Skills and elements used

Asymmetric encryption principles, RSA

$1)$ How many keys would need to be distributed in order to have private conversations among $7$ participants using symmetric encryption such that any $2$ participants conversations are private from the others?

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$2)$ How is non$-$repudiation accomplished by using asymmetric encryption?

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$3)$ Use the Euclidean algorithm to compute the gcd of $973$ and $307$ to receive credit you MUST show all of the intermediate r$0$ and r$1$ values.

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$4)$ Two numbers are considered to be coprime if they have a GCD of $1,$ determine whether the following pairs of numbers are coprime:

$15,16$

$38,56$

$37,49$

$88,24$

$17,10293$

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$5)$ Euler's phi function $($AKA totient$)$is simply the quantity of numbers from $0..$m$-1$ that are relatively prime to m$.$

Calculate $$

Calculate

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$6)$ If $($note $13,19$ are prime$)$ what is the simple calculation for $?$

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$7)$ Euler$$s theorem says $,$ for a and m that are relatively prime.

show that this is true for m $=6,$ a $=7$

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$8)$ Assume you have an RSA key pair $$and $.$

Use the public key to encrypt: $1,2,3,15$

Use the private key to decrypt: $27,17,3,9$