student

Learning Goal: I’m working on a networking exercise and need an explanation and answer to help me learn.

use the links to asnwer the questions

https://www.boxentriq.com/code-breaking/modular-ex…

https://asecuritysite.com/encryption/random3

https://www.boxentriq.com/code-breaking/big-number…

P

art 1 – Diffie Hellman:

In your Word document, choose any number you want and label the number as variable g.

In your Word document, choose any number you want and label the number as variable a.

In your Word document, choose any number you want and label the number as variable b.

Using the Random Prime Generator website, generate a large prime number (at least 128 bits) by clicking the Generate button. Copy Random Prime 1. Paste this value into your Word document labeled as variable p.

In this step, we need to get the result of ga mod p, and we’ll use the Modular Exponentiation Calculator for that. On the Modular Exponentiation Calculator page, paste the value of g in the Number (a) textbox, paste the value of a in the Exponent (b) textbox, paste the value of p in the Modulo (m) textbox. Click the Calculate button, copy the result, and paste this value into your Word document labeled as variable alpha.

This step will be similar to the previous step, but using the variable b instead of a to calculate gb mod p. Using the Modular Exponentiation Calculator, paste the value of g in the Number (a) textbox, paste the value of b in the Exponent (b) textbox, paste the value of p in the Modulo (m) textbox. Click the Calculate button, copy the result, and paste this value into your Word document labeled as variable beta.

Next, we’ll calculate Alice’s key, which is the result of betaa mod p. Using the Modular Exponentiation Calculator, paste the value of beta in the Number (a) textbox, paste the value of a in the Exponent (b) textbox, paste the value of p in the Modulo (m) textbox. Click the Calculate button, copy the result, and paste this value into your Word document labeled as variable alicekey.

Next we’ll calculate Bob’s key, which is the result of alphab mod p. Using the Modular Exponentiation Calculator, paste the value of alpha in the Number (a) textbox, paste the value of b in the Exponent (b) textbox, paste the value of p in the Modulo (m) textbox. Click the Calculate button, copy the result, and paste this value into your Word document labeled as variable bobkey.

At this point, Alice’s key and Bob’s key should match, which is the point of the Diffie-Hellman exchange – it’s a secure way for two parties to independently arrive at a shared key without a third party intercepting it. Make sure your Word document lists the values you used for g, a, b, p, alpha, beta, alicekey, and bobkey.

Part 2 – RSA:

Using the Random Prime Generator website, regenerate some prime numbers (at least 128 bits) by clicking the Generate button.

Copy Random Prime 1. Paste this value into your Word document labeled as variable p and paste it in Big Number Calculator as Number (a).

Copy Random Prime 2. Paste this value into your Word document labeled as variable q and paste it in the Big Number Calculator as Number(b).

Under Calculate, click the button labeled a*b. Copy the result and paste this value into your Word document labeled as variable n.

In the Number(a) textbox, subtract 1 from the value stored in the textbox (i.e. if the number ends in a 7, delete the 7 and replace it with a 6). In the Number(b) textbox, subtract 1 from the value stored in the textbox, just like you did for the Number(a) textbox. Under Calculate, click the button labeled a*b. Copy the result and paste this value into your Word document labeled as variable phi.

Pick any small prime number like 3 or 5 or 7, and label this value in your Word document as variable e. Place this value in the online calculator as Number (a). Copy phi from your Word document and paste it in the online calculator as Number (b). Under Calculate, click the button labeled a-1 MOD b. Copy the result and paste this value into your Word document labeled as variable d.

For the remainder of the exercise, we will be using the Modular Exponentiation Calculator. Go to that web page.

In this step, we’re going to transform plaintext into ciphertext using the formula plaintexte mod n using the Modular Exponentiation Calculator. Pick any number you want and label this value in your Word document as variable plaintext. Place this value in the Modular Exponentiation Calculator as Number (a). Copy the value for variable e from your Word document and paste it in the Exponent(b) textbox. Copy the value for variable n from your Word document and paste it in the Modulo(m) textbox. Click the Calculate button, copy the result, and paste this value into your Word document labeled as variable ciphertext.

Now, we’re going to decrypt the ciphertext using the formula ciphertextd mod n. Place the value of variable ciphertext in the Number(a) textbox. Copy the value for variable d from your Word document and paste it in the Exponent(b) textbox. The value of n should still be in the Modulo(m) textbox from the previous step, but if it’s not, copy the value for variable n from your Word document and paste it in the Modulo(m) textbox. Click the Calculate button. Take a screenshot of the Result box to show that the value of the result is the same as your original plaintext value. Paste your screenshot into your Word document.

Next, we’re going to demonstrate how to sign a message using the formula Md mod n. Pick any number you want and label this value in your Word document as variable M. This value represents a message that will be encrypted using our private key, resulting in a digital signature. Place the value of M in the Number(a) textbox. Copy the value for variable d from your Word document and paste it in the Exponent(b) textbox. Copy the value for variable n from your Word document and paste it in the Modulo(m) textbox. Click the Calculate button. Copy the result and paste this value into your Word document labeled as variable S. This value represents your digital signature.

Now, we’re going to validate the signature with the formula Se mod n. Place the value of S in the Number(a) textbox. Copy the value for variable e from your Word document and paste it in the Exponent(b) textbox. Copy the value for variable n from your Word document and paste it in the Modulo(m) textbox. Click the Calculate button. Take a screenshot of the Result box to show that the value of the result is the same as your original M value. Paste your screenshot into your Word document.

Make sure your Word document includes your values for p, q, n, phi, e, d, plaintext, ciphertext, M, and S, along with the screenshots you took along the way (please make sure the screenshots are labeled as well).

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