Interwoven (Numerical) RSA Encryption

Example:

Encrypt this message

Encryption Layer $1$ :

$p = 139, q = 103$

$n = (p - 1)(q - 1) = (139 - 1)(103 - 1) = (138)(102) = 14076$

$\phi(14076) = 4416$

We now find a number $e$ such that $1 < e < \phi(n)$ , $e = 4415$ .

Now, we need to find $d$ such that $de \mod \phi(n) \equiv 1$ - in this case, $d = \frac{4417}{4415}$

$4415 * 4415 = 19492225 = 1 + 384 * 50761$

The encryption key is $c = m^e \mod n$ - $n = 14076, e = 4415$ - $c = m^{4415} \mod 14076$

The decryption key is $m = c^d \mod n$ - $n = 14076, d = \frac{4417}{4415}$ - $m = c^{\frac{4417}{4415}} \mod 14076$

Now encrypt!

Now, re-encrypt the ciphertext.

Repeat until the $n^{th}$ layer of encryption.

Challenge:

I want somebody to find out how long it takes to decrypt (without the decryption key, range from min to max):

$1$ layer

$2$ layers

$3$ layers

... (as in, keep going!)

$15$ layers

#ComputerScience

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$