Assume Larry, Moe and Curly all use the encryption exponent $3,$ with $3$ different moduli,

$n_{\text{l}\text{a}\text{c}\text{r}\text{o}}=25777,n_{\text{m}\text{a}\text{e}}=22879$ and $n_{\text{c}\text{u}\text{r}\text{l}\text{y}}=66277.$ I sent the same two messages to all three

of them. Assume an attacker, Mallory, was able to see the encrypted messages that I

sent to Larry, Moe and Curly.

$c_{1_{\text{t}\text{a}\text{r}\text{r}\text{y}}}-=19052(mod{n}_{\text{l}\text{a}\text{c}\text{t}\text{a}\text{y}})$

$c_{1_{\text{m}\text{o}\text{e}}}-=4546(mod{n}_{\text{m}\text{a}\text{e}})$

$c_{1_{\text{c}\text{u}\text{r}\text{l}\text{y}}}-=44619(mod{n}_{\text{c}\text{u}\text{r}\text{l}\text{y}})$

$c_{2_{\text{l}\text{a}\text{r}\text{k}}}-=1708(mod{n}_{\text{l}\text{a}\text{c}\text{k}\text{y}})$

$c_{2_{\text{m}\text{o}\text{e}}}-=11733(mod{n}_{\text{m}\text{a}\text{e}})$

$c_{2_{\text{c}\text{u}\text{r}\text{l}\text{y}}}-=19731(mod{n}_{\text{c}\text{u}\text{r}\text{l}\text{y}})$

Without factoring the moduli, recovering the decryption exponent or

performing a brute force attack, recover the two messages, $m_1$ and $m_2.$ These

messages are encoded using the same methods as Exercise $1.$

Hint: Are $n_{\text{l}\text{a}\text{r}\text{k}\text{y}\text{,}}{n}_{\text{m}\text{a}\text{e}}$ and $n_{\text{c}\text{u}\text{r}\text{l}\text{y}}$ relatively prime?

Note: You can solve these using spreadsheets or you can write a script to help out as

well. If you write a script in Python, I may suggest using Python$3\mathrm{.}10.$ You can use the

pow function to calculate exponentials and inverses modulo $n.$