Math Help - encoding and decoding help

1. encoding and decoding help

I have the following....
p=311 q=173
m= 53803
Euler Totient = 53320
k=3
message is the string of digits
232 524 141 135 192 911 331 529 252 315
a1= 232 a2= 524........a10=315

In the form a^k = = b (mod 53803)

I don't know how to find b....I have been going in circles for the past 4 hours and I can't get it... please help

2. Hello,

Originally Posted by duggaboy
I have the following....
p=311 q=173
m= 53803
Euler Totient = 53320
k=3
message is the string of digits
232 524 141 135 192 911 331 529 252 315
a1= 232 a2= 524........a10=315

In the form a^k = = b (mod 53803)

I don't know how to find b....I have been going in circles for the past 4 hours and I can't get it... please help
$232^3 \equiv b_1 \mod 53803$

$232^3=12487168=232 \cdot 53803+4872 \implies 232^3 \equiv 4872 \mod 53803$

But what exactly is k ?

3. I am assuming that 3 is an okay selection for k, our assignment was to choose any k....
is there an exact way to get a "real" k?? with out just guessing?

4. Originally Posted by duggaboy
I am assuming that 3 is an okay selection for k, our assignment was to choose any k....
is there an exact way to get a "real" k?? with out just guessing?
Actually, you have to know if k is part of the public of the private key. That is to say if you have to find 232 powered to k, or powered to its inverse.

RSA - Wikipedia, the free encyclopedia

5. Oh my my....how would go about that? The example I have is where we did this in class and we just choose a random k....
the public key is the k and m....which is what i'm supposed to send to a secret partner : )