The message 58 − 0 − 24 − 23
has been encoded from single letter message units using the RSA public
key cryptosystem. The alphabet consists of the ordinary English alphabet
A - Z and the letter b which stands for space. The recipient was foolish to
adopt as his public key: n = 91, e = 59.
Find the secret key and decode the message.
I've worked out d to be 11, with 59d = 1 mod 72.
So using the formula M = C^11 mod 72, I know I have to calculate and
So calculating the first one in a table...
mod 72
n 58^n
1 58
2 52
4 40
8 16
11 = 58 x 52 x 16 = 48256
I then get 48256 = 16 mod 72 which gives me the letter Q.
But I know that the message should be LATE, so can anyone please explain where I am going wrong?!
Thanks in advance!
Another RSA question that I'm stuck on...this time with 2 message units...
The message
309 − 95 − 723
has been encoded from blocks of two-letter message units using the RSA
public key cryptosystem. The alphabet consists of the ordinary English
alphabet A - Z and the letter b which stands for space. The recipient was
foolish to adopt as his public key: n = 3599, e = 1967.
(a) Find the secret key and decode the message.
Found p = 61, q = 58.
So 1967d = 1 mod 3480.
Used Euclids alg to find d = 23.
So using , need to calculate remainders of by 3599.
First number:
n 309^n mod 3599
1 309
2 1907
4 1659
8 2645
16 3168
So 23 = 3168 x 1599 x 1907 x 309 = number in standard form
So I split the numbers up into:
3168 x 1599 = 1172 mod 3599
1907 x 309 = 2626 mod 3599
Then 1172 x 2626 = 527 mod 3599
So 527 = (27 x 19) + 14
Hence corresponding letters are T and O.
Tried doing the same thing for the second number:
n 95^n mod 3599
1 95
2 1827
4 1656
8 3497
16 3206
So 23 = 3206 x 1656 x 1907 x 309 = number in standard form
Splitting numbers:
3206 x 1656 = 611 mod 3599
1907 x 309 = 2656 mod 3599
Then 611 x 2656 = 2931 mod 3599
But 2931 / 27 = 108 which doesn't correspond to any letters!
Can anyone please explain what I am supposed to do at this point?
Thanks in advance!
Cheers for replying Moo, but how did you find 81 though? Is the method I used above not the correct way of doing it?
Also aren't you supposed to assume that the alpahebet is number starting from 0, with 26 = b, so 3 would be D and 0 would be A? Although it doesn't actually say how it's numbered in the question so not too sure....
My precious calculatorbut how did you find 81 though?
It's correct ! The part which is incorrect is :Is the method I used above not the correct way of doing it?
You took the two numbers in red from the table of 309, not of 95So 23 = 3206 x 1656 x 1907 x 309 = number in standard form
For the numeration... Yep, it may be more logical.
But I think the most important in it is to find the modulus After that, you can do everything you want