You are given the following simple 8-bit SPN with just one round and an 4-by-4 S-box (used twice: once for bits 1 through 4, and once for bits 5 to 8). The SPN operates the following way:

- an 8-bit plaintext block is XOR-ed with the key K0,
bits 1 through 4 and bits 5 to 8 are passed through the
S-box defined as follows:
0 1 2 3 4 5 6 7 8 9 A B C D E F 6 B 9 1 7 A 3 4 F 0 E D 8 2 5 C - the 8-bit output of the two S-boxes is permuted using the
following permutation:
1 2 3 4 5 6 7 8 8 1 7 2 6 3 5 4 - the result is XOR-ed with the key K1. This is the output of the cipher.

The key for this example is

1 0 0 1 1 1 0 0 1 1 0 1

1 1 0 0 0 1 0 1 0 1 1 0 1 0 1 1 1 0 1Show the decryption of the text, make sure that you get the original plaintext back.

Show the decryption of the text, make sure that you get the original plaintext back.

Ann, Brian, and Chris are using a Vigenere cipher with a long randomly generated key. Ann encrypts a message and sends it to Brian. The encryption looks like this:

WMLSWTDIRYYZICEXIMRLOQYJTFPICKHZGNPTXGSAZSRPFIPTSJXTAWVBrian decrypts the message, reads it, and decides to send it to Chris. To do this, he re-encrypts the plaintext using the same key. Unfortunately Brian's encryption device has a mechanical problem: every once in a while it inserts the letter X in the plaintext. Brian's encryption came out like this:

WMLSWTDIRYYZICEXXPDXRWQHGWVSWNEINODIIRFVEBGEQUSJNVAGVSXRYour task is to determine everything you can about the plaintext and the key. How difficult would it be to determine the remaining part of the plaintext and of the key without any assumptions about either?

**Completely optional, no extra credit.** Can you guess the rest of
the plaintext? How confident are you of your guess?

x^2 + a * x + b = y^2 + a * y + b mod 2^2m

compress(x1,x2,x3,x4,x5,x6) = x1 XOR x6, x2 XOR x5, x3 XOR x4. For instance, compress(101110) = 1 XOR 0, 0 XOR 1, 1 XOR 1 = 110

**Part 1.**Use the Merkle-Damgard construction, compute MAC for the
message 101 110 110.

**Part 2.** Is the compression function second preimage resistant?
If yes, please explain why; if no, demonstrate how you would solve the
second preimage problem.

**Part 3.** Is the compression function collision resistant? If yes,
please explain why; if no, demonstrate how you would solve the
collision problem.

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