
OR
11111011
Final HMAC
“hash”
“hash”

Derive the final HMAC using your Banner ID as the key as described above.

  1. This question will be a simple walkthrough of the signature/verification process. For this question:
    • Simple RSA will be used.
    • The public key will be E = 3 and the modulus n = 33.
    • The private key will be D = 7.
    • The message M will be the second to last digit of your Banner ID + 2.
      For example, if your Banner ID is Y00123456, your message will be 5 + 2 = 7.

 

  1. Sign your message with the private key. What is the resulting signature?
  2. Suppose that you send the message and the signature. However, suppose that Darth intercepts that message and adds 1 to both the message and the signature. For example, if the message was 5 and the signature was 11, Darth would change it to 6 and 12.Use the public key to verify that the message no longer matches the signature.

 

  1. We have seen a number of algorithms for challenge-response (including symmetric key, public key, and digital signature).Suppose that Alice and Bob have a keyed hash algorithm (that is, a MAC) with a key that they both know. Describe how they could implement challenge-response using their keyed hash algorithm.

    Specifically, suppose that Alice sent a request to Bob, and Bob needed to verify her identity. What would be the steps in this process? Specifically, what information would be sent back and forth between Alice and Bob?

 

 

  1. This will be a partial walkthrough of a single round of SHA-3 – specifically, the functions q, p, and c.

Recall that SHA-3 represents a state as a three-dimensional 5 x 5 x L array. To simplify things, we will use L  = 1 for the number of slices – that is, your answer will be a single 5 x 5 two dimensional slice.

You will encode the last two digits of your Banner ID in that slice for each of the below problems. Specifically:

  • The first, second, and third rows will all be 0.
  • The fourth row of the first slice will be the binary representation of the seventh digit of your Banner ID.
  • The fifth row of the first slice will be the binary representation of the eighth digit of your Banner ID.

For example, if your ID were 00123456, the slice S would be:
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 1 0 1
0 0 1 1 0

  1. Compute q (S)
  2. Compute p (S)
  3. Compute c (S)

 

Note: You will apply each of these directly to your original S. That is, you will not be running the result of q through p, etc.

 

 

task