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

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 and paste it in the online calculator as Number (b).

In this step, we need to get the result of ga mod p, but we need to break it up into a couple of parts. First, calculate the result of ga by pasting the value of g in the Big Number Calculator as Number (a), pasting the value of a in the Big Number Calculator as Number (b), and clicking the ab button. Next, copy the result and paste it in the Big Number Calculator as Number (a). Copy the value of p and paste it in the Number (b) textbox. Under Calculate, click the button labeled a MOD b. 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. Calculate the result of gb by pasting the value of g in the Big Number Calculator as Number (a), pasting the value of b in the Big Number Calculator as Number (b), and clicking the ab button. Copy the result and paste it in the Big Number Calculator as Number (a). Copy the value of p and paste it in the Number (b) textbox. Under Calculate, click the button labeled a MOD b. 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. We’ll break this up into a couple of parts. First, calculate the result of betaa by pasting the value of beta in the Big Number Calculator as Number (a), pasting the value of a in the Big Number Calculator as Number (b), and clicking the ab button. Next, copy the result and paste it in the Big Number Calculator as Number (a). Copy the value of p and paste it in the Number (b) textbox. Under Calculate, click the button labeled a MOD b. 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. Like the previous step, we’ll break this up into a couple of parts. First, calculate the result of alphab by pasting the value of alpha in the Big Number Calculator as Number (a), pasting the value of b in the Big Number Calculator as Number (b), and clicking the ab button. Next, copy the result and paste it in the Big Number Calculator as Number (a). Copy the value of pand paste it in the Number (b) textbox. Under Calculate, click the button labeled a MOD b. 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.

Pick any number you want and label this value in your Word document as variable plaintext. Place this value in the online calculator as Number (a). Place your value for variable e in the Number(b) textbox. Under Calculate, click the button labeled ab. Copy the result and paste this value into your Word document labeled as variable plaintexte.

Place the value of variable plaintexte in the Number(a) textbox. Copy the value for variable n from your Word document and paste it in the Number(b) textbox. Under Calculate, click the button labeled a MOD b. Copy the result and paste this value into your Word document labeled as variable ciphertext.

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 Number(b) textbox. Under Calculate, click the button labeled ab. Copy the result and paste this value into your Word document labeled as variable ciphertextd.

Place the value of ciphertextd in the Number(a) textbox. Copy the value for variable n from your Word document and paste it in the Number(b) textbox. Under Calculate, click the button labeled a MOD b. 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.

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 Number(b) textbox. Under Calculate, click the button labeled ab. Copy the result and paste this value into your Word document labeled as variable Md.

Place the value for Md in the Number(a) textbox. Copy the value for variable n from your Word document and paste it in the Number(b) textbox. Under Calculate, click the button labeled a MOD b. Copy the result and paste this value into your Word document labeled as variable S. This value represents your digital signature.

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 Number(b) textbox. Under Calculate, click the button labeled ab. Copy the result and paste this value into your Word document labeled as variable Se.

Place the value of Se in the Number(a) textbox. Copy the value for variable n from your Word document and paste it in the Number(b) textbox. Under Calculate, click the button labeled a MOD b. The result should equal the value you used for your M variable. 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, Md, S, and Se, along with the screenshots you took along the way (please make sure the screenshots are labeled as well

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

https://asecuritysite.com/encryption/random3

# Place this value in the online calculator as number (a).

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