$$Q$1)$ Two Internet users, Alice and Bob, wish to have a secure conversation over an untrusted network.$$ They decide to use the Diffie$-$Hellman protocol. Help Alice and Bob to compute their keys using the Fast Modular Exponentiation method.

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Given:

$$ P $=23,$ G$=9$

Alice chose x $=4,$ and Bob chose y $=3.$

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Q$2)$ Now use the RSA algorithm to generate two key$-$pairs for Alice and Bob using the Fast Modular Exponentiation method.

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Given:

p$=17,$ q$=11,$ e $=7$

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A$.$ Find d$?$

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B$.$ Encrypt the Message M$=88$ and find the cipher text C$?$

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C$.$ Decrypt the cipher text $($C$)$ to get back the message M$?$

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Student Name

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ID

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Serial Number

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Grade

Q#$1$

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Q#$2$

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Total

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Notes:

$$ Solve the assignment individually

$$ You have to use this cover page when submit your solution

$$ Your work must be organized, comprehensible, easy to read and follow.

$$ Submission should be printed out, not handwritten.

$$ Handwritten assignments are penalized $-1.$

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$$Q$1)$ Two Internet users, Alice and Bob, wish to have a secure conversation over an untrusted network.$$ They decide to use the Diffie$-$Hellman protocol. Help Alice and Bob to compute their keys using the Fast Modular Exponentiation method.

$$

Given:

$$ P $=23,$ G$=9$

Alice chose x $=4,$ and Bob chose y $=3.$

$$

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$$

$$

$$

$$

$$

$$

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$$

$$

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$$

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$$

$$

Q$2)$ Now use the RSA algorithm to generate two key$-$pairs for Alice and Bob using the Fast Modular Exponentiation method.

$$

Given:

p$=17,$ q$=11,$ e $=7$

$$

A$.$ Find d$?$

$$

$$

$$

$$

$$

$$

$$

B$.$ Encrypt the Message M$=88$ and find the cipher text C$?$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

C$.$ Decrypt the cipher text $($C$)$ to get back the message M$?$